In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means {µ 1 , µ 2 , µ 3 } through an analysis of variance (ANOVA), a model may specify that µ 1 < µ 2 < µ 3 , while another one may state that {µ 1 = µ 3 } < µ 2 , and finally a third model may instead suggest that all means are unrestricted. This is a challenging problem, because it involves a combination of non-nested models, as well as nested models having the same dimension.We adopt an objective Bayesian approach, and derive the posterior probability of each model under consideration. Our method is based on the intrinsic prior methodology, with suitably modifications to accommodate equality and inequality constraints. Focussing on normal ANOVA models, a comparative assessment is carried out through simulation studies, showing that correct model identification is possible even in situations where frequentist power is low. We also present an application to real data collected in a psychological experiment.
Markov switching autoregressive models (MSARMs) are efficient tools to analyse nonlinear and non-Gaussian time series. A special MSARM with two harmonic components is proposed to analyse periodic time series. We present a full Bayesian analysis based on a Gibbs sampling algorithm for model choice and the estimations of the unknown parameters, missing data and predictive distributions. The implementation and modelling steps are developed by tackling the problem of the hidden states labeling by means of random permutation sampling and constrained permutation sampling. We apply MSARMs to study a data set about air pollution that presents periodicities since the hourly mean concentration of carbon monoxide varies according to the dynamics of the 24 day-hours and of the year. Hence, we introduce in the model both a hidden state-dependent daily component and a state-independent yearly component, giving rise to periodic MSARMs.
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