On the use of Markovian stick-breaking priors
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In [10], a `Markovian stick-breaking' process which generalizes the Dirichlet process (μ, θ) with respect to a discrete base space 𝔛 was introduced. In particular, a sample from from the `Markovian stick-breaking' processs may be represented in stick-breaking form ∑_i≥ 1 P_i δ_T_i where {T_i} is a stationary, irreducible Markov chain on 𝔛 with stationary distribution μ, instead of i.i.d. {T_i} each distributed as μ as in the Dirichlet case, and {P_i} is a GEM(θ) residual allocation sequence. Although the motivation in [10] was to relate these Markovian stick-breaking processes to empirical distributional limits of types of simulated annealing chains, these processes may also be thought of as a class of priors in statistical problems. The aim of this work in this context is to identify the posterior distribution and to explore the role of the Markovian structure of {T_i} in some inference test cases.
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