Chapter
1.7 Discussion and summary
2 Adaptive Markov chain Monte Carlo: theory and methods
2.2 Adaptive MCMC algorithms
2.3 Convergence of the marginal distribution
2.4 Strong law of large numbers
2.5 Convergence of the equi-energy sampler
2.A Appendix: Proof of Section 2.5
3 Auxiliary particle filtering: recent developments
3.2 Interpretation and implementation
3.3 Applications and extensions
3.4 Further stratifying the APF
4 Monte Carlo probabilistic inference for diffusion processes: a methodological framework
4.2 Random weight continuous–discrete particle filtering
4.3 Transition density representation for a class of diffusions
4.4 Exact simulation of diffusions
4.5 Exact simulation of killed Brownian motion
4.6 Unbiased estimation of the transition density using series expansions
4.7 Discussion and directions
5 Two problems with variational expectation maximisation for Time Series models
5.2 The variational approach
5.3 Compactness of variational approximations
5.4 Variational approximations are biased
6 Approximate inference for continuous-time Markov processes
6.2 Partly observed diffusion processes
6.3 Hidden Markov characterisation
6.4 The variational approximation
6.5 The Gaussian variational approximation
6.6 Diffusions with multiplicative noise
6.8 Discussion and outlook
7 Expectation propagation and generalised EP methods for inference in switching linear dynamical systems
7.2 Notation and problem description
7.3 Assumed density filtering
7.4 Expectation propagation
7.5 Free-energy minimisation
7.6 Generalised expectation propagation
7.7 Alternative backward passes
7.A Appendix: Operations on conditional Gaussian potentials
7.B Appendix: Proof of Theorem 7.1
8 Approximate inference in switching linear dynamical systems using Gaussian mixtures
8.2 The switching linear dynamical system
8.3 Gaussian sum filtering
8.4 Expectation correction
8.5 Demonstration: traffic flow
8.6 Comparison of smoothing techniques
9 Physiological monitoring with factorial switching linear dynamical systems
10 Analysis of changepoint models
10.2 Single changepoint models
10.3 Multiple changepoint models
10.4 Comparison of methods
10.A Appendix: segment parameter estimation
11 Approximate likelihood estimation of static parameters in multi-target Models
11.2 The multi-target model
11.3 A review of the PHD filter
11.4 Approximating the marginal likelihood
11.5 SMC approximation of the PHD filter and its gradient
11.6 Parameter estimation
12 Sequential Inference for Dynamically Evolving Groups of Objects
12.2 MCMC-particles algorithm
12.4 Ground target tracking
12.5 Group stock selection
12.A Appendix: Base group representation
13 Non-commutative Harmonic Analysis in Multi-object Tracking
13.2 Harmonic analysis on finite groups
13.3 Band-limited approximations
13.4 A hidden Markov model in Fourier space
13.5 Approximations in terms of marginals
13.6 Efficient computation
14 Markov chain Monte Carlo algorithms for Gaussian processes
14.2 Gaussian process models
14.3 Non-Gaussian likelihoods and deterministic methods
14.4 Sampling algorithms for Gaussian process models
14.5 Related work and other sampling schemes
14.6 Demonstration on regression and classification
14.7 Transcriptional regulation
14.8 Dealing with large datasets
15 Nonparametric hidden Markov models
15.2 From HMMs to Bayesian HMMs
15.3 The infinite hidden Markov model
15.5 Example: unsupervised part-of-speech tagging
15.A Appendix: Equivalence of the hierarchical Polya urn and hierarchical Dirichlet process
16 Bayesian Gaussian Process Models for Multi-sensor time series prediction
16.2 The information processing problem
16.4 Trial implementation
16.5 Empirical evaluation
17 Optimal control theory and the linear Bellman equation
17.2 Discrete time control
17.3 Continuous time control
17.4 Stochastic optimal control
17.6 Path integral control
17.7 Approximate inference methods for control
18 Expectation maximisation methods for solving (PO)MDPs and optimal control problems
18.2 Markov decision processes and likelihood maximisation
18.3 Expectation maximisation in mixtures of variable length dynamic Bayesian networks
18.5 Application to POMDPs
18.B Appendix: Pruning computations
Bayesian Time Series Models
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