Bayesian time series analysis and forecasting with dynamic models
This short course will present a review of basic Bayesian ideas via sampling importance resampling, with examples of linear regressions with Gaussian or student errors, and Gaussian or double exponential priors for the coefficients. It will then present the Gibbs sampler and the Metropolis-Hastings sampler, considering examples of forward filtering backward sampling algorithms for conditionally linear dynamic models and of single move Metropolis-Hastings algorithm for a simple version of the stochastic volatility model. The course will then move to the presentation of the particle filter for nonlinear and non-Gaussian dynamic models with an example consisting of the Bootstrap filter for deriving an approximation to the likelihood of the static parameters of a simple version of the stochastic volatility model as well as the particle learning filter for fully sequential learning of states and parameters. The course will also briefly cover other advanced topics, like reversible jump MCMC, Hamiltonian Monte Carlo, Adaptive Monte Carlo, Aproximate Bayesian Computations and likelihood-free methods.