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                <h1>State Space Models: A Modern Approach</h1>
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  <div class="tex2jax_ignore mathjax_ignore section" id="state-space-models-a-modern-approach">
<h1>State Space Models: A Modern Approach<a class="headerlink" href="#state-space-models-a-modern-approach" title="Permalink to this headline">¶</a></h1>
<p>This is an interactive textbook on state space models (SSM)
using the <a class="reference external" href="https://github.com/google/jax">JAX Python library</a>.
Some of the content is covered in other books
such as  <span id="id1">[<a class="reference internal" href="bib.html#id18" title="Simo Sarkka. Bayesian Filtering and Smoothing. Cambridge University Press, 2013. URL: https://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf.">Sar13</a>]</span> and <span id="id2">[<a class="reference internal" href="bib.html#id17" title="K. P. Murphy. Probabilistic Machine Learning: Advanced Topics. MIT Press, 2023.">Mur23</a>]</span>.
However, we go into more detail, and focus on how to efficiently
implement the various algorithms in a “modern” computing environment,
exploiting recent progress
in automatic differentiation and parallel computing.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="chapters/ssm/ssm_index.html">State Space Models</a><ul>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/ssm_intro.html">What are State Space Models?</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/hmm.html">Hidden Markov Models</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/lds.html">Linear Gaussian SSMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/nlds.html">Nonlinear Gaussian SSMs</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/inference.html">States estimation (inference)</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/ssm/learning.html">Parameter estimation (learning)</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="chapters/hmm/hmm_index.html">Hidden Markov Models</a><ul>
<li class="toctree-l2"><a class="reference internal" href="chapters/hmm/hmm_filter.html">HMM filtering (forwards algorithm)</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/hmm/hmm_smoother.html">HMM smoothing (forwards-backwards algorithm)</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/hmm/hmm_viterbi.html">Viterbi algorithm</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/hmm/hmm_parallel.html">Parallel HMM  smoothing</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/hmm/hmm_sampling.html">Forwards-filtering backwards-sampling algorithm</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="chapters/lgssm/lgssm_index.html">Linear-Gaussian SSMs</a><ul>
<li class="toctree-l2"><a class="reference internal" href="chapters/lgssm/kalman_filter.html">Kalman filtering</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/lgssm/kalman_smoother.html">Kalman (RTS) smoother</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/lgssm/kalman_parallel.html">Parallel Kalman Smoother</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/lgssm/kalman_sampling.html">Forwards-filtering backwards sampling</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="chapters/extended/extended_index.html">Extended (linearized) methods</a><ul>
<li class="toctree-l2"><a class="reference internal" href="chapters/extended/extended_filter.html">Extended Kalman filtering</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/extended/extended_smoother.html">Extended Kalman smoother</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/extended/extended_parallel.html">Parallel extended Kalman smoothing</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="chapters/unscented/unscented_index.html">Unscented methods</a><ul>
<li class="toctree-l2"><a class="reference internal" href="chapters/unscented/unscented_filter.html">Unscented filtering</a></li>
<li class="toctree-l2"><a class="reference internal" href="chapters/unscented/unscented_smoother.html">Unscented smoothing</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="chapters/quadrature/quadrature_index.html">Quadrature and cubature methods</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/postlin/postlin_index.html">Posterior linearization</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/adf/adf_index.html">Assumed Density Filtering</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/vi/vi_index.html">Variational inference</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/pf/pf_index.html">Particle filtering</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/smc/smc_index.html">Sequential Monte Carlo</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/learning/learning_index.html">Offline parameter estimation (learning)</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/tracking/tracking_index.html">Multi-target tracking</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/ensemble/ensemble_index.html">Data assimilation using Ensemble Kalman filter</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/bnp/bnp_index.html">Bayesian non-parametric SSMs</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/changepoint/changepoint_index.html">Changepoint detection</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/timeseries/timeseries_index.html">Timeseries forecasting</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/gp/gp_index.html">Markovian Gaussian processes</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/ode/ode_index.html">Differential equations and SSMs</a></li>
<li class="toctree-l1"><a class="reference internal" href="chapters/control/control_index.html">Optimal control</a></li>
<li class="toctree-l1"><a class="reference internal" href="bib.html">Bibliography</a></li>
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