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  69. State Space Models: A Modern Approach
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  91. Hidden Markov Models
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  96. Linear Gaussian SSMs
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  101. Nonlinear Gaussian SSMs
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  106. States estimation (inference)
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  133. HMM smoothing (forwards-backwards algorithm)
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  138. Viterbi algorithm
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  143. Parallel HMM smoothing
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  148. Forwards-filtering backwards-sampling algorithm
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  155. Linear-Gaussian SSMs
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  165. Kalman filtering
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  170. Kalman (RTS) smoother
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  175. Parallel Kalman Smoother
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  179. <a class="reference internal" href="../lgssm/kalman_sampling.html">
  180. Forwards-filtering backwards sampling
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  197. Extended Kalman filtering
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  200. <li class="toctree-l2">
  201. <a class="reference internal" href="../extended/extended_smoother.html">
  202. Extended Kalman smoother
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  206. <a class="reference internal" href="../extended/extended_parallel.html">
  207. Parallel extended Kalman smoothing
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  229. Unscented smoothing
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  236. Quadrature and cubature methods
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  240. <a class="reference internal" href="../postlin/postlin_index.html">
  241. Posterior linearization
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  245. <a class="reference internal" href="../adf/adf_index.html">
  246. Assumed Density Filtering
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  251. Variational inference
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  256. Particle filtering
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  261. Sequential Monte Carlo
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  266. Offline parameter estimation (learning)
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  271. Multi-target tracking
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  276. Data assimilation using Ensemble Kalman filter
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  281. Bayesian non-parametric SSMs
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  286. Changepoint detection
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  291. Timeseries forecasting
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  296. Markovian Gaussian processes
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  301. Differential equations and SSMs
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  306. Optimal control
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  379. <h1>Hidden Markov Models</h1>
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  387. <div class="tex2jax_ignore mathjax_ignore section" id="hidden-markov-models">
  388. <span id="ch-hmm"></span><h1>Hidden Markov Models<a class="headerlink" href="#hidden-markov-models" title="Permalink to this headline">¶</a></h1>
  389. <p>This chapter discusses Hidden Markov Models (HMMs), which are state space models
  390. in which the latent state <span class="math notranslate nohighlight">\(\hidden_t \in \{1,\ldots,\nstates\}\)</span> is discrete.</p>
  391. <div class="toctree-wrapper compound">
  392. <ul>
  393. <li class="toctree-l1"><a class="reference internal" href="hmm_filter.html">HMM filtering (forwards algorithm)</a></li>
  394. <li class="toctree-l1"><a class="reference internal" href="hmm_smoother.html">HMM smoothing (forwards-backwards algorithm)</a></li>
  395. <li class="toctree-l1"><a class="reference internal" href="hmm_viterbi.html">Viterbi algorithm</a></li>
  396. <li class="toctree-l1"><a class="reference internal" href="hmm_parallel.html">Parallel HMM smoothing</a></li>
  397. <li class="toctree-l1"><a class="reference internal" href="hmm_sampling.html">Forwards-filtering backwards-sampling algorithm</a></li>
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