Open Collections

Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we address the problem of estimating the parameter, p, of a Bernoulli process. This problem arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. We first explore an oracle-aided trial allocation, which demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires a simple trial allocation gain quantity. Motivated by realizing this gain without an oracle, we present a trellis-based framework for representing and optimizing data-dependent stopping rules. Considering the case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements: up to 4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.

Mathematics; Information and communication, circuits; Functional analysis; Applied computer science

video/mp4

Author affiliation: Boston University

2019-04-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69965

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/