Adaptive Sampling for Estimating Distributions: A Bayesian Upper Confidence Bound Approach

TL;DR

This paper introduces a Bayesian UCB-based adaptive sampling method for estimating probability distributions, demonstrating improved performance in practical applications like SARS-CoV-2 seroprevalence surveys.

Contribution

It proposes a Bayesian variant of UCB for adaptive sampling, providing tighter confidence bounds and better estimation accuracy over existing methods.

Findings

Bayesian UCB approach outperforms traditional methods in simulations.

Application to SARS-CoV-2 seroprevalence survey shows practical effectiveness.

Significant performance gains demonstrated in real-world data.

Abstract

The problem of adaptive sampling for estimating probability mass functions (pmf) uniformly well is considered. Performance of the sampling strategy is measured in terms of the worst-case mean squared error. A Bayesian variant of the existing upper confidence bound (UCB) based approaches is proposed. It is shown analytically that the performance of this Bayesian variant is no worse than the existing approaches. The posterior distribution on the pmfs in the Bayesian setting allows for a tighter computation of upper confidence bounds which leads to significant performance gains in practice. Using this approach, adaptive sampling protocols are proposed for estimating SARS-CoV-2 seroprevalence in various groups such as location and ethnicity. The effectiveness of this strategy is discussed using data obtained from a seroprevalence survey in Los Angeles county.