bnp_index.html 18 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543
  1. <!DOCTYPE html>
  2. <html>
  3. <head>
  4. <meta charset="utf-8" />
  5. <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  6. <title>Bayesian non-parametric SSMs &#8212; State Space Models: A Modern Approach</title>
  7. <link href="../../_static/css/theme.css" rel="stylesheet">
  8. <link href="../../_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
  9. <link rel="stylesheet"
  10. href="../../_static/vendor/fontawesome/5.13.0/css/all.min.css">
  11. <link rel="preload" as="font" type="font/woff2" crossorigin
  12. href="../../_static/vendor/fontawesome/5.13.0/webfonts/fa-solid-900.woff2">
  13. <link rel="preload" as="font" type="font/woff2" crossorigin
  14. href="../../_static/vendor/fontawesome/5.13.0/webfonts/fa-brands-400.woff2">
  15. <link rel="stylesheet" type="text/css" href="../../_static/pygments.css" />
  16. <link rel="stylesheet" type="text/css" href="../../_static/sphinx-book-theme.css?digest=c3fdc42140077d1ad13ad2f1588a4309" />
  17. <link rel="stylesheet" type="text/css" href="../../_static/togglebutton.css" />
  18. <link rel="stylesheet" type="text/css" href="../../_static/copybutton.css" />
  19. <link rel="stylesheet" type="text/css" href="../../_static/mystnb.css" />
  20. <link rel="stylesheet" type="text/css" href="../../_static/sphinx-thebe.css" />
  21. <link rel="stylesheet" type="text/css" href="../../_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css" />
  22. <link rel="stylesheet" type="text/css" href="../../_static/panels-variables.06eb56fa6e07937060861dad626602ad.css" />
  23. <link rel="preload" as="script" href="../../_static/js/index.be7d3bbb2ef33a8344ce.js">
  24. <script data-url_root="../../" id="documentation_options" src="../../_static/documentation_options.js"></script>
  25. <script src="../../_static/jquery.js"></script>
  26. <script src="../../_static/underscore.js"></script>
  27. <script src="../../_static/doctools.js"></script>
  28. <script src="../../_static/clipboard.min.js"></script>
  29. <script src="../../_static/copybutton.js"></script>
  30. <script>let toggleHintShow = 'Click to show';</script>
  31. <script>let toggleHintHide = 'Click to hide';</script>
  32. <script>let toggleOpenOnPrint = 'true';</script>
  33. <script src="../../_static/togglebutton.js"></script>
  34. <script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
  35. <script src="../../_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
  36. <script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"
  37. const thebe_selector = ".thebe,.cell"
  38. const thebe_selector_input = "pre"
  39. const thebe_selector_output = ".output, .cell_output"
  40. </script>
  41. <script async="async" src="../../_static/sphinx-thebe.js"></script>
  42. <link rel="index" title="Index" href="../../genindex.html" />
  43. <link rel="search" title="Search" href="../../search.html" />
  44. <link rel="next" title="Changepoint detection" href="../changepoint/changepoint_index.html" />
  45. <link rel="prev" title="Data assimilation using Ensemble Kalman filter" href="../ensemble/ensemble_index.html" />
  46. <meta name="viewport" content="width=device-width, initial-scale=1" />
  47. <meta name="docsearch:language" content="None">
  48. <!-- Google Analytics -->
  49. </head>
  50. <body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
  51. <div class="container-fluid" id="banner"></div>
  52. <div class="container-xl">
  53. <div class="row">
  54. <div class="col-12 col-md-3 bd-sidebar site-navigation show" id="site-navigation">
  55. <div class="navbar-brand-box">
  56. <a class="navbar-brand text-wrap" href="../../index.html">
  57. <h1 class="site-logo" id="site-title">State Space Models: A Modern Approach</h1>
  58. </a>
  59. </div><form class="bd-search d-flex align-items-center" action="../../search.html" method="get">
  60. <i class="icon fas fa-search"></i>
  61. <input type="search" class="form-control" name="q" id="search-input" placeholder="Search this book..." aria-label="Search this book..." autocomplete="off" >
  62. </form><nav class="bd-links" id="bd-docs-nav" aria-label="Main">
  63. <div class="bd-toc-item active">
  64. <ul class="nav bd-sidenav">
  65. <li class="toctree-l1">
  66. <a class="reference internal" href="../../root.html">
  67. State Space Models: A Modern Approach
  68. </a>
  69. </li>
  70. </ul>
  71. <ul class="current nav bd-sidenav">
  72. <li class="toctree-l1">
  73. <a class="reference internal" href="../scratch.html">
  74. Scratchpad
  75. </a>
  76. </li>
  77. <li class="toctree-l1 has-children">
  78. <a class="reference internal" href="../ssm/ssm_index.html">
  79. Introduction
  80. </a>
  81. <input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/>
  82. <label for="toctree-checkbox-1">
  83. <i class="fas fa-chevron-down">
  84. </i>
  85. </label>
  86. <ul>
  87. <li class="toctree-l2">
  88. <a class="reference internal" href="../ssm/hmm.html">
  89. Hidden Markov Models
  90. </a>
  91. </li>
  92. <li class="toctree-l2">
  93. <a class="reference internal" href="../ssm/hsmm.html">
  94. Hidden Semi-Markov Models
  95. </a>
  96. </li>
  97. <li class="toctree-l2">
  98. <a class="reference internal" href="../ssm/lgssm.html">
  99. Linear Gaussian SSMs
  100. </a>
  101. </li>
  102. <li class="toctree-l2">
  103. <a class="reference internal" href="../ssm/nonlin.html">
  104. Non-Linear Gaussian SSMs
  105. </a>
  106. </li>
  107. <li class="toctree-l2">
  108. <a class="reference internal" href="../ssm/nongauss.html">
  109. Non-Gaussian SSMs
  110. </a>
  111. </li>
  112. <li class="toctree-l2">
  113. <a class="reference internal" href="../ssm/switching.html">
  114. Switching SSMs
  115. </a>
  116. </li>
  117. <li class="toctree-l2">
  118. <a class="reference internal" href="../ssm/deep.html">
  119. Deep SSMs
  120. </a>
  121. </li>
  122. <li class="toctree-l2">
  123. <a class="reference internal" href="../ssm/rnn.html">
  124. Recurrent Neural Networks
  125. </a>
  126. </li>
  127. </ul>
  128. </li>
  129. <li class="toctree-l1 has-children">
  130. <a class="reference internal" href="../hmm/hmm_index.html">
  131. Inference in discrete SSMs
  132. </a>
  133. <input class="toctree-checkbox" id="toctree-checkbox-2" name="toctree-checkbox-2" type="checkbox"/>
  134. <label for="toctree-checkbox-2">
  135. <i class="fas fa-chevron-down">
  136. </i>
  137. </label>
  138. <ul>
  139. <li class="toctree-l2">
  140. <a class="reference internal" href="../hmm/hmm_filter.html">
  141. HMM filtering (forwards algorithm)
  142. </a>
  143. </li>
  144. <li class="toctree-l2">
  145. <a class="reference internal" href="../hmm/hmm_smoother.html">
  146. HMM smoothing (forwards-backwards algorithm)
  147. </a>
  148. </li>
  149. <li class="toctree-l2">
  150. <a class="reference internal" href="../hmm/hmm_viterbi.html">
  151. Viterbi algorithm
  152. </a>
  153. </li>
  154. <li class="toctree-l2">
  155. <a class="reference internal" href="../hmm/hmm_parallel.html">
  156. Parallel HMM smoothing
  157. </a>
  158. </li>
  159. <li class="toctree-l2">
  160. <a class="reference internal" href="../hmm/hmm_sampling.html">
  161. Forwards-filtering backwards-sampling algorithm
  162. </a>
  163. </li>
  164. </ul>
  165. </li>
  166. <li class="toctree-l1 has-children">
  167. <a class="reference internal" href="../lgssm/lgssm_index.html">
  168. Inference in linear-Gaussian SSMs
  169. </a>
  170. <input class="toctree-checkbox" id="toctree-checkbox-3" name="toctree-checkbox-3" type="checkbox"/>
  171. <label for="toctree-checkbox-3">
  172. <i class="fas fa-chevron-down">
  173. </i>
  174. </label>
  175. <ul>
  176. <li class="toctree-l2">
  177. <a class="reference internal" href="../lgssm/kalman_filter.html">
  178. Kalman filtering
  179. </a>
  180. </li>
  181. <li class="toctree-l2">
  182. <a class="reference internal" href="../lgssm/kalman_smoother.html">
  183. Kalman (RTS) smoother
  184. </a>
  185. </li>
  186. <li class="toctree-l2">
  187. <a class="reference internal" href="../lgssm/kalman_parallel.html">
  188. Parallel Kalman Smoother
  189. </a>
  190. </li>
  191. <li class="toctree-l2">
  192. <a class="reference internal" href="../lgssm/kalman_sampling.html">
  193. Forwards-filtering backwards sampling
  194. </a>
  195. </li>
  196. </ul>
  197. </li>
  198. <li class="toctree-l1 has-children">
  199. <a class="reference internal" href="../extended/extended_index.html">
  200. Extended (linearized) methods
  201. </a>
  202. <input class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" type="checkbox"/>
  203. <label for="toctree-checkbox-4">
  204. <i class="fas fa-chevron-down">
  205. </i>
  206. </label>
  207. <ul>
  208. <li class="toctree-l2">
  209. <a class="reference internal" href="../extended/extended_filter.html">
  210. Extended Kalman filtering
  211. </a>
  212. </li>
  213. <li class="toctree-l2">
  214. <a class="reference internal" href="../extended/extended_smoother.html">
  215. Extended Kalman smoother
  216. </a>
  217. </li>
  218. <li class="toctree-l2">
  219. <a class="reference internal" href="../extended/extended_parallel.html">
  220. Parallel extended Kalman smoothing
  221. </a>
  222. </li>
  223. </ul>
  224. </li>
  225. <li class="toctree-l1 has-children">
  226. <a class="reference internal" href="../unscented/unscented_index.html">
  227. Unscented methods
  228. </a>
  229. <input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" type="checkbox"/>
  230. <label for="toctree-checkbox-5">
  231. <i class="fas fa-chevron-down">
  232. </i>
  233. </label>
  234. <ul>
  235. <li class="toctree-l2">
  236. <a class="reference internal" href="../unscented/unscented_filter.html">
  237. Unscented filtering
  238. </a>
  239. </li>
  240. <li class="toctree-l2">
  241. <a class="reference internal" href="../unscented/unscented_smoother.html">
  242. Unscented smoothing
  243. </a>
  244. </li>
  245. </ul>
  246. </li>
  247. <li class="toctree-l1">
  248. <a class="reference internal" href="../quadrature/quadrature_index.html">
  249. Quadrature and cubature methods
  250. </a>
  251. </li>
  252. <li class="toctree-l1">
  253. <a class="reference internal" href="../postlin/postlin_index.html">
  254. Posterior linearization
  255. </a>
  256. </li>
  257. <li class="toctree-l1">
  258. <a class="reference internal" href="../adf/adf_index.html">
  259. Assumed Density Filtering
  260. </a>
  261. </li>
  262. <li class="toctree-l1">
  263. <a class="reference internal" href="../vi/vi_index.html">
  264. Variational inference
  265. </a>
  266. </li>
  267. <li class="toctree-l1">
  268. <a class="reference internal" href="../pf/pf_index.html">
  269. Particle filtering
  270. </a>
  271. </li>
  272. <li class="toctree-l1">
  273. <a class="reference internal" href="../smc/smc_index.html">
  274. Sequential Monte Carlo
  275. </a>
  276. </li>
  277. <li class="toctree-l1 has-children">
  278. <a class="reference internal" href="../learning/learning_index.html">
  279. Offline parameter estimation (learning)
  280. </a>
  281. <input class="toctree-checkbox" id="toctree-checkbox-6" name="toctree-checkbox-6" type="checkbox"/>
  282. <label for="toctree-checkbox-6">
  283. <i class="fas fa-chevron-down">
  284. </i>
  285. </label>
  286. <ul>
  287. <li class="toctree-l2">
  288. <a class="reference internal" href="../learning/em.html">
  289. Expectation Maximization (EM)
  290. </a>
  291. </li>
  292. <li class="toctree-l2">
  293. <a class="reference internal" href="../learning/sgd.html">
  294. Stochastic Gradient Descent (SGD)
  295. </a>
  296. </li>
  297. <li class="toctree-l2">
  298. <a class="reference internal" href="../learning/vb.html">
  299. Variational Bayes (VB)
  300. </a>
  301. </li>
  302. <li class="toctree-l2">
  303. <a class="reference internal" href="../learning/mcmc.html">
  304. Markov Chain Monte Carlo (MCMC)
  305. </a>
  306. </li>
  307. </ul>
  308. </li>
  309. <li class="toctree-l1">
  310. <a class="reference internal" href="../tracking/tracking_index.html">
  311. Multi-target tracking
  312. </a>
  313. </li>
  314. <li class="toctree-l1">
  315. <a class="reference internal" href="../ensemble/ensemble_index.html">
  316. Data assimilation using Ensemble Kalman filter
  317. </a>
  318. </li>
  319. <li class="toctree-l1 current active">
  320. <a class="current reference internal" href="#">
  321. Bayesian non-parametric SSMs
  322. </a>
  323. </li>
  324. <li class="toctree-l1">
  325. <a class="reference internal" href="../changepoint/changepoint_index.html">
  326. Changepoint detection
  327. </a>
  328. </li>
  329. <li class="toctree-l1">
  330. <a class="reference internal" href="../timeseries/timeseries_index.html">
  331. Timeseries forecasting
  332. </a>
  333. </li>
  334. <li class="toctree-l1">
  335. <a class="reference internal" href="../gp/gp_index.html">
  336. Markovian Gaussian processes
  337. </a>
  338. </li>
  339. <li class="toctree-l1">
  340. <a class="reference internal" href="../ode/ode_index.html">
  341. Differential equations and SSMs
  342. </a>
  343. </li>
  344. <li class="toctree-l1">
  345. <a class="reference internal" href="../control/control_index.html">
  346. Optimal control
  347. </a>
  348. </li>
  349. <li class="toctree-l1">
  350. <a class="reference internal" href="../../bib.html">
  351. Bibliography
  352. </a>
  353. </li>
  354. </ul>
  355. </div>
  356. </nav> <!-- To handle the deprecated key -->
  357. <div class="navbar_extra_footer">
  358. Powered by <a href="https://jupyterbook.org">Jupyter Book</a>
  359. </div>
  360. </div>
  361. <main class="col py-md-3 pl-md-4 bd-content overflow-auto" role="main">
  362. <div class="topbar container-xl fixed-top">
  363. <div class="topbar-contents row">
  364. <div class="col-12 col-md-3 bd-topbar-whitespace site-navigation show"></div>
  365. <div class="col pl-md-4 topbar-main">
  366. <button id="navbar-toggler" class="navbar-toggler ml-0" type="button" data-toggle="collapse"
  367. data-toggle="tooltip" data-placement="bottom" data-target=".site-navigation" aria-controls="navbar-menu"
  368. aria-expanded="true" aria-label="Toggle navigation" aria-controls="site-navigation"
  369. title="Toggle navigation" data-toggle="tooltip" data-placement="left">
  370. <i class="fas fa-bars"></i>
  371. <i class="fas fa-arrow-left"></i>
  372. <i class="fas fa-arrow-up"></i>
  373. </button>
  374. <div class="dropdown-buttons-trigger">
  375. <button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn" aria-label="Download this page"><i
  376. class="fas fa-download"></i></button>
  377. <div class="dropdown-buttons">
  378. <!-- ipynb file if we had a myst markdown file -->
  379. <!-- Download raw file -->
  380. <a class="dropdown-buttons" href="../../_sources/chapters/bnp/bnp_index.md"><button type="button"
  381. class="btn btn-secondary topbarbtn" title="Download source file" data-toggle="tooltip"
  382. data-placement="left">.md</button></a>
  383. <!-- Download PDF via print -->
  384. <button type="button" id="download-print" class="btn btn-secondary topbarbtn" title="Print to PDF"
  385. onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf</button>
  386. </div>
  387. </div>
  388. <!-- Source interaction buttons -->
  389. <div class="dropdown-buttons-trigger">
  390. <button id="dropdown-buttons-trigger" class="btn btn-secondary topbarbtn"
  391. aria-label="Connect with source repository"><i class="fab fa-github"></i></button>
  392. <div class="dropdown-buttons sourcebuttons">
  393. <a class="repository-button"
  394. href="https://github.com/ssm-jax/ssm-book"><button type="button" class="btn btn-secondary topbarbtn"
  395. data-toggle="tooltip" data-placement="left" title="Source repository"><i
  396. class="fab fa-github"></i>repository</button></a>
  397. <a class="issues-button"
  398. href="https://github.com/ssm-jax/ssm-book/issues/new?title=Issue%20on%20page%20%2Fchapters/bnp/bnp_index.html&body=Your%20issue%20content%20here."><button
  399. type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip" data-placement="left"
  400. title="Open an issue"><i class="fas fa-lightbulb"></i>open issue</button></a>
  401. </div>
  402. </div>
  403. <!-- Full screen (wrap in <a> to have style consistency -->
  404. <a class="full-screen-button"><button type="button" class="btn btn-secondary topbarbtn" data-toggle="tooltip"
  405. data-placement="bottom" onclick="toggleFullScreen()" aria-label="Fullscreen mode"
  406. title="Fullscreen mode"><i
  407. class="fas fa-expand"></i></button></a>
  408. <!-- Launch buttons -->
  409. </div>
  410. <!-- Table of contents -->
  411. <div class="d-none d-md-block col-md-2 bd-toc show noprint">
  412. </div>
  413. </div>
  414. </div>
  415. <div id="main-content" class="row">
  416. <div class="col-12 col-md-9 pl-md-3 pr-md-0">
  417. <!-- Table of contents that is only displayed when printing the page -->
  418. <div id="jb-print-docs-body" class="onlyprint">
  419. <h1>Bayesian non-parametric SSMs</h1>
  420. <!-- Table of contents -->
  421. <div id="print-main-content">
  422. <div id="jb-print-toc">
  423. </div>
  424. </div>
  425. </div>
  426. <div>
  427. <div class="tex2jax_ignore mathjax_ignore section" id="bayesian-non-parametric-ssms">
  428. <span id="ch-bnp"></span><h1>Bayesian non-parametric SSMs<a class="headerlink" href="#bayesian-non-parametric-ssms" title="Permalink to this headline">¶</a></h1>
  429. </div>
  430. <script type="text/x-thebe-config">
  431. {
  432. requestKernel: true,
  433. binderOptions: {
  434. repo: "binder-examples/jupyter-stacks-datascience",
  435. ref: "master",
  436. },
  437. codeMirrorConfig: {
  438. theme: "abcdef",
  439. mode: "python"
  440. },
  441. kernelOptions: {
  442. kernelName: "python3",
  443. path: "./chapters/bnp"
  444. },
  445. predefinedOutput: true
  446. }
  447. </script>
  448. <script>kernelName = 'python3'</script>
  449. </div>
  450. <!-- Previous / next buttons -->
  451. <div class='prev-next-area'>
  452. <a class='left-prev' id="prev-link" href="../ensemble/ensemble_index.html" title="previous page">
  453. <i class="fas fa-angle-left"></i>
  454. <div class="prev-next-info">
  455. <p class="prev-next-subtitle">previous</p>
  456. <p class="prev-next-title">Data assimilation using Ensemble Kalman filter</p>
  457. </div>
  458. </a>
  459. <a class='right-next' id="next-link" href="../changepoint/changepoint_index.html" title="next page">
  460. <div class="prev-next-info">
  461. <p class="prev-next-subtitle">next</p>
  462. <p class="prev-next-title">Changepoint detection</p>
  463. </div>
  464. <i class="fas fa-angle-right"></i>
  465. </a>
  466. </div>
  467. </div>
  468. </div>
  469. <footer class="footer">
  470. <p>
  471. By Kevin Murphy, Scott Linderman, et al.<br/>
  472. &copy; Copyright 2021.<br/>
  473. </p>
  474. </footer>
  475. </main>
  476. </div>
  477. </div>
  478. <script src="../../_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
  479. </body>
  480. </html>