Probability Estimation with Truncated Inverse Binomial Sampling

TL;DR

This paper introduces a comprehensive theory of truncated inverse binomial sampling, unifying fixed-size and inverse binomial sampling, and proposes an adaptive Monte Carlo method for probability estimation that is significantly more efficient.

Contribution

It develops a general theory encompassing fixed-size and inverse binomial sampling, and proposes an efficient adaptive Monte Carlo method for probability estimation.

Findings

The theory includes classical Chernoff-Hoeffding bounds as a special case.

The proposed method is orders of magnitude more efficient than existing approaches.

The method is applicable to a wide range of probability estimation problems.

Abstract

In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding bound is an immediate consequence of the theory. Moreover, we propose a rigorous and efficient method for probability estimation, which is an adaptive Monte Carlo estimation method based on truncated inverse binomial sampling. Our proposed method of probability estimation can be orders of magnitude more efficient as compared to existing methods in literature and widely used software.