Direct sampling from conditional distributions by sequential maximum likelihood estimations

TL;DR

This paper introduces an approximate sampling algorithm for log-affine models that replaces the computationally intensive UMVUE with the more efficient MLE, simplifying implementation while maintaining practical effectiveness.

Contribution

It proposes an approximate method for direct sampling from conditional distributions in log-affine models using MLE instead of UMVUE, reducing computational complexity.

Findings

The approximate algorithm is efficient and easy to implement.

It performs well despite being an approximation.

It eliminates the need for prior knowledge of connection matrices.

Abstract

We can directly sample from the conditional distribution of any log-affine model. The algorithm is a Markov chain on a bounded integer lattice, and its transition probability is the ratio of the UMVUE (uniformly minimum variance unbiased estimator) of the expected counts to the total number of counts. The computation of the UMVUE accounts for most of the computational cost, which makes the implementation challenging. Here, we investigated an approximate algorithm that replaces the UMVUE with the MLE (maximum likelihood estimator). Although it is generally not exact, it is efficient and easy to implement; no prior study is required, such as about the connection matrices of the holonomic ideal in the original algorithm.