. We define a subclass of dynamic linear models with unknown hyperpara‐meter called d‐inverse‐gamma models. We then approximate the marginal probability density functions of the hyperparameter and the state vector by the data augmentation algorithm of Tanner and Wong. We prove that the regularity conditions for convergence hold. For practical implementation a forward‐filtering‐backward‐sampling algorithm is suggested, and the relation to Gibbs sampling is discussed in detail.

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand.

Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers nite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidenti ability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian estimation of all latent variables, model parameters, and parameters that determine the probability law of the latent process is carried out by a new MCMC method called permutation sampling. The permutation sampler rst samples from the unconstrained posterior-which often can be done in a convenient multimove manner-and then applies a permutation of the current labeling of the states of the latent process. In a rst run, the random permutation sampler used selected the permutation randomly. The MCMC output of the random permutation sampler is explored to nd suitable identi ability constraints. In a second run, the permutation sampler was used to sample from the constrained posterior by imposing identi ablity constraints. This time a suitable permutation is applied if the identi ability constraint is violated. For illustration, two detailed case studies are presented, namely nite mixture modeling of fetal lamb data and Markov switching autoregressive modeling of the U.S. quarterly real gross national product data.

Please cite this article as: Frühwirth-Schnatter, S., Wagner, H., Stochastic model specification search for Gaussian and partial non-Gaussian state space models. Journal of Econometrics (2009Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T

This paper discusses the problem of estimating marginal likelihoods for mixture and Markov switching model. Estimation is based on the method of bridge sampling (Meng and Wong 1996; Statistica Sinica 11, 552-86.) where Markov Chain Monte Carlo (MCMC) draws from the posterior density are combined with an i.i.d. sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC draws using a mixture of complete data posteriors. Whereas the importance sampling estimator as well as the reciprocal importance sampling estimator are sensitive to the tail behaviour of the importance density, we demonstrate that the bridge sampling estimator is far more robust. Our case studies range from computing marginal likelihoods for a mixture of multivariate normal distributions, testing for the inhomogeneity of a discrete time Poisson process, to testing for the presence of Markov switching and order selection in the MSAR model.