In this paper we provide a unified likelihood treatment of a wide class of
non-Gaussian time series, semi-parametric and non-parametric regression,
spectral density estimation and panel data problems. The methods rely on the
use of Markov chain Monte Carlo to carry out non-Gaussian simulation
smoothing and Bayesian posterior analysis of parameters, and on importance
sampling to estimate the likelihood function for classical inference. We
exploit the structure of the models to ensure that our methods are highly
efficient, delivering MCMC simulations with little autocorrelation and
highly effective estimates of the likelihood.



Some key words: Blocking; Durations; Exponential family; Importance
sampling; Markov chain Monte Carlo; Non-parametric regression; Panel data;
Penalised likelihood; Poisson counts; Semi-parametric regression; Simulation
smoother; Spectral density estimation; Splines; Stochastic volatility.