Bayesian learning under non-stationary dependence
Bayesian learning under non-stationary dependence
We study limit beliefs in a learning-by-experimentation environment where: (a) givenan opportunity for experimentation, an agent decides to experiment if past experimen-tation is below a history-dependent threshold; (b) an experimentation opportunity ariseswith a conditional probability that is non-decreasing in the extent of past experimenta-tion; (c) the degree of monotonicity in (b) is governed by a parameter which is unknownto a Bayesian agent making inferences based on observed history. Since experimentationopportunities are dependent and heterogeneously distributed random variables with sam-ple moments that do not necessarily concentrate around their population counterparts,the usual techniques for establishing asymptotic learning based on laws of large numberscannot be used. We overcome this difficulty by establishing a novela.s.positive asymp-totic lower bound for the sample mean of experimentation opportunities. We can thusestablish that asymptotic learning of the true value of the initially unknown parameteroccurs, with convergence of posterior beliefs taking place at an exponential rate.
Bose, Subir
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Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Makris, Miltiadis
966df0dc-9caf-409e-9cbe-f2a800cdffda
Bose, Subir
b5482f8d-03c8-4755-87e2-32576546edbc
Magdalinos, Tassos
ded74727-1ed4-417d-842f-00ea86a3bc31
Makris, Miltiadis
966df0dc-9caf-409e-9cbe-f2a800cdffda
[Unknown type: UNSPECIFIED]
Abstract
We study limit beliefs in a learning-by-experimentation environment where: (a) givenan opportunity for experimentation, an agent decides to experiment if past experimen-tation is below a history-dependent threshold; (b) an experimentation opportunity ariseswith a conditional probability that is non-decreasing in the extent of past experimenta-tion; (c) the degree of monotonicity in (b) is governed by a parameter which is unknownto a Bayesian agent making inferences based on observed history. Since experimentationopportunities are dependent and heterogeneously distributed random variables with sam-ple moments that do not necessarily concentrate around their population counterparts,the usual techniques for establishing asymptotic learning based on laws of large numberscannot be used. We overcome this difficulty by establishing a novela.s.positive asymp-totic lower bound for the sample mean of experimentation opportunities. We can thusestablish that asymptotic learning of the true value of the initially unknown parameteroccurs, with convergence of posterior beliefs taking place at an exponential rate.
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In preparation date: 2020
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Local EPrints ID: 472028
URI: http://eprints.soton.ac.uk/id/eprint/472028
PURE UUID: df6268bb-cfd1-4a45-932e-b5ec47ca336e
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Date deposited: 24 Nov 2022 17:30
Last modified: 17 Mar 2024 07:56
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Author:
Subir Bose
Author:
Miltiadis Makris
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