1 Introduction. - 2 Probabilistic Inference in Signal Processing. - 2. 1 Introduction. - 2. 2 The likelihood function. - 2. 3 Bayesian data analysis. - 2. 4 Prior probabilities. - 2. 5 The removal of nuisance parameters. - 2. 6 Model selection using Bayesian evidence. - 2. 7 The general linear model. - 2. 8 Interpretations of the general linear model. - 2. 9 Example of marginalization. - 2. 10 Example of model selection. - 2. 11 Concluding remarks. - 3 Numerical Bayesian Inference. - 3. 1 The normal approximation. - 3. 2 Optimization. - 3. 3 Integration. - 3. 4 Numerical quadrature. - 3. 5 Asymptotic approximations. - 3. 6 The Monte Carlo method. - 3. 7 The generation of random variates. - 3. 8 Evidence using importance sampling. - 3. 9 Marginal densities. - 3. 10 Opportunities for variance reduction. - 3. 11 Summary. - 4 Markov Chain Monte Carlo Methods. - 4. 1 Introduction. - 4. 2 Background on Markov chains. - 4. 3 The canonical distribution. - 4. 4 The Gibbs sampler. - 4. 5 The Metropolis-Hastings algorithm. - 4. 6 Dynamical sampling methods. - 4. 7 Implementation of simulated annealing. - 4. 8 Other issues. - 4. 9 Free energy estimation. - 4. 10 Summary. - 5 Retrospective Changepoint Detection. - 5. 1 Introduction. - 5. 2 The simple Bayesian step detector. - 5. 3 The detection of changepoints using the general linear model. - 5. 4 Recursive Bayesian estimation. - 5. 5 Detection of multiple changepoints. - 5. 6 Implementation details. - 5. 7 Multiple changepoint results. - 5. 8 Concluding Remarks. - 6 Restoration of Missing Samples in Digital Audio Signals. - 6. 1 Introduction. - 6. 2 Model formulation. - 6. 3 The EM algorithm. - 6. 4 Gibbs sampling. - 6. 5 Implementation issues. - 6. 6 Relationship between the three restoration methods. - 6. 7 Simulations. - 6. 8 Discussion. - 6. 9 Concluding remarks. - 7 Integration in Bayesian Data Analysis. - 7. 1 Polynomial data. -7. 2 Decay problem. - 7. 3 General model selection. - 7. 4 Summary. - 8 Conclusion. - 8. 1 A review of the work. - 8. 2 Further work. - A The General Linear Model. - A. 1 Integrating out model amplitudes. - A. 1. 1 Least squares. - A. 1. 2 Orthogonalization. - A. 2 Integrating out the standard deviation. - A. 3 Marginal density for a linear coefficient. - A. 4 Marginal density for standard deviation. - A. 5 Conditional density for a linear coefficient. - A. 6 Conditional density for standard deviation. - B Sampling from a Multivariate Gaussian Density. - C Hybrid Monte Carlo Derivations. - C. 1 Full Gaussian likelihood. - C. 2 Student-t distribution. - C. 3 Remark. - D EM Algorithm Derivations. - D. l Expectation. - D. 2 Maximization. - E Issues in Sampling Based Approaches to Integration. - E. 1 Marginalizing using the conditional density. - E. 2 Approximating the conditional density. - E. 3 Gibbs sampling from the joint density. - E. 4 Reverse importance sampling. - F Detailed Balance. - F. 1 Detailed balance in the Gibbs sampler. - F. 2 Detailed balance in the Metropolis Hastings algorithm. - F. 3 Detailed balance in the Hybrid Monte Carlo algorithm. - F. 4 Remarks. - References. Language: English