{ "cells": [ { "cell_type": "markdown", "id": "3672fa62", "metadata": { "scrolled": false }, "source": [ "

\n", " \n", "\n", "

\n", "\n", "## Interactive Bayesian Linear Regression with Metropolis-Hastings \n", "\n", "### Michael J. Pyrcz, Professor, The University of Texas at Austin \n", "\n", "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*" ] }, { "cell_type": "markdown", "id": "c708d65d", "metadata": {}, "source": [ "This is an interactive demonstration of Bayesian linear regression. First, here's some details:\n", "\n", "#### Bayesian Updating\n", "\n", "The frequentist formulation of the linear regression model is: \n", "\n", "\\begin{equation}\n", "y = b_1 \\times x + b_0 + \\sigma\n", "\\end{equation}\n", "\n", "where $x$ is the predictor feature, $b_1$ is the slope parameter, $b_0$ is the intercept parameter and $\\sigma$ is the error or noise. There is an analytical form for the ordinary least squares solution to fit the available data while minimizing the L2 norm of the data error vector.\n", "\n", "For the Bayesian formulation of linear regression is we pose the model as a prediction of the distribution of the response, $Y$, now a random variable:\n", "\n", "\\begin{equation}\n", "Y \\sim N(\\beta^{T}X, \\sigma^{2} I)\n", "\\end{equation}\n", "\n", "We estimate the model parameter distributions through Bayesian updating for infering the model parameters from a prior and likelihood from training data.\n", "\n", "\\begin{equation}\n", "p(\\beta | y, X) = \\frac{p(y,X| \\beta) p(\\beta)}{p(y,X)}\n", "\\end{equation}\n", "\n", "In general for continuous features we are not able to directly calculate the posterior and we must use a sampling method, such as Markov chain Monte Carlo (McMC) to sample the posterior.\n", "\n", "For a complete lecture with linked Python workflows check out:\n", "\n", "* [Bayesian Linear Regression Lecture](https://www.youtube.com/watch?v=LzZ5b3wdZQk&list=PLG19vXLQHvSC2ZKFIkgVpI9fCjkN38kwf&index=33)\n", "\n", "* [Bayesian Probability Lecture](https://www.youtube.com/watch?v=Ppwfr8H177M&list=PLG19vXLQHvSB-D4XKYieEku9GQMQyAzjJ&index=6)\n", "\n", "Here's my McMC Metropolis-Hastings workflow with more details:\n", "\n", "* [Bayesian Linear Regression Workflow](https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceMachineLearning_Simple_Bayesian_Linear_Regression.ipynb)\n", "\n", "and here's my Bayesian linear regression workflow with the pymc3 Python package:\n", "\n", "* [Bayesian Linear Regression Workflow with the pymc3 Python Package](https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnalytics_BayesianRegression.ipynb)\n", "\n", "#### Bayesian Linear Regression with the Metropolis-Hastings Sampler\n", "\n", "Here's the basic steps of the Metropolis-Hastings Sampler: \n", "\n", "For $\\ell = 1, \\ldots, L$:\n", "\n", "1. Assign random values for the the initial sample of model parameters, $\\beta(\\ell = 1) = b_1(\\ell = 1)$, $b_0(\\ell = 1)$ and $\\sigma^2(\\ell = 1)$. \n", "2. Propose new model parameters based on a proposal function, $\\beta^{\\prime} = b_1$, $b_0$ and $\\sigma^2$. \n", "3. Calculate probability of acceptance of the new proposal, as the ratio of the posterior probability of the new model parameters given the data to the previous model parameters given the data multiplied by the probability of the old step given the new step divided by the probability of the new step given the old. \n", "\n", "\\begin{equation}\n", "P(\\beta \\rightarrow \\beta^{\\prime}) = min\\left(\\frac{p(\\beta^{\\prime}|y,X) }{ p(\\beta | y,X)} \\cdot \\frac{p(\\beta^{\\prime}|\\beta) }{ p(\\beta | \\beta^{\\prime})},1\\right)\n", "\\end{equation}\n", "\n", "4. Apply Monte Carlo simulation to conditionally accept the proposal, if accepted, $\\ell = \\ell + 1$, and sample $\\beta(\\ell) = \\beta^{\\prime}$\n", "5. Go to step 2.\n", "\n", "Let's talk about this system. First the left hand side:\n", "\n", "\\begin{equation}\n", "\\frac{p(\\beta^{\\prime}|y,X) }{ p(\\beta | y,X)}\n", "\\end{equation}\n", "\n", "We are calculating the ratio of the posterior probability (likelihood times prior) of the model parameters given the data and prior model for proposed sample over the current sample. \n", "\n", "* As you will see below it is quite practical to calculate this ratio.\n", "* If the proposed sampled is more likely than the current sample, we will have a value greater than 1.0, it will truncate to 1.0 and we accept the proposed sample.\n", "* If the proposed sample is less likely than the current sample, we will have a value less than 1.0, then we will use Monte Carlo sampling to randomly choice the proposed sample with this probability of acceptance.\n", "\n", "This proceedure allows us to walk through the model parameter space and sample the parameters with the current rates, after the burn-in chain.\n", "\n", "Now, what about this part of the equation?\n", "\n", "\\begin{equation}\n", "\\frac{p(\\beta^{\\prime}|\\beta) }{ p(\\beta | \\beta^{\\prime})}\n", "\\end{equation}\n", "\n", "There is a problem with this procedure if we use asymmetric probability distributions for the model parameters! \n", "\n", "* E.g. for example, if we use a positively skewed distribution (e.g., log normal) then we are more likely to step to larger values due to this distribution, and not due to the prior nor the likelihood.\n", "\n", "* This term removes this bias, so that we have fair samples!\n", "\n", "You will see below that we remove this issue by assuming symmetric model parameter distributions, even though many use na assymetric gamma distribution for sigma, given it cannot have negative values.\n", "\n", "* My goal is the simplest possible demonstration.\n", "\n", "#### Our Simplified Demonstration Metropolis Sampling\n", "\n", "Let's further specify this workflow for our simple demonstration. \n", "\n", "1. I have assumed a Gaussian, symmetric distribution for all model parameters as a result this relationship holds for all possible model parameter, current and proposed.\n", "\n", "\\begin{equation}\n", "\\frac{p(\\beta^{\\prime}|\\beta) }{ p(\\beta | \\beta^{\\prime})} = 1.0\n", "\\end{equation}\n", "\n", " So we now have this simplified probability of proposal acceptance, note this is know as Metropolis Sampling.\n", " \n", "\\begin{equation}\n", "P(\\beta \\rightarrow \\beta^{\\prime}) = min \\left( \\frac{p(\\beta^{\\prime}|y,X) }{ p(\\beta | y,X)},1 \\right) \n", "\\end{equation}\n", "\n", "2. Now, let's substitute our Bayesian formulation for our Bayesian linear regression model.\n", "\n", "\\begin{equation}\n", "p(\\beta^{\\prime} | y, X) = \\frac{p(y,X| \\beta^{\\prime}) p(\\beta^{\\prime})}{p(y,X)} \\quad \\text{ and } \\quad p(\\beta | y, X) = \\frac{p(y,X| \\beta) p(\\beta)}{p(y,X)}\n", "\\end{equation}\n", "\n", " If we substitute these into our probability of acceptance above we get this.\n", "\n", "\n", "\\begin{equation}\n", "P(\\beta \\rightarrow \\beta^{\\prime}) = min \\left( \\frac{p(\\beta^{\\prime}|y,X) }{ p(\\beta | y,X)},1 \\right) = min \\left( \\frac{ \\left( \\frac{p(y,X| \\beta_{new}) p(\\beta_{new}) } {p(y,X)} \\right) }{ \\left( \\frac{ p(y,X| \\beta) p(\\beta)}{p(y,X)} \\right) },1 \\right)\n", "\\end{equation}\n", "\n", " Note that the evidence terms cancel out.\n", "\n", "\\begin{equation}\n", "P(\\beta \\rightarrow \\beta^{\\prime}) = min \\left( \\frac{ p(y,X| \\beta_{new}) p(\\beta_{new}) }{ p(y,X| \\beta) p(\\beta)},1 \\right)\n", "\\end{equation}\n", "\n", " Since we are working with a likelihood ratio, we can work with densities instead of probabilities.\n", "\n", "\\begin{equation}\n", "P(\\beta \\rightarrow \\beta^{\\prime}) = min \\left( \\frac{ f(y,X| \\beta_{new}) f(\\beta_{new}) }{ f(y,X| \\beta) f(\\beta) } ,1 \\right)\n", "\\end{equation}\n", "\n", "3. Finally for improved solution stability we can calculate the natural log ratio:\n", "\n", "\\begin{equation}\n", "ln(P(\\beta \\rightarrow \\beta^{\\prime})) = min \\left( ln \\left[ \\frac{ f(y,X| \\beta_{new}) f(\\beta_{new}) }{ f(y,X| \\beta) f(\\beta) } \\right],0 \\right) = min \\left( \\left[ln(f(y,X| \\beta_{new})) + ln(f(\\beta_{new})) \\right] - \\left[ ln(f(y,X| \\beta)) + ln(f(\\beta)) \\right],0 \\right)\n", "\\end{equation}\n", "\n", "4. We calculate probability of proposal acceptance, as exponentiation of the above. \n", "\n", "5. How do we calculate the likelihood density? If we assume independence between all of the data we can take the product sum of the probabilities (densities) of all the response values given the predictor and model parameter sample! Given, the Gaussian assumption for the response feature, we can calculate the densities for each data from the Gaussian PDF.\n", "\n", "\\begin{equation}\n", "f_{y,X | \\beta}(y) \\sim N [ b_1 \\cdot X + b_0, \\sigma ]\n", "\\end{equation}\n", "\n", " and under the assumption of indepedence we can take the produce sum over all training data.\n", "\n", "\\begin{equation}\n", "f(y,X| \\beta) = \\prod_{\\alpha = 1}^{n} f_{y,X | \\beta}(y_{\\alpha})\n", "\\end{equation}\n", "\n", "Note, this workflow was developed with assistance from Fortunato Nucera's Medium Article [Mastering Bayesian Linear Regression from Scratch: A Metropolis-Hastings Implementation in Python](https://medium.com/@tinonucera/bayesian-linear-regression-from-scratch-a-metropolis-hastings-implementation-63526857f191). I highly recommend this accessible description and demonstration. Thank you, Fortunato.\n", "\n", "#### Load and Configure the Required Libraries\n", "\n", "The following code loads the required libraries and sets a plotting default." ] }, { "cell_type": "code", "execution_count": 38, "id": "09e9ba4b", "metadata": {}, "outputs": [], "source": [ "supress_warnings = True # supress warnings?\n", "import numpy as np # arrays and matrix math\n", "import pandas as pd # DataFrames\n", "import matplotlib.pyplot as plt # plotting\n", "from matplotlib.patches import Rectangle # build a custom legend\n", "from matplotlib.ticker import (MultipleLocator, AutoMinorLocator) # control of axes ticks\n", "from matplotlib.gridspec import GridSpec # nonstandard subplots\n", "from matplotlib.patches import Ellipse # plot prior model\n", "import scipy.stats as stats # parametric distributions\n", "from sklearn.linear_model import LinearRegression # frequentist model for comparison\n", "from ipywidgets import interactive # widgets and interactivity\n", "from ipywidgets import widgets \n", "from ipywidgets import Layout\n", "from ipywidgets import Label\n", "from ipywidgets import VBox, HBox\n", "cmap = plt.cm.inferno # default color bar, no bias and friendly for color vision defeciency\n", "plt.rc('axes', axisbelow=True) # grid behind plotting elements\n", "if supress_warnings == True:\n", " import warnings # supress any warnings for this demonstration\n", " warnings.filterwarnings('ignore') \n", "plt.rc('axes', axisbelow=True) # set axes and grids in the background for all plots\n", "seed = 73073 # random number seed" ] }, { "cell_type": "markdown", "id": "c2f9b1c7", "metadata": {}, "source": [ "#### Declare Functions\n", "\n", "The following functions include:\n", " \n", "* **next_proposal** - propose a next model parameters from previous previous model parameters, this is the proposal method, parameterized by step standarrd deviation and Gaussian distribution.\n", "\n", "* **likelihood_density** - calculate the product of all the densities for all the data given the model parameters. Since we are working with the log densities, we sum over all the data.\n", "\n", "* **prior_density** - calculate the product of the densities for all the model parameters given the prior model. Since we are working with the log densities, we sum over all the model parameters. This is an assumption of independence.\n", "\n", "* **add_grid** - improved grid for the plotting." ] }, { "cell_type": "code", "execution_count": 41, "id": "678335dc", "metadata": {}, "outputs": [], "source": [ "def next_proposal(prev_theta, step_stdev = 0.5): # assuming a Gaussian distribution centered on previous theta and step stdev \n", " out_theta = stats.multivariate_normal(mean=prev_theta,cov=np.eye(3)*step_stdev**2).rvs(1)\n", " return out_theta\n", "\n", "def likelihood_density(x,y,theta): # likelihood - probability (density) of the data given the model\n", " density = np.sum(stats.norm.logpdf(y, loc=theta[0]*x+theta[1],scale=theta[2])) # assume independence, sum is product in log space\n", " return density\n", "\n", "def prior_density_mv(theta,prior): # prior - probability (density) of the model parameters given the prior \n", " mean = np.array([prior[0,0],prior[1,0],prior[2,0]]); cov = np.zeros([3,3]); cov[0,0] = prior[0,1]; cov[1,1] = prior[1,1]; cov[2,2] = prior[2,1]\n", " prior_out = stats.multivariate_normal.logpdf(theta,mean=mean,cov=cov,allow_singular=True)\n", " return prior_out\n", "\n", "def prior_density_sum_log(theta,prior): # prior - probability (density) of the model parameters given the prior \n", " mean = np.array([prior[0,0],prior[1,0],prior[2,0]]); cov = np.zeros([3,3]); cov[0,0] = prior[0,1]; cov[1,1] = prior[1,1]; cov[2,2] = prior[2,1]\n", " prior_out = np.log(stats.norm.pdf(theta[0], prior[0][0], prior[0][1])) + np.log(stats.norm.pdf(theta[1], prior[1][0], prior[1][1])) + np.log(stats.norm.pdf(theta[2], prior[2][0], prior[2][1]))\n", " return prior_out\n", "\n", "def add_grid():\n", " plt.gca().grid(True, which='major',linewidth = 1.0); plt.gca().grid(True, which='minor',linewidth = 0.2) # add y grids\n", " plt.gca().tick_params(which='major',length=7); plt.gca().tick_params(which='minor', length=4)\n", " plt.gca().xaxis.set_minor_locator(AutoMinorLocator()); plt.gca().yaxis.set_minor_locator(AutoMinorLocator()) # turn on minor ticks" ] }, { "cell_type": "markdown", "id": "e2aae770", "metadata": {}, "source": [ "#### Build a Dataset with Known Truth Model Parameters for Linear Regression\n", "\n", "Let's build a simple dataset with known linear regresin parameters, $b_1$ is the slope parameter, $b_0$ is the intercept parameter and $\\sigma$ is the error or noise." ] }, { "cell_type": "code", "execution_count": 44, "id": "55a1c55a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(seed = seed) # set random number seed\n", "\n", "data_b1 = 3; data_b0 = 20; data_sigma = 5; n = 100 # set data model parameters\n", "\n", "x = np.random.rand(n)*30 # random x values\n", "y = data_b1*x+data_b0 + np.random.normal(loc=0.0,scale=data_sigma,size=n) # y as a linear function of x + random noise \n", "\n", "xhat = np.linspace(-10,40,100) # set of x values to predict and visualize the model\n", "linear_model = LinearRegression().fit(x.reshape(-1, 1),y) # instantiate and train the frequentist linear regression model\n", "yhat = linear_model.predict(xhat.reshape(-1, 1)) # make predictions for model plotting\n", "\n", "plt.subplot(111)\n", "plt.scatter(x, y,c='red',s=10,edgecolor='black')\n", "plt.plot(xhat,yhat,c='red'); add_grid()\n", "plt.xlabel(\"Predictor Feature\"); plt.ylabel(\"Response Feature\"); plt.title('Data and Linear Regression Model')\n", "plt.gca().add_patch(Rectangle((1.5,93.0),4.3,23,facecolor='white',edgecolor='black',linewidth=0.5))\n", "plt.annotate('$b_1$ = ' + str(np.round(linear_model.coef_[0],2)),[2,110])\n", "plt.annotate('$b_0$ = ' + str(np.round(linear_model.intercept_,2)),[2,103])\n", "plt.annotate('$\\sigma$ = ' + str(np.round(data_sigma,2)),[2,96])\n", "plt.xlim([0,30]); plt.ylim([0,120])\n", "\n", "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.2, hspace=0.5); plt.show()" ] }, { "cell_type": "markdown", "id": "5222fe81", "metadata": {}, "source": [ "#### Assume the Prior Model\n", "\n", "We assume a multivariate Gaussian distribution for the slope and intercept parameters, $f_{b_1,b_0,\\sigma}(b_1,b_0,\\sigma)$ with indepedence between $b_1$, $b_0$, and $\\sigma$.\n", "\n", "* For a naive prior assume a very large standard deviation.\n", "We will work in log probability and log density to improve stability of the system. \n", "\n", "* We want to avoid product sums of a many values near zero as the the probabilities will disappear due to computer floating point precision. \n", "* In log space, we can add calculate probabilities of independent events by summing (instead of multiplication) these negative values " ] }, { "cell_type": "code", "execution_count": 47, "id": "d3750f8f", "metadata": {}, "outputs": [], "source": [ "prior = np.zeros([3,2]) # prior distributions\n", "prior[0,:] = [4.0,1.0] # Gaussian prior model for slope, mean and standard deviation\n", "prior[1,:] = [13.0,3.0] # Gaussian prior model for intercept, mean and standard deviation\n", "prior[2,:] = [7.0,1.0] # Gaussian prior model for sigma, k (shape) and phi (scale), recall mean = k x phi, var = k x phi^2 " ] }, { "cell_type": "markdown", "id": "061571e6", "metadata": {}, "source": [ "#### Bayesian Linear Regression with McMC Metropolis-Hastings \n", "\n", "The Bayesian linear regression with McMC Metropolis-Hastings workflow.\n", "\n", "1. assign an random initial set of model parameters\n", "2. apply a proposal rule to assign a new set of model parameters given the previous set of model paramters\n", "3. calculate the ratio of the likelihood of the new model parameters over the previous model parameters given the data\n", "4. conditionally accept the proposal based on this ratio, i.e., if proposal is more like accept it, if less likely with a probability based on the ratio.\n", "5. goto to 2." ] }, { "cell_type": "code", "execution_count": 50, "id": "cb53b91d", "metadata": {}, "outputs": [], "source": [ "l = widgets.Text(value=' Interactive Bayesian Linear Regression with McMC Metropolis-Hastings Demo, Prof. Michael Pyrcz, The University of Texas at Austin',\n", " layout=Layout(width='890px', height='30px'))\n", "\n", "max_accepted = widgets.IntSlider(min=2, max = 600, value=10, step = 20, description = '$\\ell$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "# radius = widgets.FloatSlider(min=10, max = 500, value=110, step = 10, description = r'$r$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "# minpts = widgets.IntSlider(min=2, max = 20, value=4, step = 1, description = r'$min_{pts}$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "\n", "ui = widgets.HBox([max_accepted],)\n", "ui2 = widgets.VBox([l,ui],)\n", "\n", "def run_plot(max_accepted):\n", "\n", " np.random.seed(seed = seed)\n", " step_stdev = 0.2\n", " \n", " thetas = np.random.rand(3).reshape(1,-1) # seed a random first step\n", " accepted = 0\n", " \n", " while accepted < max_accepted:\n", " theta_new = next_proposal(thetas[-1,:],step_stdev=step_stdev) # next proposal\n", " \n", " log_like_new = likelihood_density(x,y,theta_new) # new and prior likelihoods, log of density\n", " log_like = likelihood_density(x,y,thetas[-1,:])\n", " \n", " log_prior_new = prior_density_mv(theta_new,prior) # new and prior prior, log of density\n", " log_prior = prior_density_mv(thetas[-1,:],prior)\n", " \n", " likelihood_prior_proposal_ratio = np.exp((log_like_new + log_prior_new) - (log_like + log_prior)) # calculate log ratio\n", " \n", " if likelihood_prior_proposal_ratio > np.random.rand(1): # conditionally accept by likelihood ratio\n", " thetas = np.vstack((thetas,theta_new)); accepted += 1\n", " \n", " df = pd.DataFrame(np.vstack([thetas[:,0],thetas[:,1],thetas[:,2]]).T, columns= ['Slope','Intercept','Sigma'])\n", " \n", " fig = plt.figure(constrained_layout=False)\n", " gs = GridSpec(2, 2, figure=fig)\n", " \n", " ax1 = fig.add_subplot(gs[:, 0])\n", " \n", " burn_chain = 250\n", " alpha = 0.1\n", " max_sample = 1000\n", " viz_buff = 50\n", " \n", " alpha_burn = np.arange(0,burn_chain,dtype='float')\n", " alpha_burn = 1+(alpha_burn - max_accepted)/viz_buff\n", " alpha_burn = np.where(alpha_burn<0, 0, alpha_burn)\n", " alpha_burn = alpha_burn[alpha_burn <= 1.0]\n", "\n", " lower_b1 = stats.norm.ppf(alpha/2.0,loc=prior[0,0],scale=prior[0,1]); upper_b1 = stats.norm.ppf(1-alpha/2.0,loc=prior[0,0],scale=prior[0,1])\n", " lower_b0 = stats.norm.ppf(alpha/2.0,loc=prior[1,0],scale=prior[1,1]); upper_b0 = stats.norm.ppf(1-alpha/2.0,loc=prior[1,0],scale=prior[1,1])\n", " \n", " ax1.scatter(prior[0,0],prior[1,0],color='black',marker='x',s=30)\n", " ax1.annotate('Prior',[prior[0,0]+0.1,prior[1,0]+0.1],color='black') \n", " ell = Ellipse(xy=(prior[0,0],prior[1,0]),width=(upper_b1 - lower_b1), height=(upper_b0 - lower_b0),angle=0.0,ls='--') \n", " ell.set_edgecolor('black'); ell.set_facecolor('none')\n", " ax1.add_artist(ell)\n", " ax1.scatter(linear_model.coef_[0],linear_model.intercept_,color='black',marker='x',s=30)\n", " ax1.annotate('OLS',[linear_model.coef_[0]+0.1,linear_model.intercept_+0.1],color='black')\n", " ax1.scatter(thetas[:burn_chain,0],thetas[:burn_chain,1],s=20,marker = 'o',c='black',edgecolor='black',alpha=alpha_burn,linewidth=1.0,cmap=plt.cm.inferno,zorder=10)\n", " if max_accepted > burn_chain:\n", " ax1.scatter(thetas[burn_chain:,0],thetas[burn_chain:,1],s=30,c=np.arange(burn_chain,max_accepted+1,1),alpha=1.0,edgecolor='black',linewidth=0.1,cmap=plt.cm.inferno,zorder=10)\n", " ax1.scatter(thetas[-1,0],thetas[-1,1],s=50,c='white',alpha=1.0,edgecolor='black',linewidth=1.0,cmap=plt.cm.inferno,zorder=100)\n", " ax1.plot(thetas[:burn_chain,0],thetas[:burn_chain,1],color='black',linewidth=1.0,zorder=1)\n", " add_grid(); ax1.set_xlabel('Slope, $b_1$'); ax1.set_ylabel('Intercept, $b_0$'); ax1.set_title('McMC Samples Bayesian Linear Regression') \n", " ax1.set_xlim([0,5]); ax1.set_ylim([0,25])\n", " \n", " ax2 = fig.add_subplot(gs[0, 1])\n", " ax2.plot(np.arange(0,accepted+1,1),thetas[:,0],c='red',zorder=100) \n", " ax2.scatter(accepted,thetas[-1,0],s=50,c='white',alpha=1.0,edgecolor='black',linewidth=1.0,cmap=plt.cm.inferno,zorder=100)\n", " ax2.set_xlabel('McMC Metropolis-Hastings Sample'); ax2.set_ylabel(r'$b_1$'); ax2.set_title(\"McMC Slope Samples\"); add_grid()\n", " ax2.plot([0,max_sample],[linear_model.coef_[0],linear_model.coef_[0]],c='darkred',lw=0.5,zorder=10)\n", " ax2.annotate('Linear Regression',[max_sample*0.70,linear_model.coef_[0]-0.8],color='darkred')\n", " ax2.plot([0,max_sample],[prior[0,0],prior[0,0]],c='black',zorder=10)\n", " ax2.annotate('Prior Model',[max_sample*0.8,prior[0,0]-0.8])\n", " lower = stats.norm.ppf(alpha/2.0,loc=prior[0,0],scale=prior[0,1])\n", " ax2.plot([0,max_sample],[lower,lower],c='black',ls='--',lw=0.5,zorder=10)\n", " upper = stats.norm.ppf(1-alpha/2.0,loc=prior[0,0],scale=prior[0,1])\n", " ax2.plot([0,max_sample],[upper,upper],c='black',ls='--',lw=0.5,zorder=10)\n", " ax2.fill_between([0,max_sample],[lower,lower],[upper,upper],color='black',alpha=0.05,zorder=1)\n", " ax2.set_xlim([0,max_sample]); ax2.set_ylim([0,10])\n", " \n", " ax3 = fig.add_subplot(gs[1, 1])\n", " ax3.plot(np.arange(0,accepted+1,1),thetas[:,1],c='red',zorder=100) \n", " ax3.scatter(accepted,thetas[-1,1],s=50,c='white',alpha=1.0,edgecolor='black',linewidth=1.0,cmap=plt.cm.inferno,zorder=100)\n", " ax3.set_xlabel('McMC Metropolis-Hastings Sample'); ax3.set_ylabel(r'$b_0$'); ax3.set_title(\"McMC Intercept Samples\"); add_grid()\n", " ax3.plot([0,max_sample],[linear_model.intercept_,linear_model.intercept_],c='darkred',lw=0.5,zorder=10)\n", " ax3.annotate('Linear Regression',[max_sample*0.70,linear_model.intercept_-2.2],color='darkred')\n", " ax3.plot([0,max_sample],[prior[1,0],prior[1,0]],c='black',zorder=10)\n", " ax3.annotate('Prior Model',[max_sample*0.8,prior[1,0]-2.2])\n", " lower = stats.norm.ppf(alpha/2.0,loc=prior[1,0],scale=prior[1,1])\n", " ax3.plot([0,max_sample],[lower,lower],c='black',ls='--',lw=0.5,zorder=10)\n", " upper = stats.norm.ppf(1-alpha/2.0,loc=prior[1,0],scale=prior[1,1])\n", " ax3.plot([0,max_sample],[upper,upper],c='black',ls='--',lw=0.5,zorder=10)\n", " ax3.fill_between([0,max_sample],[lower,lower],[upper,upper],color='black',alpha=0.05,zorder=1)\n", " ax3.set_xlim([0,max_sample]); ax3.set_ylim([0,30])\n", " \n", " plt.subplots_adjust(left=0.0, bottom=0.0, right=1.5, top=1.0, wspace=0.2, hspace=0.5); plt.show()\n", " \n", "# connect the function to make the samples and plot to the widgets \n", "interactive_plot = widgets.interactive_output(run_plot, {'max_accepted':max_accepted})\n", "interactive_plot.clear_output(wait = True) # reduce flickering by delaying plot updating " ] }, { "cell_type": "markdown", "id": "b79a1e8c", "metadata": {}, "source": [ "### Interactive Bayesian Linear Regression with McMC Metropolis-Hastings Demonstration \n", "\n", "#### Michael Pyrcz, Professor, The University of Texas at Austin " ] }, { "cell_type": "code", "execution_count": 55, "id": "483a17df", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "103cd41f4556408094e991d1706a7329", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Text(value=' Interactive Bayesian Linear Regression with McMC Metropolis-Hastings…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6de44def5933456d834c03cf26092f7c", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '
', 'i…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(ui2, interactive_plot) # display the interactive plot" ] }, { "cell_type": "markdown", "id": "d5bcc4e5-2ce0-47b8-a9d0-8d9b069c911a", "metadata": {}, "source": [ "#### All the Computational Details\n", "\n", "Now rebuild the dashboard to focus on the MCMC Metropolis samples and the calculation of the acceptance criteria.\n", "\n", "* to visualize all the math, I reduce the number of data to 2!" ] }, { "cell_type": "code", "execution_count": 58, "id": "01fdad2b-a414-4b3e-8ab8-e06f388ae712", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "seed = 72066\n", "np.random.seed(seed = seed) # set random number seed\n", "\n", "data_b1 = 2.0; data_b0 = 4.0; data_sigma = 1; n = 2 # set data model parameters\n", "\n", "x = np.array([10,25]) # random x values\n", "y = data_b1*x+data_b0 + np.random.normal(loc=0.0,scale=data_sigma,size=n) # y as a linear function of x + random noise \n", "\n", "xhat = np.linspace(-10,40,100) # set of x values to predict and visualize the model\n", "linear_model = LinearRegression().fit(x.reshape(-1, 1),y) # instantiate and train the frequentist linear regression model\n", "yhat = linear_model.predict(xhat.reshape(-1, 1)) # make predictions for model plotting\n", "\n", "plt.subplot(111)\n", "plt.scatter(x, y,c='red',s=20,edgecolor='black',zorder=10)\n", "plt.plot(xhat,yhat,c='red'); add_grid()\n", "plt.xlabel(\"Predictor Feature\"); plt.ylabel(\"Response Feature\"); plt.title('Data and Linear Regression Model')\n", "plt.gca().add_patch(Rectangle((1.5,93.0),4.3,23,facecolor='white',edgecolor='black',linewidth=0.5))\n", "plt.annotate('$b_1$ = ' + str(np.round(linear_model.coef_[0],2)),[2,110])\n", "plt.annotate('$b_0$ = ' + str(np.round(linear_model.intercept_,2)),[2,103])\n", "plt.annotate('$\\sigma$ = ' + str(np.round(data_sigma,2)),[2,96])\n", "plt.xlim([0,30]); plt.ylim([0,120])\n", "\n", "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.2, hspace=0.5); plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "51b1061d-e8bc-4db4-bd7e-c7121b270e87", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 63, "id": "b36e44a5-5be6-47b5-9564-8a585b5fcbd8", "metadata": {}, "outputs": [], "source": [ "l = widgets.Text(value=' Interactive Bayesian Linear Regression with McMC Metropolis-Hastings Demo, Prof. Michael Pyrcz, The University of Texas at Austin',\n", " layout=Layout(width='890px', height='30px'))\n", "\n", "max_accepted = widgets.IntSlider(min=1, max = 600, value=1, step = 1, description = '$\\ell$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "# radius = widgets.FloatSlider(min=10, max = 500, value=110, step = 10, description = r'$r$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "# minpts = widgets.IntSlider(min=2, max = 20, value=4, step = 1, description = r'$min_{pts}$',orientation='horizontal', style = {'description_width': 'initial'}, continuous_update=False)\n", "\n", "ui3 = widgets.HBox([max_accepted],)\n", "ui4 = widgets.VBox([l,ui3],)\n", "\n", "def run_plot2(max_accepted):\n", " seed = 13\n", " np.random.seed(seed = seed)\n", " datacolors = ['blue','purple']\n", " \n", " prior2 = np.zeros([3,2]) # prior distributions\n", " prior2[0,:] = [3.0,0.5] # Gaussian prior model for slope, mean and standard deviation\n", " prior2[1,:] = [1.2,0.3] # Gaussian prior model for intercept, mean and standard deviation\n", " prior2[2,:] = [2.5,0.5] # Gaussian prior model for sigma, k (shape) and phi (scale), recall mean = k x phi, var = k x phi^2 \n", " \n", " step_stdev = 0.4\n", " \n", " thetas = np.random.rand(3).reshape(1,-1) # seed a random first step\n", " accepted = 0; attempts = 0\n", " \n", " while accepted < max_accepted:\n", " selected = False\n", " theta_new = next_proposal(thetas[-1,:],step_stdev=step_stdev) # next proposal\n", " \n", " log_like_new = likelihood_density(x,y,theta_new) # new and prior likelihoods, log of density\n", " log_like = likelihood_density(x,y,thetas[-1,:])\n", " \n", " log_prior_new = prior_density_sum_log(theta_new,prior2) # new and prior prior, log of density\n", " log_prior = prior_density_sum_log(thetas[-1,:],prior2)\n", " \n", " likelihood_prior_proposal_ratio = np.exp((log_like_new + log_prior_new) - (log_like + log_prior)) # calculate log ratio\n", " \n", " attempts = attempts + 1\n", " if likelihood_prior_proposal_ratio > np.random.rand(1): # conditionally accept by likelihood ratio\n", " thetas = np.vstack((thetas,theta_new)); accepted += 1; selected = True\n", " \n", " df = pd.DataFrame(np.vstack([thetas[:,0],thetas[:,1],thetas[:,2]]).T, columns= ['Slope','Intercept','Sigma'])\n", " \n", " prev_b1 = thetas[-2][0]; prev_b0 = thetas[-2][1]; prev_sigma = thetas[-2][2]\n", " prop_b1 = theta_new[0]; prop_b0 = theta_new[1]; prop_sigma = theta_new[2]\n", " \n", " fig = plt.figure(constrained_layout=False)\n", " gs = GridSpec(2, 2, figure=fig)\n", " \n", " ax1 = fig.add_subplot(gs[0, 0])\n", " \n", " burn_chain = 10\n", " alpha = 0.1\n", " max_sample = 1000\n", " viz_buff = 50\n", " \n", " alpha_burn = np.arange(0,burn_chain,dtype='float')\n", " alpha_burn = 1+(alpha_burn - max_accepted)/viz_buff\n", " alpha_burn = np.where(alpha_burn<0, 0, alpha_burn)\n", " alpha_burn = alpha_burn[alpha_burn <= 1.0]\n", "\n", " lower_b1 = stats.norm.ppf(alpha/2.0,loc=prior2[0,0],scale=prior[0,1]); upper_b1 = stats.norm.ppf(1-alpha/2.0,loc=prior2[0,0],scale=prior2[0,1])\n", " lower_b0 = stats.norm.ppf(alpha/2.0,loc=prior2[1,0],scale=prior[1,1]); upper_b0 = stats.norm.ppf(1-alpha/2.0,loc=prior2[1,0],scale=prior2[1,1])\n", " \n", " ax1.scatter(prior2[0,0],prior2[1,0],color='black',marker='x',s=30,zorder=100)\n", " ax1.annotate('Prior',[prior2[0,0]+0.1,prior2[1,0]+0.1],color='black',zorder=100) \n", " ell = Ellipse(xy=(prior2[0,0],prior2[1,0]),width=(upper_b1 - lower_b1), height=(upper_b0 - lower_b0),angle=0.0,ls='--') \n", "\n", " ell.set_edgecolor('black'); ell.set_facecolor('none')\n", " ax1.add_artist(ell)\n", " ax1.scatter(linear_model.coef_[0],linear_model.intercept_,color='black',marker='x',s=30,zorder=100)\n", " ax1.annotate('OLS',[linear_model.coef_[0]+0.1,linear_model.intercept_+0.1],color='black',zorder=100)\n", " ax1.scatter(thetas[:burn_chain,0],thetas[:burn_chain,1],s=20,marker = 'o',c='black',edgecolor='black',alpha=alpha_burn,linewidth=1.0,cmap=plt.cm.inferno,zorder=10)\n", " if max_accepted > burn_chain:\n", " ax1.scatter(thetas[burn_chain:,0],thetas[burn_chain:,1],s=30,c=np.arange(burn_chain,max_accepted+1,1),alpha=1.0,edgecolor='black',linewidth=0.1,cmap=plt.cm.inferno,zorder=10)\n", " ax1.scatter(thetas[-1,0],thetas[-1,1],s=50,c='white',alpha=1.0,edgecolor='black',linewidth=1.0,cmap=plt.cm.inferno,zorder=100)\n", " ax1.plot(thetas[:burn_chain,0],thetas[:burn_chain,1],color='black',linewidth=1.0,zorder=1)\n", " \n", " plt.annotate('Number of Attempts: ' + str(attempts) + ', Number Accepted: ' + str(accepted),[0.15,-4.2],size = 8)\n", " \n", " add_grid(); ax1.set_xlabel('Slope, $b_1$'); ax1.set_ylabel('Intercept, $b_0$'); ax1.set_title('McMC Samples Bayesian Linear Regression') \n", " ax1.set_xlim([0,5.0]); ax1.set_ylim([-5,10])\n", " \n", " prev_y_hat = prev_b1*x+prev_b0; prop_y_hat = prop_b1*x+prop_b0\n", " \n", " ax2 = fig.add_subplot(gs[1, 0]) # priors\n", " \n", " x_values = np.linspace(-2.0,5.0,500)\n", " \n", " b1_prior = stats.norm.pdf(x_values, prior2[0][0], prior2[0][1])\n", " b0_prior = stats.norm.pdf(x_values, prior2[1][0], prior2[1][1])\n", " sigma_prior = stats.norm.pdf(x_values, prior2[2][0], prior2[2][1])\n", " \n", " ax2.plot(x_values,b0_prior,color='green',label=r'$b_0$')\n", " ax2.plot(x_values,b1_prior,color='red',label=r'$b_1$')\n", " ax2.plot(x_values,sigma_prior,color='black',label=r'$\\sigma$')\n", " ax2.set_xlim([-2.0,5.0]); ax2.set_ylim([0,2.5]); ax2.set_ylabel('Density'); ax2.set_title('Prior Probability')\n", " \n", " prev_b1_den = stats.norm.pdf(prev_b1, prior2[0][0], prior2[0][1]); prev_b1_lden = np.log(prev_b1_den)\n", " prev_b0_den = stats.norm.pdf(prev_b0, prior2[1][0], prior2[1][1]); prev_b0_lden = np.log(prev_b0_den)\n", " prev_sigma_den = stats.norm.pdf(prev_sigma, prior2[2][0], prior2[2][1]); prev_sigma_lden = np.log(prev_sigma_den)\n", " \n", " prop_b1_den = stats.norm.pdf(prop_b1, prior2[0][0], prior2[0][1]); prop_b1_lden = np.log(prop_b1_den)\n", " prop_b0_den = stats.norm.pdf(prop_b0, prior2[1][0], prior2[1][1]); prop_b0_lden = np.log(prop_b0_den)\n", " prop_sigma_den = stats.norm.pdf(prop_sigma, prior2[2][0], prior2[2][1]); prop_sigma_lden = np.log(prop_sigma_den)\n", " \n", " ax2.plot([prev_b1,prev_b1],[0,prev_b1_den],color='red',alpha=0.5)\n", " ax2.plot([prop_b1,prop_b1],[0,prop_b1_den],color='red')\n", " ax2.scatter([prev_b1],[prev_b1_den],color='red',edgecolor='black',zorder=3,alpha=0.5)\n", " ax2.scatter([prop_b1],[prop_b1_den],color='red',edgecolor='black',zorder=3,alpha=1.0)\n", " \n", " ax2.plot([prev_b0,prev_b0],[0,prev_b0_den],color='green',alpha=0.5)\n", " ax2.plot([prop_b0,prop_b0],[0,prop_b0_den],color='green')\n", " ax2.scatter([prev_b0],[prev_b0_den],color='green',edgecolor='black',zorder=3,alpha=0.5)\n", " ax2.scatter([prop_b0],[prop_b0_den],color='green',edgecolor='black',zorder=3,alpha=1.0)\n", "\n", " ax2.plot([prev_sigma,prev_sigma],[0,prev_sigma_den],color='black',alpha=0.5)\n", " ax2.plot([prop_sigma,prop_sigma],[0,prop_sigma_den],color='black')\n", " ax2.scatter([prev_sigma],[prev_sigma_den],color='grey',edgecolor='black',zorder=3,alpha=0.5)\n", " ax2.scatter([prop_sigma],[prop_sigma_den],color='grey',edgecolor='black',zorder=3,alpha=1.0)\n", " \n", " prev_sum_log = prev_b1_lden + prev_b0_lden + prev_sigma_lden\n", " prev_prior_note = f\"{np.exp(prev_sum_log):.2e}\"\n", " \n", " prop_sum_log = prop_b1_lden + prop_b0_lden + prop_sigma_lden\n", " prop_prior_note = f\"{np.exp(prop_sum_log):.2e}\"\n", " \n", " ax2.annotate(r'$P(\\beta) = exp(log(f(b_1)) + log(f(b_0)) + log(f(b_{\\sigma}))) )$',[-1.8,2.3], size = 8)\n", " ax2.annotate(r'$ = exp($' \n", " + str(np.round(prev_b1_lden,1)) + ' + ' \n", " + str(np.round(prev_b0_lden,1)) + ' + ' \n", " + str(np.round(prev_sigma_lden,1)) + '$) = exp($' + str(np.round(prev_sum_log,1)) \n", " + '$) = $' + f'{prev_prior_note}',[-1.42,2.1], size = 8)\n", " \n", " \n", " ax2.annotate(r'$P(\\beta^{\\prime}) = exp(log(f(b_1^{\\prime})) + log(f(b_0^{\\prime})) + log(f(b_{\\sigma}^{\\prime}))) )$',[-1.8,1.8], size = 8)\n", " ax2.annotate(r'$ = exp($' \n", " + str(np.round(prop_b1_lden,1)) + ' + ' \n", " + str(np.round(prop_b0_lden,1)) + ' + ' \n", " + str(np.round(prop_sigma_lden,1)) + '$) = exp($' + str(np.round(prop_sum_log,1)) \n", " + '$) = $' + f'{prop_prior_note}',[-1.42,1.6], size = 8)\n", " \n", " ax2.legend(loc='upper right')\n", " \n", " ax3 = fig.add_subplot(gs[1, 1]) # likelihood \n", " \n", " prev_y_hat = prev_b1*x+prev_b0; prop_y_hat = prop_b1*x+prop_b0 \n", " prev_like_lden = stats.norm.logpdf(y, loc=prev_y_hat,scale=prev_sigma) # assume independence, sum is product in log space\n", " prop_like_lden = stats.norm.logpdf(y, loc=prop_y_hat,scale=prop_sigma)\n", " prev_like_lsum = np.sum(prev_like_lden); prop_like_lsum = np.sum(prop_like_lden) # assume independence, sum is product in log space\n", " prev_like = np.exp(prev_like_lsum); prop_like = np.exp(prop_like_lsum)\n", " \n", " prev_like_note = f\"{prev_like:.2e}\"; prop_like_note = f\"{prop_like:.2e}\"\n", " \n", " x_values = np.linspace(0.0,100.0,500)\n", "\n", " for idata in range(0,2):\n", " d_prev = stats.norm.pdf(x_values, prev_y_hat[idata], prev_sigma)\n", " ax3.plot(x_values,d_prev,color=datacolors[idata],alpha=0.5)\n", " ax3.scatter(y[idata],np.exp(prev_like_lden[idata]),color=datacolors[idata],edgecolor='black',alpha=0.5,zorder=10)\n", " \n", " d_prop = stats.norm.pdf(x_values, prop_y_hat[idata], prop_sigma)\n", " ax3.plot(x_values,d_prop,color=datacolors[idata],alpha=1.0)\n", " ax3.scatter(y[idata],np.exp(prop_like_lden[idata]),color=datacolors[idata],edgecolor='black',zorder=10)\n", " \n", " ax3.set_xlim([0,100.0]); ax3.set_ylim([0,1.0]) \n", " ax3.annotate(r'$P(x,y | \\beta) = exp(log(f(\\hat{y}_1)) + log(f(\\hat{y}_2))) )$',[2.0,0.93], size = 8)\n", " ax3.annotate(r'$ = exp($' \n", " + str(np.round(prev_like_lden[0],1)) + ' + ' \n", " + str(np.round(prev_like_lden[1],1)) + '$) = exp($' + str(np.round(prev_like_lsum,1)) \n", " + '$) = $' + f'{prev_like_note}',[13.0,0.85], size = 8)\n", " \n", " \n", " ax3.set_xlim([0,100.0]); ax3.set_ylim([0,1.0])\n", " ax3.set_xlabel('Response Feature'); ax3.set_ylabel('Density'); ax3.set_title('Likelihood Probability')\n", " \n", " ax3.annotate(r'$P(x,y | \\beta^{\\prime}) = exp(log(f^{\\prime}(\\hat{y}_1)) + log(f^{\\prime}(\\hat{y}_2))) )$',[2.0,0.76], size = 8)\n", " ax3.annotate(r'$ = exp($' \n", " + str(np.round(prop_like_lden[0],1)) + ' + ' \n", " + str(np.round(prop_like_lden[1],1)) + '$) = exp($' + str(np.round(prop_like_lsum,1)) \n", " + '$) = $' + f'{prop_like_note}',[13.0,0.68], size = 8)\n", " \n", " ax4 = fig.add_subplot(gs[0, 1]) # models\n", " \n", " for idata in range(0,2):\n", " ax4.scatter(x[idata], y[idata],c=datacolors[idata],s=20,marker='o',edgecolor='black',zorder=10)\n", " ax4.scatter(x[idata], prev_y_hat[idata],c=datacolors[idata],s=20,marker='x',alpha=0.5,zorder=10)\n", " ax4.scatter(x[idata], prop_y_hat[idata],c=datacolors[idata],s=20,marker='x',alpha=1.0,zorder=10)\n", " \n", " x_values = np.linspace(0.0,30.0,500)\n", " \n", " prev_model = prev_b1*x_values+prev_b0; prop_model = prop_b1*x_values+prop_b0 \n", " \n", " ax4.plot(x_values,prev_model,c='red',alpha=0.5); ax4.plot(x_values,prop_model,c='red',alpha=1.0); add_grid()\n", " \n", " # ax4.annotate(r'$P(Acceptance) = exp( \\left( log(f^{\\prime}(\\hat{y})) + log(P(\\beta^{\\prime})) \\right) - \\left({log(f(\\hat{y})) + log(P(\\beta))} \\right))$',[1.0,110.0], size = 8)\n", " # ax4.annotate(r'$ = exp($' + str(np.round(log_like_new,1)) + ' + ' + str(np.round(log_prior_new,1)) + '$) - ($' + str(np.round(log_like,1)) + ' + ' + str(np.round(log_prior,1)) + '$) )$',[6.5,98], size = 8)\n", "\n", " ax4.annotate(r'$P(Acceptance) = $',[1.0,100.0], size = 8)\n", " ax4.annotate(r'$\\frac{ f(\\hat{y},x|\\beta^{\\prime}) \\cdot P(\\beta^{\\prime})}{ f(\\hat{y},x|\\beta) \\cdot P(\\beta)}$',[8.0,100.0], size = 12)\n", " ax4.annotate(r'$P(Acceptance) = exp( ( log(f^{\\prime}(\\hat{y})) + log(P(\\beta^{\\prime})) ) - ({log(f(\\hat{y})) + log(P(\\beta))} )) $',[1.0,80.0], size = 8)\n", " ax4.annotate(r'$ = exp($' + str(np.round(log_like_new,1)) + ' + ' + str(np.round(log_prior_new,1)) + '$) - ($' + str(np.round(log_like,1)) + ' + ' + str(np.round(log_prior,1)) + '$) )$',[6.5,72.0], size = 8)\n", " \n", " prob_acceptance = np.exp((log_like_new + log_prior_new)-(log_like + log_prior))\n", " prob_acceptance_note = f\"{np.exp(prob_acceptance):.2e}\"\n", "\n", " if selected == True:\n", " ax4.annotate(r'$ = $' + str(np.round(prob_acceptance,2)) + ' Result : Selected',[6.5,64], size = 8) \n", " else:\n", " ax4.annotate(r'$ = $' + str(np.round(prob_acceptance,2)) + ' Result : Rejected',[6.5,64], size = 8) \n", " \n", " ax4.set_xlabel(\"Predictor Feature\"); ax4.set_ylabel(\"Response Feature\"); ax4.set_title('Data and Linear Regression Model')\n", " ax4.set_xlim([0,30]); ax4.set_ylim([0,120])\n", " \n", " plt.subplots_adjust(left=0.0, bottom=0.0, right=1.5, top=1.0, wspace=0.2, hspace=0.5); plt.show()\n", "\n", "# connect the function to make the samples and plot to the widgets \n", "interactive_plot2 = widgets.interactive_output(run_plot2, {'max_accepted':max_accepted})\n", "interactive_plot2.clear_output(wait = True) # reduce flickering by delaying plot updating " ] }, { "cell_type": "raw", "id": "967a3f95-c0e6-4dd3-85cc-287c2a537212", "metadata": {}, "source": [] }, { "cell_type": "code", "execution_count": 65, "id": "0b4e3180-248b-4a9a-bb1e-1496da28dfb2", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "18605621e36d42a6978b4a685280bfb2", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Text(value=' Interactive Bayesian Linear Regression with McMC Metropolis-Hastings…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7579ae63aee14ac4a77934e187feadd4", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '
', 'i…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(ui4, interactive_plot2) # display the interactive plot" ] }, { "cell_type": "code", "execution_count": null, "id": "4ba223af-44c2-4cec-af74-a503f57ef4ad", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "96c3d27d-46da-49ed-9e0d-fcb99d6690a1", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "a90501df-746c-4509-9fe0-7de5a07d106a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 17, "id": "7945443b-94dc-46b7-a938-c61b0aa9e678", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "seed = 13\n", "np.random.seed(seed = seed)\n", "datacolors = ['blue','purple']\n", "\n", "prior2 = np.zeros([3,2]) # prior distributions\n", "prior2[0,:] = [3.0,0.5] # Gaussian prior model for slope, mean and standard deviation\n", "prior2[1,:] = [1.2,0.3] # Gaussian prior model for intercept, mean and standard deviation\n", "prior2[2,:] = [2.5,0.5] # Gaussian prior model for sigma, k (shape) and phi (scale), recall mean = k x phi, var = k x phi^2 \n", "\n", "step_stdev = 0.4\n", "\n", "thetas = np.random.rand(3).reshape(1,-1) # seed a random first step\n", "accepted = 0; attempts = 0\n", "\n", "max_accepted = 100\n", "\n", "while accepted < max_accepted:\n", " selected = False\n", " theta_new = next_proposal(thetas[-1,:],step_stdev=step_stdev) # next proposal\n", " \n", " log_like_new = likelihood_density(x,y,theta_new) # new and prior likelihoods, log of density\n", " log_like = likelihood_density(x,y,thetas[-1,:])\n", " \n", " log_prior_new = prior_density_sum_log(theta_new,prior2) # new and prior prior, log of density\n", " log_prior = prior_density_sum_log(thetas[-1,:],prior2)\n", " \n", " likelihood_prior_proposal_ratio = np.exp((log_like_new + log_prior_new) - (log_like + log_prior)) # calculate log ratio\n", "\n", " attempts = attempts + 1\n", " if likelihood_prior_proposal_ratio > np.random.rand(1): # conditionally accept by likelihood ratio\n", " thetas = np.vstack((thetas,theta_new)); accepted += 1; selected = True\n", "\n", "df = pd.DataFrame(np.vstack([thetas[:,0],thetas[:,1],thetas[:,2]]).T, columns= ['Slope','Intercept','Sigma'])\n", "\n", "prev_b1 = thetas[-2][0]; prev_b0 = thetas[-2][1]; prev_sigma = thetas[-2][2]\n", "prop_b1 = theta_new[0]; prop_b0 = theta_new[1]; prop_sigma = theta_new[2]\n", "\n", "fig = plt.figure(constrained_layout=False)\n", "gs = GridSpec(2, 2, figure=fig)\n", " \n", "ax1 = fig.add_subplot(gs[0, 0])\n", "\n", "burn_chain = 10\n", "alpha = 0.1\n", "max_sample = 1000\n", "viz_buff = 50\n", "\n", "alpha_burn = np.arange(0,burn_chain,dtype='float')\n", "alpha_burn = 1+(alpha_burn - max_accepted)/viz_buff\n", "alpha_burn = np.where(alpha_burn<0, 0, alpha_burn)\n", "alpha_burn = alpha_burn[alpha_burn <= 1.0]\n", "ax1.scatter(prior2[0][0],prior2[1][0],color='black',marker='x',s=30)\n", "ax1.annotate('Prior',[prior2[0][0]+0.1,prior2[1][0]+0.1],color='black') \n", "ell = Ellipse(xy=(prior2[0][0],prior2[1][0]),width=prior2[0][1]*8.0, height=prior2[1][1]*8.0,angle=0.0,ls='--') \n", "ell.set_edgecolor('black'); ell.set_facecolor('none')\n", "ax1.add_artist(ell)\n", "ax1.scatter(linear_model.coef_[0],linear_model.intercept_,color='black',marker='x',s=30)\n", "ax1.annotate('OLS',[linear_model.coef_[0]+0.1,linear_model.intercept_+0.1],color='black')\n", "ax1.scatter(thetas[:burn_chain,0],thetas[:burn_chain,1],s=20,marker = 'o',c='black',edgecolor='black',alpha=alpha_burn,linewidth=1.0,cmap=plt.cm.inferno,zorder=10)\n", "if max_accepted > burn_chain:\n", " ax1.scatter(thetas[burn_chain:,0],thetas[burn_chain:,1],s=30,c=np.arange(burn_chain,max_accepted+1,1),alpha=1.0,edgecolor='black',linewidth=0.1,cmap=plt.cm.inferno,zorder=10)\n", "ax1.scatter(thetas[-1,0],thetas[-1,1],s=50,c='white',alpha=1.0,edgecolor='black',linewidth=1.0,cmap=plt.cm.inferno,zorder=100)\n", "ax1.plot(thetas[:burn_chain,0],thetas[:burn_chain,1],color='black',linewidth=1.0,zorder=1)\n", "\n", "plt.annotate('Number of Attempts: ' + str(attempts) + ', Number Accepted: ' + str(accepted),[0.15,-4.2],size = 8)\n", "\n", "add_grid(); ax1.set_xlabel('Slope, $b_1$'); ax1.set_ylabel('Intercept, $b_0$'); ax1.set_title('McMC Samples Bayesian Linear Regression') \n", "ax1.set_xlim([0,5.0]); ax1.set_ylim([-5,10])\n", "\n", "prev_y_hat = prev_b1*x+prev_b0; prop_y_hat = prop_b1*x+prop_b0\n", "\n", "ax2 = fig.add_subplot(gs[1, 0]) # priors\n", "\n", "x_values = np.linspace(-2.0,5.0,500)\n", "\n", "b1_prior = stats.norm.pdf(x_values, prior2[0][0], prior2[0][1])\n", "b0_prior = stats.norm.pdf(x_values, prior2[1][0], prior2[1][1])\n", "sigma_prior = stats.norm.pdf(x_values, prior2[2][0], prior2[2][1])\n", "\n", "ax2.plot(x_values,b0_prior,color='green',label=r'$b_0$')\n", "ax2.plot(x_values,b1_prior,color='red',label=r'$b_1$')\n", "ax2.plot(x_values,sigma_prior,color='black',label=r'$\\sigma$')\n", "ax2.set_xlim([-2.0,5.0]); ax2.set_ylim([0,2.5]); ax2.set_ylabel('Density'); ax2.set_title('Prior Probability Calculations')\n", "\n", "prev_b1_den = stats.norm.pdf(prev_b1, prior2[0][0], prior2[0][1]); prev_b1_lden = np.log(prev_b1_den)\n", "prev_b0_den = stats.norm.pdf(prev_b0, prior2[1][0], prior2[1][1]); prev_b0_lden = np.log(prev_b0_den)\n", "prev_sigma_den = stats.norm.pdf(prev_sigma, prior2[2][0], prior2[2][1]); prev_sigma_lden = np.log(prev_sigma_den)\n", "\n", "prop_b1_den = stats.norm.pdf(prop_b1, prior2[0][0], prior2[0][1]); prop_b1_lden = np.log(prop_b1_den)\n", "prop_b0_den = stats.norm.pdf(prop_b0, prior2[1][0], prior2[1][1]); prop_b0_lden = np.log(prop_b0_den)\n", "prop_sigma_den = stats.norm.pdf(prop_sigma, prior2[2][0], prior2[2][1]); prop_sigma_lden = np.log(prop_sigma_den)\n", "\n", "ax2.plot([prev_b1,prev_b1],[0,prev_b1_den],color='red',alpha=0.5)\n", "ax2.plot([prop_b1,prop_b1],[0,prop_b1_den],color='red')\n", "ax2.scatter([prev_b1],[prev_b1_den],color='red',edgecolor='black',zorder=3,alpha=0.5)\n", "ax2.scatter([prop_b1],[prop_b1_den],color='red',edgecolor='black',zorder=3,alpha=1.0)\n", "\n", "ax2.plot([prev_b0,prev_b0],[0,prev_b0_den],color='green',alpha=0.5)\n", "ax2.plot([prop_b0,prop_b0],[0,prop_b0_den],color='green')\n", "ax2.scatter([prev_b0],[prev_b0_den],color='green',edgecolor='black',zorder=3,alpha=0.5)\n", "ax2.scatter([prop_b0],[prop_b0_den],color='green',edgecolor='black',zorder=3,alpha=1.0)\n", "\n", "ax2.plot([prev_sigma,prev_sigma],[0,prev_sigma_den],color='black',alpha=0.5)\n", "ax2.plot([prop_sigma,prop_sigma],[0,prop_sigma_den],color='black')\n", "ax2.scatter([prev_sigma],[prev_sigma_den],color='grey',edgecolor='black',zorder=3,alpha=0.5)\n", "ax2.scatter([prop_sigma],[prop_sigma_den],color='grey',edgecolor='black',zorder=3,alpha=1.0)\n", "\n", "prev_sum_log = prev_b1_lden + prev_b0_lden + prev_sigma_lden\n", "prev_prior_note = f\"{np.exp(prev_sum_log):.2e}\"\n", "\n", "prop_sum_log = prop_b1_lden + prop_b0_lden + prop_sigma_lden\n", "prop_prior_note = f\"{np.exp(prop_sum_log):.2e}\"\n", "\n", "ax2.annotate(r'$P(\\beta) = exp(log(f(b_1)) + log(f(b_0)) + log(f(b_{\\sigma}))) )$',[-1.8,2.3], size = 8)\n", "ax2.annotate(r'$ = exp($' \n", " + str(np.round(prev_b1_lden,1)) + ' + ' \n", " + str(np.round(prev_b0_lden,1)) + ' + ' \n", " + str(np.round(prev_sigma_lden,1)) + '$) = exp($' + str(np.round(prev_sum_log,1)) \n", " + '$) = $' + f'{prev_prior_note}',[-1.42,2.1], size = 8)\n", "\n", "\n", "ax2.annotate(r'$P(\\beta^{\\prime}) = exp(log(f(b_1^{\\prime})) + log(f(b_0^{\\prime})) + log(f(b_{\\sigma}^{\\prime}))) )$',[-1.8,1.8], size = 8)\n", "ax2.annotate(r'$ = exp($' \n", " + str(np.round(prop_b1_lden,1)) + ' + ' \n", " + str(np.round(prop_b0_lden,1)) + ' + ' \n", " + str(np.round(prop_sigma_lden,1)) + '$) = exp($' + str(np.round(prop_sum_log,1)) \n", " + '$) = $' + f'{prop_prior_note}',[-1.42,1.6], size = 8)\n", "\n", "ax2.legend(loc='upper right')\n", "\n", "ax3 = fig.add_subplot(gs[1, 1]) # likelihood \n", "\n", "prev_y_hat = prev_b1*x+prev_b0; prop_y_hat = prop_b1*x+prop_b0 \n", "prev_like_lden = stats.norm.logpdf(y, loc=prev_y_hat,scale=prev_sigma) # assume independence, sum is product in log space\n", "prop_like_lden = stats.norm.logpdf(y, loc=prop_y_hat,scale=prop_sigma)\n", "prev_like_lsum = np.sum(prev_like_lden); prop_like_lsum = np.sum(prop_like_lden) # assume independence, sum is product in log space\n", "prev_like = np.exp(prev_like_lsum); prop_like = np.exp(prop_like_lsum)\n", "\n", "prev_like_note = f\"{prev_like:.2e}\"; prop_like_note = f\"{prop_like:.2e}\"\n", "\n", "x_values = np.linspace(0.0,120.0,500)\n", "\n", "for idata in range(0,2):\n", " d_prev = stats.norm.pdf(x_values, prev_y_hat[idata], prev_sigma)\n", " ax3.plot(x_values,d_prev,color=datacolors[idata],alpha=0.5)\n", " ax3.scatter(y[idata],np.exp(prev_like_lden[idata]),color=datacolors[idata],edgecolor='black',alpha=0.5,zorder=10)\n", "\n", " d_prop = stats.norm.pdf(x_values, prop_y_hat[idata], prop_sigma)\n", " ax3.plot(x_values,d_prop,color=datacolors[idata],alpha=1.0)\n", " ax3.scatter(y[idata],np.exp(prop_like_lden[idata]),color=datacolors[idata],edgecolor='black',zorder=10)\n", "\n", "ax3.set_xlim([0,120.0]); ax3.set_ylim([0,1.0])\n", "ax3.set_xlabel('Response Feature'); ax3.set_ylabel('Density'); ax3.set_title('Likelihood Probability Calculations')\n", "\n", "ax3.annotate(r'$P(x,y | \\beta) = exp(log(f(\\hat{y}_1)) + log(f(\\hat{y}_2))) )$',[2.0,0.93], size = 8)\n", "ax3.annotate(r'$ = exp($' \n", " + str(np.round(prev_like_lden[0],1)) + ' + ' \n", " + str(np.round(prev_like_lden[1],1)) + '$) = exp($' + str(np.round(prev_like_lsum,1)) \n", " + '$) = $' + f'{prev_like_note}',[13.0,0.85], size = 8)\n", "\n", "\n", "ax3.set_xlim([0,100.0]); ax3.set_ylim([0,1.0])\n", "ax3.set_xlabel('Response Feature'); ax3.set_ylabel('Density'); ax3.set_title('Likelihood Probability Calculations')\n", "\n", "ax3.annotate(r'$P(x,y | \\beta^{\\prime}) = exp(log(f^{\\prime}(\\hat{y}_1)) + log(f^{\\prime}(\\hat{y}_2))) )$',[2.0,0.76], size = 8)\n", "ax3.annotate(r'$ = exp($' \n", " + str(np.round(prop_like_lden[0],1)) + ' + ' \n", " + str(np.round(prop_like_lden[1],1)) + '$) = exp($' + str(np.round(prop_like_lsum,1)) \n", " + '$) = $' + f'{prop_like_note}',[13.0,0.68], size = 8)\n", "\n", "ax4 = fig.add_subplot(gs[0, 1]) # models\n", "\n", "for idata in range(0,2):\n", " ax4.scatter(x[idata], y[idata],c=datacolors[idata],s=20,marker='o',edgecolor='black',zorder=10)\n", " ax4.scatter(x[idata], prev_y_hat[idata],c=datacolors[idata],s=20,marker='x',alpha=0.5,zorder=10)\n", " ax4.scatter(x[idata], prop_y_hat[idata],c=datacolors[idata],s=20,marker='x',alpha=1.0,zorder=10)\n", "\n", "x_values = np.linspace(0.0,30.0,500)\n", "\n", "prev_model = prev_b1*x_values+prev_b0; prop_model = prop_b1*x_values+prop_b0 \n", "\n", "ax4.plot(x_values,prev_model,c='red',alpha=0.5); ax4.plot(x_values,prop_model,c='red',alpha=1.0); add_grid()\n", "\n", "ax4.annotate(r'$P(Acceptance) = $',[1.0,100.0], size = 8)\n", "ax4.annotate(r'$\\frac{ f(\\hat{y},x|\\beta^{\\prime}) \\cdot P(\\beta^{\\prime})}{ f(\\hat{y},x|\\beta) \\cdot P(\\beta)}$',[8.0,100.0], size = 12)\n", "ax4.annotate(r'$P(Acceptance) = exp( ( log(f^{\\prime}(\\hat{y})) + log(P(\\beta^{\\prime})) ) - ({log(f(\\hat{y})) + log(P(\\beta))} )) $',[1.0,80.0], size = 8)\n", "ax4.annotate(r'$ = exp($' + str(np.round(log_like_new,1)) + ' + ' + str(np.round(log_prior_new,1)) + '$) - ($' + str(np.round(log_like,1)) + ' + ' + str(np.round(log_prior,1)) + '$) )$',[6.5,72.0], size = 8)\n", "\n", "prob_acceptance = np.exp((log_like_new + log_prior_new)-(log_like + log_prior))\n", "\n", "if selected == True:\n", " ax4.annotate(r'$ = $' + str(np.round(prob_acceptance,1)) + ' Result : Selected',[6.5,64], size = 8) \n", "else:\n", " ax4.annotate(r'$ = $' + str(np.round(prob_acceptance,1)) + ' Result : Rejected',[6.5,64], size = 8) \n", "\n", "ax4.set_xlabel(\"Predictor Feature\"); ax4.set_ylabel(\"Response Feature\"); ax4.set_title('Data and Linear Regression Model')\n", "ax4.set_xlim([0,30]); ax4.set_ylim([0,120])\n", "\n", "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.5, top=1.0, wspace=0.2, hspace=0.5); plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "e727c947-5163-4d6f-b964-9cfccdf8cc18", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "90ac588c-6443-4c1c-b616-11dec4238c46", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 18, "id": "d782ac28-d4a0-4bee-a794-5472940b6c0f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.86585355, 0.99888602, 1.1319185 , 1.26495097, 1.39798344,\n", " 1.53101591, 1.66404838, 1.79708085, 1.93011333, 2.0631458 ,\n", " 2.19617827, 2.32921074, 2.46224321, 2.59527569, 2.72830816,\n", " 2.86134063, 2.9943731 , 3.12740557, 3.26043804, 3.39347052,\n", " 3.52650299, 3.65953546, 3.79256793, 3.9256004 , 4.05863288,\n", " 4.19166535, 4.32469782, 4.45773029, 4.59076276, 4.72379523,\n", " 4.85682771, 4.98986018, 5.12289265, 5.25592512, 5.38895759,\n", " 5.52199007, 5.65502254, 5.78805501, 5.92108748, 6.05411995,\n", " 6.18715242, 6.3201849 , 6.45321737, 6.58624984, 6.71928231,\n", " 6.85231478, 6.98534726, 7.11837973, 7.2514122 , 7.38444467,\n", " 7.51747714, 7.65050961, 7.78354209, 7.91657456, 8.04960703,\n", " 8.1826395 , 8.31567197, 8.44870445, 8.58173692, 8.71476939,\n", " 8.84780186, 8.98083433, 9.1138668 , 9.24689928, 9.37993175,\n", " 9.51296422, 9.64599669, 9.77902916, 9.91206164, 10.04509411,\n", " 10.17812658, 10.31115905, 10.44419152, 10.57722399, 10.71025647,\n", " 10.84328894, 10.97632141, 11.10935388, 11.24238635, 11.37541883,\n", " 11.5084513 , 11.64148377, 11.77451624, 11.90754871, 12.04058118,\n", " 12.17361366, 12.30664613, 12.4396786 , 12.57271107, 12.70574354,\n", " 12.83877602, 12.97180849, 13.10484096, 13.23787343, 13.3709059 ,\n", " 13.50393837, 13.63697085, 13.77000332, 13.90303579, 14.03606826,\n", " 14.16910073, 14.30213321, 14.43516568, 14.56819815, 14.70123062,\n", " 14.83426309, 14.96729557, 15.10032804, 15.23336051, 15.36639298,\n", " 15.49942545, 15.63245792, 15.7654904 , 15.89852287, 16.03155534,\n", " 16.16458781, 16.29762028, 16.43065276, 16.56368523, 16.6967177 ,\n", " 16.82975017, 16.96278264, 17.09581511, 17.22884759, 17.36188006,\n", " 17.49491253, 17.627945 , 17.76097747, 17.89400995, 18.02704242,\n", " 18.16007489, 18.29310736, 18.42613983, 18.5591723 , 18.69220478,\n", " 18.82523725, 18.95826972, 19.09130219, 19.22433466, 19.35736714,\n", " 19.49039961, 19.62343208, 19.75646455, 19.88949702, 20.02252949,\n", " 20.15556197, 20.28859444, 20.42162691, 20.55465938, 20.68769185,\n", " 20.82072433, 20.9537568 , 21.08678927, 21.21982174, 21.35285421,\n", " 21.48588668, 21.61891916, 21.75195163, 21.8849841 , 22.01801657,\n", " 22.15104904, 22.28408152, 22.41711399, 22.55014646, 22.68317893,\n", " 22.8162114 , 22.94924387, 23.08227635, 23.21530882, 23.34834129,\n", " 23.48137376, 23.61440623, 23.74743871, 23.88047118, 24.01350365,\n", " 24.14653612, 24.27956859, 24.41260106, 24.54563354, 24.67866601,\n", " 24.81169848, 24.94473095, 25.07776342, 25.2107959 , 25.34382837,\n", " 25.47686084, 25.60989331, 25.74292578, 25.87595825, 26.00899073,\n", " 26.1420232 , 26.27505567, 26.40808814, 26.54112061, 26.67415309,\n", " 26.80718556, 26.94021803, 27.0732505 , 27.20628297, 27.33931544,\n", " 27.47234792, 27.60538039, 27.73841286, 27.87144533, 28.0044778 ,\n", " 28.13751028, 28.27054275, 28.40357522, 28.53660769, 28.66964016,\n", " 28.80267263, 28.93570511, 29.06873758, 29.20177005, 29.33480252,\n", " 29.46783499, 29.60086747, 29.73389994, 29.86693241, 29.99996488,\n", " 30.13299735, 30.26602982, 30.3990623 , 30.53209477, 30.66512724,\n", " 30.79815971, 30.93119218, 31.06422466, 31.19725713, 31.3302896 ,\n", " 31.46332207, 31.59635454, 31.72938702, 31.86241949, 31.99545196,\n", " 32.12848443, 32.2615169 , 32.39454937, 32.52758185, 32.66061432,\n", " 32.79364679, 32.92667926, 33.05971173, 33.19274421, 33.32577668,\n", " 33.45880915, 33.59184162, 33.72487409, 33.85790656, 33.99093904,\n", " 34.12397151, 34.25700398, 34.39003645, 34.52306892, 34.6561014 ,\n", " 34.78913387, 34.92216634, 35.05519881, 35.18823128, 35.32126375,\n", " 35.45429623, 35.5873287 , 35.72036117, 35.85339364, 35.98642611,\n", " 36.11945859, 36.25249106, 36.38552353, 36.518556 , 36.65158847,\n", " 36.78462094, 36.91765342, 37.05068589, 37.18371836, 37.31675083,\n", " 37.4497833 , 37.58281578, 37.71584825, 37.84888072, 37.98191319,\n", " 38.11494566, 38.24797813, 38.38101061, 38.51404308, 38.64707555,\n", " 38.78010802, 38.91314049, 39.04617297, 39.17920544, 39.31223791,\n", " 39.44527038, 39.57830285, 39.71133532, 39.8443678 , 39.97740027,\n", " 40.11043274, 40.24346521, 40.37649768, 40.50953016, 40.64256263,\n", " 40.7755951 , 40.90862757, 41.04166004, 41.17469251, 41.30772499,\n", " 41.44075746, 41.57378993, 41.7068224 , 41.83985487, 41.97288735,\n", " 42.10591982, 42.23895229, 42.37198476, 42.50501723, 42.6380497 ,\n", " 42.77108218, 42.90411465, 43.03714712, 43.17017959, 43.30321206,\n", " 43.43624454, 43.56927701, 43.70230948, 43.83534195, 43.96837442,\n", " 44.10140689, 44.23443937, 44.36747184, 44.50050431, 44.63353678,\n", " 44.76656925, 44.89960173, 45.0326342 , 45.16566667, 45.29869914,\n", " 45.43173161, 45.56476408, 45.69779656, 45.83082903, 45.9638615 ,\n", " 46.09689397, 46.22992644, 46.36295892, 46.49599139, 46.62902386,\n", " 46.76205633, 46.8950888 , 47.02812128, 47.16115375, 47.29418622,\n", " 47.42721869, 47.56025116, 47.69328363, 47.82631611, 47.95934858,\n", " 48.09238105, 48.22541352, 48.35844599, 48.49147847, 48.62451094,\n", " 48.75754341, 48.89057588, 49.02360835, 49.15664082, 49.2896733 ,\n", " 49.42270577, 49.55573824, 49.68877071, 49.82180318, 49.95483566,\n", " 50.08786813, 50.2209006 , 50.35393307, 50.48696554, 50.61999801,\n", " 50.75303049, 50.88606296, 51.01909543, 51.1521279 , 51.28516037,\n", " 51.41819285, 51.55122532, 51.68425779, 51.81729026, 51.95032273,\n", " 52.0833552 , 52.21638768, 52.34942015, 52.48245262, 52.61548509,\n", " 52.74851756, 52.88155004, 53.01458251, 53.14761498, 53.28064745,\n", " 53.41367992, 53.54671239, 53.67974487, 53.81277734, 53.94580981,\n", " 54.07884228, 54.21187475, 54.34490723, 54.4779397 , 54.61097217,\n", " 54.74400464, 54.87703711, 55.01006958, 55.14310206, 55.27613453,\n", " 55.409167 , 55.54219947, 55.67523194, 55.80826442, 55.94129689,\n", " 56.07432936, 56.20736183, 56.3403943 , 56.47342677, 56.60645925,\n", " 56.73949172, 56.87252419, 57.00555666, 57.13858913, 57.27162161,\n", " 57.40465408, 57.53768655, 57.67071902, 57.80375149, 57.93678396,\n", " 58.06981644, 58.20284891, 58.33588138, 58.46891385, 58.60194632,\n", " 58.7349788 , 58.86801127, 59.00104374, 59.13407621, 59.26710868,\n", " 59.40014115, 59.53317363, 59.6662061 , 59.79923857, 59.93227104,\n", " 60.06530351, 60.19833599, 60.33136846, 60.46440093, 60.5974334 ,\n", " 60.73046587, 60.86349834, 60.99653082, 61.12956329, 61.26259576,\n", " 61.39562823, 61.5286607 , 61.66169318, 61.79472565, 61.92775812,\n", " 62.06079059, 62.19382306, 62.32685554, 62.45988801, 62.59292048,\n", " 62.72595295, 62.85898542, 62.99201789, 63.12505037, 63.25808284,\n", " 63.39111531, 63.52414778, 63.65718025, 63.79021273, 63.9232452 ,\n", " 64.05627767, 64.18931014, 64.32234261, 64.45537508, 64.58840756,\n", " 64.72144003, 64.8544725 , 64.98750497, 65.12053744, 65.25356992,\n", " 65.38660239, 65.51963486, 65.65266733, 65.7856998 , 65.91873227,\n", " 66.05176475, 66.18479722, 66.31782969, 66.45086216, 66.58389463,\n", " 66.71692711, 66.84995958, 66.98299205, 67.11602452, 67.24905699])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prev_model" ] }, { "cell_type": "code", "execution_count": 19, "id": "34dd54ad-c525-46e7-8dbf-8eecb10a2ec9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.06012024, 0.12024048, 0.18036072, 0.24048096,\n", " 0.3006012 , 0.36072144, 0.42084168, 0.48096192, 0.54108216,\n", " 0.6012024 , 0.66132265, 0.72144289, 0.78156313, 0.84168337,\n", " 0.90180361, 0.96192385, 1.02204409, 1.08216433, 1.14228457,\n", " 1.20240481, 1.26252505, 1.32264529, 1.38276553, 1.44288577,\n", " 1.50300601, 1.56312625, 1.62324649, 1.68336673, 1.74348697,\n", " 1.80360721, 1.86372745, 1.9238477 , 1.98396794, 2.04408818,\n", " 2.10420842, 2.16432866, 2.2244489 , 2.28456914, 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28.13627255, 28.19639279,\n", " 28.25651303, 28.31663327, 28.37675351, 28.43687375, 28.49699399,\n", " 28.55711423, 28.61723447, 28.67735471, 28.73747495, 28.79759519,\n", " 28.85771543, 28.91783567, 28.97795591, 29.03807615, 29.09819639,\n", " 29.15831663, 29.21843687, 29.27855711, 29.33867735, 29.3987976 ,\n", " 29.45891784, 29.51903808, 29.57915832, 29.63927856, 29.6993988 ,\n", " 29.75951904, 29.81963928, 29.87975952, 29.93987976, 30. ])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_values" ] }, { "cell_type": "code", "execution_count": 20, "id": "4ed69461-befc-47c5-a01a-8fc171a33e0a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.86585355, 0.99888602, 1.1319185 , 1.26495097, 1.39798344,\n", " 1.53101591, 1.66404838, 1.79708085, 1.93011333, 2.0631458 ,\n", " 2.19617827, 2.32921074, 2.46224321, 2.59527569, 2.72830816,\n", " 2.86134063, 2.9943731 , 3.12740557, 3.26043804, 3.39347052,\n", " 3.52650299, 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41.44075746, 41.57378993, 41.7068224 , 41.83985487, 41.97288735,\n", " 42.10591982, 42.23895229, 42.37198476, 42.50501723, 42.6380497 ,\n", " 42.77108218, 42.90411465, 43.03714712, 43.17017959, 43.30321206,\n", " 43.43624454, 43.56927701, 43.70230948, 43.83534195, 43.96837442,\n", " 44.10140689, 44.23443937, 44.36747184, 44.50050431, 44.63353678,\n", " 44.76656925, 44.89960173, 45.0326342 , 45.16566667, 45.29869914,\n", " 45.43173161, 45.56476408, 45.69779656, 45.83082903, 45.9638615 ,\n", " 46.09689397, 46.22992644, 46.36295892, 46.49599139, 46.62902386,\n", " 46.76205633, 46.8950888 , 47.02812128, 47.16115375, 47.29418622,\n", " 47.42721869, 47.56025116, 47.69328363, 47.82631611, 47.95934858,\n", " 48.09238105, 48.22541352, 48.35844599, 48.49147847, 48.62451094,\n", " 48.75754341, 48.89057588, 49.02360835, 49.15664082, 49.2896733 ,\n", " 49.42270577, 49.55573824, 49.68877071, 49.82180318, 49.95483566,\n", " 50.08786813, 50.2209006 , 50.35393307, 50.48696554, 50.61999801,\n", " 50.75303049, 50.88606296, 51.01909543, 51.1521279 , 51.28516037,\n", " 51.41819285, 51.55122532, 51.68425779, 51.81729026, 51.95032273,\n", " 52.0833552 , 52.21638768, 52.34942015, 52.48245262, 52.61548509,\n", " 52.74851756, 52.88155004, 53.01458251, 53.14761498, 53.28064745,\n", " 53.41367992, 53.54671239, 53.67974487, 53.81277734, 53.94580981,\n", " 54.07884228, 54.21187475, 54.34490723, 54.4779397 , 54.61097217,\n", " 54.74400464, 54.87703711, 55.01006958, 55.14310206, 55.27613453,\n", " 55.409167 , 55.54219947, 55.67523194, 55.80826442, 55.94129689,\n", " 56.07432936, 56.20736183, 56.3403943 , 56.47342677, 56.60645925,\n", " 56.73949172, 56.87252419, 57.00555666, 57.13858913, 57.27162161,\n", " 57.40465408, 57.53768655, 57.67071902, 57.80375149, 57.93678396,\n", " 58.06981644, 58.20284891, 58.33588138, 58.46891385, 58.60194632,\n", " 58.7349788 , 58.86801127, 59.00104374, 59.13407621, 59.26710868,\n", " 59.40014115, 59.53317363, 59.6662061 , 59.79923857, 59.93227104,\n", " 60.06530351, 60.19833599, 60.33136846, 60.46440093, 60.5974334 ,\n", " 60.73046587, 60.86349834, 60.99653082, 61.12956329, 61.26259576,\n", " 61.39562823, 61.5286607 , 61.66169318, 61.79472565, 61.92775812,\n", " 62.06079059, 62.19382306, 62.32685554, 62.45988801, 62.59292048,\n", " 62.72595295, 62.85898542, 62.99201789, 63.12505037, 63.25808284,\n", " 63.39111531, 63.52414778, 63.65718025, 63.79021273, 63.9232452 ,\n", " 64.05627767, 64.18931014, 64.32234261, 64.45537508, 64.58840756,\n", " 64.72144003, 64.8544725 , 64.98750497, 65.12053744, 65.25356992,\n", " 65.38660239, 65.51963486, 65.65266733, 65.7856998 , 65.91873227,\n", " 66.05176475, 66.18479722, 66.31782969, 66.45086216, 66.58389463,\n", " 66.71692711, 66.84995958, 66.98299205, 67.11602452, 67.24905699])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prev_model" ] }, { "cell_type": "code", "execution_count": 21, "id": "a513262d-d123-48a0-872c-86148461f753", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.0774713540954743" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.exp((log_like_new + log_prior_new) - (log_like + log_prior)) \n", "log_prior_new" ] }, { "cell_type": "code", "execution_count": 22, "id": "3f6d8206-789c-4b99-b8f1-1d1c0e6f0b9c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9393166007525864" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prop_b0" ] }, { "cell_type": "code", "execution_count": 23, "id": "4add366e-ed8a-4597-8b3f-3cb388f2d704", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([21.40059848, 52.09252131])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prop_b1*x+prop_b0 " ] }, { "cell_type": "code", "execution_count": 24, "id": "69f7c62c-c082-40a9-982b-d563e43c25d3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1.66298989, -2.14098245])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.norm.logpdf(y, loc=prev_y_hat,scale=prev_sigma)" ] }, { "cell_type": "code", "execution_count": 25, "id": "1585e3ec-adff-4e7e-b1aa-d60d3a40de0e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.8039723325663415" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prev_like_lsum" ] }, { "cell_type": "code", "execution_count": 26, "id": "506d20c4-ab91-49d7-9b4b-9238fcaef388", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-6.145788383779414" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prior_density_sum_log(thetas[-5,:],prior2)" ] }, { "cell_type": "code", "execution_count": 27, "id": "15116dcb-1eff-4583-8980-7a2e56cdd444", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2.12672831, 0.94720754, 1.91168969])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "thetas[-3,:]" ] }, { "cell_type": "code", "execution_count": null, "id": "6c4f56c9-6b66-4239-acfb-6df3e6c7ebab", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 28, "id": "572339b5-7a76-43b3-8750-d6038a4bfb7c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.77770241, 0.23754122, 0.82427853],\n", " [ 1.66035659, -0.1392681 , 1.07730594],\n", " [ 2.15265314, 0.45220619, 0.65915509],\n", " [ 2.15773382, 0.31575772, 1.09509353],\n", " [ 2.21068667, 0.37556535, 1.45531294],\n", " [ 2.27010684, 0.73723954, 1.46119722],\n", " [ 2.12710622, 0.94737138, 0.95044608],\n", " [ 2.1121221 , 0.63820646, 1.10134416],\n", " [ 2.10033924, 0.90256777, 1.43033308],\n", " [ 2.12016611, 1.04346074, 1.73340839],\n", " [ 2.18145441, 1.10605144, 1.81511031],\n", " [ 2.20292526, 0.82209306, 2.27144143],\n", " [ 2.02040228, 1.32494335, 2.34443427],\n", " [ 2.23300823, 1.41713588, 2.01850288],\n", " [ 2.18723227, 1.35682367, 1.74228125],\n", " [ 2.20226296, 1.0752467 , 1.71050241],\n", " [ 2.10931103, 1.36966993, 1.97690895],\n", " [ 2.13945961, 1.08579741, 2.52831003],\n", " [ 2.11491617, 1.29848683, 2.62414267],\n", " [ 2.15976596, 0.60617536, 2.89463413],\n", " [ 2.2405659 , 1.2917247 , 2.20351709],\n", " [ 2.2492796 , 0.95151866, 2.22413621],\n", " [ 2.05396749, 1.27653568, 2.0300448 ],\n", " [ 2.12386928, 0.81573134, 2.11757561],\n", " [ 2.28298428, 1.08158056, 2.91929073],\n", " [ 2.26960334, 1.15530475, 3.12023311],\n", " [ 2.18441923, 1.26033204, 3.27881308],\n", " [ 2.1242187 , 1.63552327, 2.45198837],\n", " [ 2.24192475, 1.29092152, 2.10232355],\n", " [ 2.04589524, 1.09447759, 2.6427219 ],\n", " [ 2.19297582, 1.32342304, 2.15218205],\n", " [ 2.07174196, 1.14703429, 2.28047509],\n", " [ 2.2504484 , 0.8287201 , 2.05069094],\n", " [ 2.07009892, 1.36769888, 2.17028928],\n", " [ 2.17511003, 1.41918569, 2.37560644],\n", " [ 2.28633027, 1.45336795, 2.83011649],\n", " [ 2.11426844, 0.65463617, 2.47695309],\n", " [ 2.13301585, 0.69562184, 2.04104528],\n", " [ 2.12932659, 0.68159341, 2.16964856],\n", " [ 2.11498453, 0.77712891, 2.1497046 ],\n", " [ 2.05208863, 1.54318841, 2.40817223],\n", " [ 2.10839225, 1.31116892, 2.52962724],\n", " [ 2.14244308, 1.50367003, 2.64341469],\n", " [ 2.05308583, 1.29108862, 2.2225465 ],\n", " [ 2.16628673, 1.11423933, 2.66859231],\n", " [ 2.09260512, 1.56469942, 2.70162015],\n", " [ 2.05570245, 1.16859383, 2.45807555],\n", " [ 2.31608178, 0.88773532, 3.30324459],\n", " [ 2.35993466, 0.98966008, 3.16437677],\n", " [ 2.28845303, 0.94207858, 2.74931026],\n", " [ 2.06325867, 1.68454502, 2.91244729],\n", " [ 2.26528427, 1.36511384, 2.35820819],\n", " [ 2.13956529, 1.53398376, 2.51594432],\n", " [ 2.08380784, 1.39053107, 2.4129103 ],\n", " [ 2.09407832, 1.110194 , 1.82016926],\n", " [ 2.13706098, 1.09485189, 1.52798317],\n", " [ 2.20298802, 1.47351201, 1.63771752],\n", " [ 2.05925411, 1.30745842, 1.49671968],\n", " [ 2.18064485, 1.42200489, 2.57186253],\n", " [ 2.12156113, 1.3616697 , 2.16310219],\n", " [ 2.04501727, 1.40579825, 2.04345413],\n", " [ 2.11385859, 1.55045268, 2.57755293],\n", " [ 2.16342028, 1.1625967 , 2.82616442],\n", " [ 2.19394291, 1.06748622, 2.28620621],\n", " [ 2.1437199 , 1.24760157, 2.33323606],\n", " [ 2.22204745, 0.86849599, 1.95271491],\n", " [ 2.24810651, 0.79424325, 2.3223986 ],\n", " [ 2.00031004, 0.84057923, 2.59302971],\n", " [ 2.26171621, 1.52980741, 3.03099891],\n", " [ 1.97680598, 1.52625801, 2.84002065],\n", " [ 2.15554476, 1.64096105, 2.57837915],\n", " [ 2.24952841, 1.23989507, 3.06528898],\n", " [ 2.15873534, 1.31210674, 3.18217689],\n", " [ 2.13859342, 0.83538255, 2.398414 ],\n", " [ 2.11462107, 1.22897677, 2.81824743],\n", " [ 2.12445702, 1.20344616, 2.61188975],\n", " [ 2.12151194, 1.40059048, 2.61135147],\n", " [ 2.04777641, 1.19772205, 3.11804274],\n", " [ 2.28782207, 0.58387129, 2.43590968],\n", " [ 2.31717974, 0.63879887, 2.34951121],\n", " [ 2.35385409, 0.94151782, 2.25971497],\n", " [ 2.17728243, 0.57140585, 2.26310643],\n", " [ 2.05349017, 0.74961305, 2.76094086],\n", " [ 1.98287128, 1.07906507, 2.72693396],\n", " [ 2.22658986, 1.39821779, 2.89232148],\n", " [ 2.03925702, 1.09687424, 2.98119717],\n", " [ 2.09826757, 0.96967048, 3.28265309],\n", " [ 2.26123458, 1.09698812, 2.48919359],\n", " [ 2.11385049, 1.07564888, 2.67247244],\n", " [ 2.18962263, 1.24350628, 2.1179613 ],\n", " [ 2.29025678, 1.28418291, 2.63398229],\n", " [ 2.20599315, 1.20656101, 2.47475381],\n", " [ 2.1283404 , 1.23235243, 2.63355928],\n", " [ 2.09301896, 1.02319817, 1.94664086],\n", " [ 2.10798809, 0.86522026, 1.94354539],\n", " [ 2.15317179, 0.57896231, 1.91999707],\n", " [ 2.20018576, 0.31795346, 2.06550134],\n", " [ 2.08290301, 1.26683318, 2.02012028],\n", " [ 2.12672831, 0.94720754, 1.91168969],\n", " [ 2.21277345, 0.86585355, 2.10077043],\n", " [ 2.04612819, 0.9393166 , 1.90265268]])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "thetas" ] }, { "cell_type": "code", "execution_count": 29, "id": "63cf6324-978e-45ba-9e19-10ec32ede7de", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.12931109110098168 0.9116509033852626 0.39084704230201245\n" ] } ], "source": [ "prop_b1_den = stats.norm.pdf(prop_b1, prior2[0][0], prior2[0][1]); prop_b1_lden = np.log(prop_b1_den)\n", "prop_b0_den = stats.norm.pdf(prop_b0, prior2[1][0], prior2[1][1]); prop_b0_lden = np.log(prop_b0_den)\n", "prop_sigma_den = stats.norm.pdf(prop_sigma, prior2[2][0], prior2[2][1]); prop_sigma_lden = np.log(prop_sigma_den)\n", "print(prop_b1_den,prop_b0_den,prop_sigma_den)" ] }, { "cell_type": "code", "execution_count": 30, "id": "33d10756-0563-437e-8d85-ca1fefebee22", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.0774713540954743" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean = np.array([prior2[0,0],prior2[1,0],prior2[2,0]]); cov = np.zeros([3,3]); cov[0,0] = prior2[0,1]; cov[1,1] = prior2[1,1]; cov[2,2] = prior2[2,1]\n", "sum_log = np.log(stats.norm.pdf(theta_new[0], prior2[0][0], prior2[0][1])) + np.log(stats.norm.pdf(theta_new[1], prior2[1][0], prior2[1][1])) + np.log(stats.norm.pdf(theta_new[2], prior2[2][0], prior2[2][1]))\n", "sum_log\n", "# stats.multivariate_normal.logpdf(theta_new,mean=mean,cov=cov,allow_singular=True)\n" ] }, { "cell_type": "code", "execution_count": null, "id": "1cb1099f-a88c-4c86-92e0-d20703effc78", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 31, "id": "66d10b26-db88-4315-92bf-307d72c340e2", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'prior_density' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[31], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mprior_density\u001b[49m(theta_new,prior2)\n", "\u001b[1;31mNameError\u001b[0m: name 'prior_density' is not defined" ] } ], "source": [ "prior_density(theta_new,prior2)" ] }, { "cell_type": "code", "execution_count": null, "id": "8b134a0d-4a8e-4f05-a6a2-017b817dd05e", "metadata": {}, "outputs": [], "source": [ "prop_b1,prop_b0,prop_sigma" ] }, { "cell_type": "code", "execution_count": null, "id": "ad103433-e62b-4e18-99ec-16dc5ed5f5f4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "7c586efb-6577-473f-9f39-01e4906ee52e", "metadata": {}, "outputs": [], "source": [ "theta_new" ] }, { "cell_type": "code", "execution_count": null, "id": "3cf0f320-312b-4010-8a90-219d3921887c", "metadata": {}, "outputs": [], "source": [ "prior2" ] }, { "cell_type": "markdown", "id": "c9db45c3", "metadata": {}, "source": [ "#### Comments\n", "\n", "This was an interactive demonstration of Bayesian Linear Regression with McMC Metropolis-Hastings Sampling.\n", "\n", "I have many other demonstrations on data analytics and machine learning, e.g. on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n", " \n", "I hope this was helpful,\n", "\n", "*Michael*\n", "\n", "#### The Author:\n", "\n", "### Michael J Pyrcz, Professor, The University of Texas at Austin \n", "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n", "\n", "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n", "\n", "For more about Michael check out these links:\n", "\n", "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig) | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n", "\n", "#### Want to Work Together?\n", "\n", "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n", "\n", "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n", "\n", "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n", "\n", "* I can be reached at mpyrcz@austin.utexas.edu.\n", "\n", "I'm always happy to discuss,\n", "\n", "*Michael*\n", "\n", "Michael Pyrcz, Ph.D., P.Eng. Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n", "\n", "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig) | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.4" } }, "nbformat": 4, "nbformat_minor": 5 }