| |
| |
| |
| Introduction: basic notions about Bayesian inference | |
| |
| |
| |
| Basic notions | |
| |
| |
| |
| Simple dependence structures | |
| |
| |
| |
| Synthesis of conditional distributions | |
| |
| |
| |
| Choice of the prior distribution | |
| |
| |
| |
| Bayesian inference in the linear regression model | |
| |
| |
| |
| Markov chain Monte Carlo methods | |
| |
| |
| |
| Gibbs sampler | |
| |
| |
| |
| Metropolis-Hastings algorithm | |
| |
| |
| |
| Adaptive rejection Metropolis sampling | |
| |
| |
| Problems | |
| |
| |
| |
| Dynamic linear models | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| A simple example | |
| |
| |
| |
| State space models | |
| |
| |
| |
| Dynamic linear models | |
| |
| |
| |
| Dynamic linear models in package dlm | |
| |
| |
| |
| Examples of nonlinear and non-Gaussian state space models | |
| |
| |
| |
| State estimation and forecasting | |
| |
| |
| |
| Filtering | |
| |
| |
| |
| Kalman filter for dynamic linear models | |
| |
| |
| |
| Filtering with missing observations | |
| |
| |
| |
| Smoothing | |
| |
| |
| |
| Forecasting | |
| |
| |
| |
| The innovation process and model checking | |
| |
| |
| |
| Controllability and observability of time-invariant DLMs | |
| |
| |
| |
| Filter stability | |
| |
| |
| Problems | |
| |
| |
| |
| Model specification | |
| |
| |
| |
| Classical tools for time series analysis | |
| |
| |
| |
| Empirical methods | |
| |
| |
| |
| ARIMA models | |
| |
| |
| |
| Univariate DLMs for time series analysis | |
| |
| |
| |
| Trend models | |
| |
| |
| |
| Seasonal factor models | |
| |
| |
| |
| Fourier form seasonal models | |
| |
| |
| |
| General periodic components | |
| |
| |
| |
| DLM representation of ARIMA models | |
| |
| |
| |
| Example: estimating the output gap | |
| |
| |
| |
| Regression models | |
| |
| |
| |
| Models for multivariate time series | |
| |
| |
| |
| DLMs for longitudinal data | |
| |
| |
| |
| Seemingly unrelated time series equations | |
| |
| |
| |
| Seemingly unrelated regression models | |
| |
| |
| |
| Hierarchical DLMs | |
| |
| |
| |
| Dynamic regression | |
| |
| |
| |
| Common factors | |
| |
| |
| |
| Multivariate ARMA models | |
| |
| |
| Problems | |
| |
| |
| |
| Models with unknown parameters | |
| |
| |
| |
| Maximum likelihood estimation | |
| |
| |
| |
| Bayesian inference | |
| |
| |
| |
| Conjugate Bayesian inference | |
| |
| |
| |
| Unknown covariance matrices: conjugate inference | |
| |
| |
| |
| Specification of Wt by discount factors | |
| |
| |
| |
| A discount factor model for time-varying Vt | |
| |
| |
| |
| Simulation-based Bayesian inference | |
| |
| |
| |
| Drawing the states given y1:T: forward filtering backward sampling | |
| |
| |
| |
| General strategies for MCMC | |
| |
| |
| |
| Illustration: Gibbs sampling for a local level model | |
| |
| |
| |
| Unknown variances | |
| |
| |
| |
| Constant unknown variances: d Inverse Gamma Prior | |
| |
| |
| |
| Multivariate extensions | |
| |
| |
| |
| A model for outliers and structural breaks | |
| |
| |
| |
| Further examples | |
| |
| |
| |
| Estimating the output gap: Bayesian inference | |
| |
| |
| |
| Dynamic regression | |
| |
| |
| |
| Factor models | |
| |
| |
| Problems | |
| |
| |
| |
| Sequential Monte Carlo methods | |
| |
| |
| |
| The basic particle filter | |
| |
| |
| |
| A simple example | |
| |
| |
| |
| Auxiliary particle filter | |
| |
| |
| |
| Sequential Monte Carlo with unknown parameters | |
| |
| |
| |
| A simple example with unknown parameters | |
| |
| |
| |
| Concluding remarks | |
| |
| |
| |
| Useful distributions | |
| |
| |
| |
| Matrix algebra: Singular Value Decomposition | |
| |
| |
| Index | |
| |
| |
| References | |