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Title	Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation
Creator	Murray-Bruce, John
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-10-29T14:33
Description	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.
Extent	32.0
Subject	Mathematics Information and communication, circuits Functional analysis Applied computer science
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: Boston University
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-04-28
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0378479
URI	http://hdl.handle.net/2429/69965
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Postdoctoral
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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