Polynomial time perfect sampler for discretized dirichlet distribution

@inproceedings{Matsui2008PolynomialTP,
  title={Polynomial time perfect sampler for discretized dirichlet distribution},
  author={Tomomi Matsui and Shuji Kijima},
  year={2008}
}
In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. The Dirichlet distribution appears as prior and posterior distribution for the multinomial distribution in many statistical methods in bioinformatics. Our algorithm is a monotone coupling from the past algorithm, which is a Las Vegas type randomized algorithm. We propose a new Markov chain whose limit distribution is a discretized Dirichlet distribution. Our algorithm simulates… 

Polynomial time approximate or perfect samplers for discretized Dirichlet distribution

TLDR
This paper proposes two Markov chains for sampling random vectors that are distributed according to discretized Dirichlet distribution and gives a perfect sampler that is based on monotone coupling from the past.

Polynomial-time Perfect Sampler for Closed Jackson Networks with Single Servers

TLDR
A new ergodic Markov chain is proposed whose unique stationary distribution is the product form solution of a closed Jackson Network, thus a new sampler is proposed, based on monotone Coupling from the Past and realizes the sampling from the target distribution exactly.

References

SHOWING 1-10 OF 18 REFERENCES

Polynomial Time Approximate Sampler for Discretized Dirichlet Distribution

TLDR
It is shown that the Markov chain is rapidly mixing, that is, the mixing time of the chain is bounded by (1/2)n(n - 1)ln((δ - n)e − 1) where n is the dimension (the number of parameters), 1/Δ is the grid size for discretization, and e is the error bound.

A Guide to Exact Simulation

TLDR
The results show that CFTP works at least as well as standard MCMC, with convergence monitored by the method of Raftery & Lewis (1992, 1996).

Exact sampling with coupled Markov chains and applications to statistical mechanics

TLDR
This work describes a simple variant of this method that determines on its own when to stop and that outputs samples in exact accordance with the desired distribution, and uses couplings which have also played a role in other sampling schemes.

How to Get a Perfectly Random Sample from a Generic Markov Chain and Generate a Random Spanning Tree of a Directed Graph

TLDR
Algorithms for generating a random sample from the state space of a Markov chain in accordance with the steady-state probability law of the chain are given, improving on earlier results and exploiting the duality between the two problems.

Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: justification and implications.

  • T. Burr
  • Mathematics
    Theoretical population biology
  • 2000
TLDR
This paper examines a quasi-equilibrium theory of rare alleles for subdivided populations that follow an island-model version of the Wright-Fisher model of evolution and introduces a new and simpler proof for the expected number of alleles implied by the Ewens Sampling Formula.

Randomized algorithms - approximation, generation and counting

TLDR
Randomized Al algorithms discusses two problems of fine pedigree: counting and generation, both of which are of fundamental importance to discrete mathematics and probability, and uses the technique of coupling before introducing "path coupling" a new technique which radically simplifies and improves upon previous methods in the area.

The Bayesian choice

TLDR
This paperback edition, a reprint of the 2001 edition, is a graduate-level textbook that introduces Bayesian statistics and decision theory and was awarded the 2004 DeGroot Prize for setting a new standard for modern textbooks dealing with Bayesian methods.

Maximum-likelihood and markov chain monte carlo approaches to estimate inbreeding and effective size from allele frequency changes.

TLDR
All the new estimates presented here were found to be better than the F-statistics classically used, and the likelihood and Bayesian approaches give better results than the classical F-Statistics when markers exhibiting a low polymorphism are used.

Bayesian haplotype inference for multiple linked single-nucleotide polymorphisms.

TLDR
A new Monte Carlo approach that can accurately and rapidly infer haplotypes for a large number of linked SNPs and is robust to the violation of Hardy-Weinberg equilibrium, to the presence of missing data, and to occurrences of recombination hotspots is proposed.

Empirical Bayes procedure for estimating genetic distance between populations and effective population size.

TLDR
An empirical Bayes procedure to estimate genetic distances between populations using allele frequencies is developed and it is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis.