Computational issues on the blocked Gibbs algorithm

초록

Nonparametric Bayesian methodology uses information from the data to infer the posterior distribution of the model parameters, without requiring the researcher to specify a prior distribution. This extends the Bayesian framework to scenarios where the underlying probability distributions are not known to have a fixed number of parameters. Instead, nonparametric Bayesian models use infinite-dimensional parameter spaces to allow for greater flexibility. When employing a nonparametric Bayesian hierarchical model with the blocked Gibbs sampler algorithm, estimating the number of latent components is a critical task. This is challenging because it requires using the concept of infinity within the MCMC process to identify a suitable, arbitrary value that effectively characterizes the complexity of the data. In this paper, we present two distinct methodologies including finite approximation and dynamic adjustment for implementing nonparametric Bayesian analysis.

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