Dynamic Linear Models with R (eBook)

Preface 6
Contents 9
1 Introduction: basic notions about Bayesian inference 12
1.1 Basic notions 13
1.2 Simple dependence structures 16
1.3 Synthesis of conditional distributions 22
1.4 Choice of the prior distribution 25
1.5 Bayesian inference in the linear regression model 29
1.6 Markov chain Monte Carlo methods 33
Problems 40
2 Dynamic linear models 41
2.1 Introduction 41
2.2 A simple example 45
2.3 State space models 49
2.4 Dynamic linear models. 51
2.5 Dynamic linear models in package dlm 53
2.6 Examples of nonlinear and non-Gaussian state space models 58
2.7 State estimation and forecasting 59
2.8 Forecasting 76
2.9 The innovation process and model checking 83
2.10 Controllability and observability of time-invariant DLMs 87
2.11 Filter stability 90
Problems 93
3 Model specification 95
3.1 Classical tools for time series analysis 95
3.2 Univariate DLMs for time series analysis 98
3.3 Models for multivariate time series 135
Problems 152
4 Models with unknown parameters 153
4.1 Maximum likelihood estimation 154
4.2 Bayesian inference 158
4.3 Conjugate Bayesian inference 159
4.4 Simulation-based Bayesian inference 170
4.5 Unknown variances 177
4.6 Further examples 196
Problems 216
5 Sequential Monte Carlo methods 217
5.1 The basic particle filter 218
5.2 Auxiliary particle filter 226
5.3 Sequential Monte Carlo with unknown parameters 229
5.4 Concluding remarks 238
A Useful distributions 240
B Matrix algebra: Singular Value Decomposition 246
Index 249
References 252