Abstract
In this paper, we propose a Markov chain for sampling a random vector distributed according to a discretized Dirichlet distribution. We show that our Markov chain is rapidly mixing, that is, the mixing time of our chain is bounded by (1/2)n(n - 1)ln((δ - n)ε − 1) where n is the dimension (the number of parameters), 1/Δ is the grid size for discretization, and ε is the error bound. Thus the obtained bound does not depend on the magnitudes of parameters and linear to the logarithm of the inverse of grid size. We estimate the mixing time by using the path coupling method. We also show the rate of convergence of our chain experimentally.
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Matsui, T., Motoki, M., Kamatani, N. (2003). Polynomial Time Approximate Sampler for Discretized Dirichlet Distribution. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_69
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DOI: https://doi.org/10.1007/978-3-540-24587-2_69
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20695-8
Online ISBN: 978-3-540-24587-2
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