## Bayesian Time Series ModelsDavid Barber, A. Taylan Cemgil, Silvia Chiappa 'What's going to happen next?' Time series data hold the answers, and Bayesian methods represent the cutting edge in learning what they have to say. This ambitious book is the first unified treatment of the emerging knowledge-base in Bayesian time series techniques. Exploiting the unifying framework of probabilistic graphical models, the book covers approximation schemes, both Monte Carlo and deterministic, and introduces switching, multi-object, non-parametric and agent-based models in a variety of application environments. It demonstrates that the basic framework supports the rapid creation of models tailored to specific applications and gives insight into the computational complexity of their implementation. The authors span traditional disciplines such as statistics and engineering and the more recently established areas of machine learning and pattern recognition. Readers with a basic understanding of applied probability, but no experience with time series analysis, are guided from fundamental concepts to the state-of-the-art in research and practice. |

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### Contents

1 Inference and estimation in probabilistic time series models David Barber A Taylan Cemgil and Silvia Chiappa | 1 |

theory and methods Yves Atchadé Gersende Fort Eric Moulines and Pierre Priouret | 32 |

recent developments Nick Whiteley and Adam M Johansen | 52 |

a methodological framework Omiros Papaspiliopoulos | 82 |

5 Two problems with variational expectation maximisation for Time Series models Richard Eric Turner and Maneesh Sahani | 104 |

6 Approximate inference for continuoustime Markov processes Cédric Archambeau and Manfred Opper | 125 |

7 Expectation propagation and generalised EP methods for inference in switching linear dynamical systems Onno Zoeter and Tom Heskes | 141 |

8 Approximate inference in switching linear dynamical systems using Gaussian mixtures David Barber | 166 |

11 Approximate likelihood estimation of static parameters in multitarget Models Sumeetpal S Singh Nick Whiteley and Simon J Godsill | 225 |

12 Sequential Inference for Dynamically Evolving Groups of Objects Sze Kim Pang Simon J Godsill Jack Li François Septier and Simon Hill | 245 |

13 Noncommutative Harmonic Analysis in Multiobject Tracking Risi Kondor | 277 |

14 Markov chain Monte Carlo algorithms for Gaussian processes Michalis K Titsias Magnus Rattray and Neil D Lawrence | 295 |

15 Nonparametric hidden Markov models Jurgen Van Gael and Zoubin Ghahramani | 317 |

16 Bayesian Gaussian Process Models for Multisensor time series prediction Michael A Osborne Alex Rogers Stephen J Roberts Sarvapali D Ramchu... | 341 |

17 Optimal control theory and the linear Bellman equation Hilbert J Kappen | 363 |

18 Expectation maximisation methods for solving POMDPs and optimal control problems Marc Toussaint Amos Storkey and Stefan Harmeling | 388 |

### Common terms and phrases

adaptive applications approach assume auxiliary Bayesian Bayesian inference chain Monte Carlo changepoint components compute conditional consider convergence correlations corresponding covariance deﬁned deﬁnition denote detection Dirichlet process efﬁcient equation exact example factor ﬁltering ﬁnd ﬁnite ﬁrst ﬁxed Fourier free-energy function Gaussian process Gibbs sampler given GP prior group structure hidden Markov model hyperparameters iHMM independent inference inﬁnite initialised integral iteration kernel Laplace approximation linear dynamical system M-step machine learning marginal likelihood Markov chain Markov chain Monte matrix maximisation MCMC methods minimisation mixture Monte Carlo methods noise normalised observations obtained optimal control parameters particle ﬁlter Poisson Polya urn posterior distribution prediction probability problem propagation proposal distribution recursion representation resampling scheme Section segment sensor sequence simulation smoothing solution space speciﬁc Statistics step stochastic switch target distribution Theorem tracking transition density update variance variational approximation vector weights X-factor