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Abstract:
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Markov Chain Monte Carlo (MCMC) is an extremely popular class of statistical methods for simulating autocorrelated draws from target distributions, including posterior distributions in Bayesian analysis. An important consideration in using simulated MCMC draws for inference is that they have converged to the distribution of interest. Since the distribution is typically of a non-standard form, convergence cannot generally be proven and, instead, is assessed with convergence diagnostics. Although parameters used in the MCMC framework are typically continuous, there are situations in which one wants to simulate a categorical variable. Examples include indicators for model inclusion in Bayesian variable selection and latent categorical components in mixture modeling. Traditional convergence diagnostics focus on continuous variables and may be inappropriate for categorical variables. Two convergence diagnostic are proposed by modeling the data using either a NDARMA(p,q) or a GLARMA process. Performance of the convergence diagnostics is evaluated under various simulations. The diagnostics are applied to a data set where MCMC is used to fit Bayesian models with categorical parameters.
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