Economic and financial data frequently exhibit dynamic patterns, driven by unobserved processes that relate to the behaviour of economic agents, or to institutional and technological change. To gain insight into such 'latent' processes is of paramount importance in terms of both understanding the economy and producing accurate, readily up-dated, forecasts of its future performance. Using a Bayesian approach, new simulationbased statistical methods for analyzing latent variable models are proposed. Emphasis is given to the development of relatively simple techniques that are applicable to a wide range of empirically relevant models, with a view to improving the access of non-specialists to this powerful form of statistical analysis.