Bayesian Methods for Global Optimization in the Gaussian Case

Mathematics and Its Applications - Bayesian Approach to Global Optimization ◽

10.1007/978-94-009-0909-0_5 ◽

1989 ◽

pp. 79-116

Author(s):

Jonas Mockus

Keyword(s):

Global Optimization ◽

Bayesian Methods ◽

Gaussian Case

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Bayesian Methods in Global Optimization

Operations Research ’91 ◽

10.1007/978-3-642-48417-9_6 ◽

1992 ◽

pp. 16-18

Author(s):

Bruno Betrò

Keyword(s):

Global Optimization ◽

Bayesian Methods

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Bayesian methods in global optimization

Journal of Global Optimization ◽

10.1007/bf00120661 ◽

1991 ◽

Vol 1 (1) ◽

pp. 1-14 ◽

Cited By ~ 31

Author(s):

Bruno Betr�

Keyword(s):

Global Optimization ◽

Bayesian Methods

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Bayesian Applications in Auditory Research

Journal of Speech Language and Hearing Research ◽

10.1044/2018_jslhr-h-astm-18-0228 ◽

2019 ◽

Vol 62 (3) ◽

pp. 577-586 ◽

Cited By ~ 9

Author(s):

Garnett P. McMillan ◽

John B. Cannon

Keyword(s):

Monte Carlo ◽

Markov Chain ◽

Bayesian Methods ◽

Prior Distribution ◽

Interim Analysis ◽

Iterative Process ◽

Bayes Theorem ◽

Sound Therapy ◽

The Many ◽

Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

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