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Abstract:
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We propose a generalized algorithm for approximate computation of the posterior distribution. The posterior distribution has good convergence properties, namely, if the data is derived from a given probability distribution, then it can be shown under fairly general settings that the posterior concentrates around arbitrary small neighbourhoods of the data generating distribution. However, the exact computation of posterior distributions is often difficult, mostly because of the underlying dependence structure. Several approximation techniques like Markov Chain Monte Carlo, Mean Field Variational Inference algorithms have been proposed that approximate the posterior distribution. However, very few results are known about the consistency properties of such approximation algorithms. We propose a more generalized method of constructing an approximation algorithm, in the form of Iterative Random functions, consisting of sequential application of a Posterior Update step followed by a Lipschitz operation step, and study its consistency properties.
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