Add files via upload

Interactive_Bayesian_Updating.ipynb

@@ -102,7 +102,7 @@
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+   "execution_count": 1,
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       "text/plain": [
-       "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 640x480 with 1 Axes>', 'i…"
+       "Output()"
       ]
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      "metadata": {},
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       "text/plain": [
-       "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 640x480 with 2 Axes>', 'i…"
+       "Output()"
       ]
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      "metadata": {},
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    ]
   },
   {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Exploration to Appraisal Example\n",
+    "\n",
+    "Let's modify the above dashboard to demonstrate a powerful solution for a commonly encounter problem in resource exploration.\n",
+    "\n",
+    "* prior distribution - from an exploration campaign, usually including 2D seismic / remote sensing data along with analog mature resources (using statistical from similar and better sampled settings)\n",
+    "\n",
+    "* likelihood distribution - from an appraisal campaign, usually including sparse wells/ drill holes (large spacings) and 3D seismic / remote sensing\n",
+    "\n",
+    "Now we can apply Bayesian updating to calculate a,\n",
+    "\n",
+    "* posterior distribution - updating the exploration prior distribution with the appraisal likelihood distribution.\n",
+    "\n",
+    "Let's take a mining example, i.e., a gold mine. For example, the estimated proven and probablity reserves at Bingham Canyon Mine, Utah, USA is 2.09 million onces. Let's use this to guide our units and ranges. "
+   ]
+  },
+  {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "l = widgets.Text(value='                                 Gold Resources Bayesian Updating Demo, Michael Pyrcz, Professor, The University of Texas at Austin',\n",
+    "        layout=Layout(width='900px', height='30px'))\n",
+    "# P_happening_label = widgets.Text(value='Probability of Happening',layout=Layout(width='50px',height='30px',line-size='0 px'))\n",
+    "mu_prior = widgets.FloatSlider(min=0.0, max = 2.0, value=0.5, step = 0.1, description = r'$\\mu_{Au,prior}$',orientation='horizontal', \n",
+    "        style = {'description_width':'initial'},layout=Layout(width='400px',height='30px'),continuous_update=False,readout_format='.3f')\n",
+    "sigma_prior = widgets.FloatSlider(min = 0, max = 1.0, value=0.1, step = 0.02, description = r'$\\sigma_{Au,prior}$',orientation='horizontal', \n",
+    "        style = {'description_width': 'initial'},layout=Layout(width='400px', height='30px'),continuous_update=False,readout_format='.3f')\n",
+    "\n",
+    "mu_like = widgets.FloatSlider(min=0.0, max = 2.0, value=1.0, step = 0.1, description = r'$\\mu_{Au,like}$',orientation='horizontal', \n",
+    "        style = {'description_width':'initial'},layout=Layout(width='400px',height='30px'),continuous_update=False,readout_format='.3f')\n",
+    "sigma_like = widgets.FloatSlider(min=0, max = 1.0, value=0.1, step = 0.02, description = r'$\\sigma_{Au,like}$',orientation='horizontal', \n",
+    "        style = {'description_width': 'initial'},layout=Layout(width='400px', height='30px'),continuous_update=False,readout_format='.3f')\n",
+    "\n",
+    "ui_prior = widgets.VBox([mu_prior,sigma_prior],)\n",
+    "ui_like = widgets.VBox([mu_like,sigma_like],)\n",
+    "\n",
+    "ui_summary3 = widgets.HBox([ui_prior,ui_like,],)\n",
+    "ui2_summary3 = widgets.VBox([l,ui_summary3],)\n",
+    "\n",
+    "def run_plot_summary3(mu_prior,sigma_prior,mu_like,sigma_like):\n",
+    "    sigma2_prior = sigma_prior*sigma_prior; sigma2_like = sigma_like*sigma_like\n",
+    "    mu_post = (mu_like * sigma2_prior + mu_prior * sigma2_like)/((1 - sigma2_like)*(sigma2_prior - 1) + 1)\n",
+    "    sigma2_post = (sigma2_prior * sigma2_like)/((1 - sigma2_like)*(sigma2_prior - 1) + 1)\n",
+    "    \n",
+    "    values = np.linspace(-3,3,1000)\n",
+    "    PDF_prior = st.norm.pdf(values,loc = mu_prior,scale = math.sqrt(sigma2_prior))\n",
+    "    PDF_like = st.norm.pdf(values,loc = mu_like,scale = math.sqrt(sigma2_like))\n",
+    "    PDF_post = st.norm.pdf(values,loc = mu_post,scale = math.sqrt(sigma2_post))\n",
+    "    \n",
+    "    pvalues = np.linspace(0.001,0.999,1000)                   # CDF\n",
+    "    Perc_prior = st.norm.ppf(pvalues,loc = mu_prior,scale = math.sqrt(sigma2_prior))\n",
+    "    Perc_like = st.norm.ppf(pvalues,loc = mu_like,scale = math.sqrt(sigma2_like))\n",
+    "    Perc_post = st.norm.ppf(pvalues,loc = mu_post,scale = math.sqrt(sigma2_post))\n",
+    "    \n",
+    "    plt.subplot(121)\n",
+    "    plt.plot(values,PDF_prior,c='green',label='Prior, Exploration',zorder=10); plt.fill_between(values,PDF_prior,color='green',alpha=0.05,zorder=1)\n",
+    "    plt.plot(values,PDF_like,c='red',label='Likelihood, New Appraisal Data',zorder=10); plt.fill_between(values,PDF_like,color='red',alpha=0.05,zorder=1) \n",
+    "    plt.plot(values,PDF_post,c='black',label='Posterior, Exploration + New Appraisal Data',zorder=10); plt.fill_between(values,PDF_post,color='black',alpha=0.05,zorder=1)\n",
+    "    \n",
+    "    plt.xlabel('Gold Reserves (million ounces)'); plt.ylabel('Density'); plt.title('Gold Mine Reserves, Bayesian Updating Gaussian, PDFs')\n",
+    "    plt.xlim([0.0,2.0]); plt.ylim(0,10); add_grid(); plt.legend(loc = 'upper left')\n",
+    "    \n",
+    "    plt.subplot(122)\n",
+    "    plt.plot(Perc_prior,pvalues,c='green',label='Prior, Exploration')\n",
+    "    plt.plot(Perc_like,pvalues,c='red',label='Likelihood, New Appraisal Data')\n",
+    "    plt.plot(Perc_post,pvalues,c='black',label='Posterior, Exploration + New Appraisal Data')\n",
+    "    \n",
+    "    plt.xlabel('Gold Reserves (million ounces)'); plt.ylabel('Cumulative Probability'); plt.title('Gold Mine Reserves, Bayesian Updating Gaussian, CDFs')\n",
+    "    plt.xlim([0.,2.0]); plt.ylim([0,1]); add_grid(); plt.legend(loc = 'lower right')\n",
+    "    \n",
+    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=2., top=1.0, wspace=0.2, hspace=0.1); plt.show()\n",
+    "        \n",
+    "interactive_plot_summary3 = widgets.interactive_output(run_plot_summary3, \n",
+    "    {'mu_prior':mu_prior,'sigma_prior':sigma_prior,'mu_like':mu_like,'sigma_like':sigma_like})\n",
+    "interactive_plot_summary3.clear_output(wait = True) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
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-       "model_id": "b4f1ca08d731472986942298dc82a0a1",
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        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "VBox(children=(Text(value='                                                      Bayesian Updating Demo, Micha…"
+       "VBox(children=(Text(value='                                 Gold Resources Bayesian Updating Demo, Michael Pyr…"
       ]
      },
      "metadata": {},
@@ -700,12 +782,12 @@
     {
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        "version_major": 2,
        "version_minor": 0
       },
       "text/plain": [
-       "Output(outputs=({'output_type': 'display_data', 'data': {'text/plain': '<Figure size 640x480 with 2 Axes>', 'i…"
+       "Output()"
       ]
      },
      "metadata": {},
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     }
    ],
    "source": [
-    "display(ui2_summary2, interactive_plot_summary2)                           # display the interactive plot"
+    "display(ui2_summary3, interactive_plot_summary3)                           # display the interactive plot"
    ]
   },
   {
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    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.4"
+   "version": "3.13.9"
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