TY - JOUR

T1 - A generalization of the Savage-Dickey density ratio for testing equality and order constrained hypotheses

AU - Mulder, Joris

AU - Wagenmakers, Eric-Jan

AU - Marsman, Maarten

N1 - Funding
Mulder is supported by an ERC starting grant (758791).

PY - 2022

Y1 - 2022

N2 - The Savage–Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli and Wasserman such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This article presents an extension of this generalization when the hypothesis has equality as well as order constraints on the parameters of interest. The methodology is used for a constrained multivariate t-test using the JZS Bayes factor and a constrained hypothesis test under the multinomial model.

AB - The Savage–Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli and Wasserman such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This article presents an extension of this generalization when the hypothesis has equality as well as order constraints on the parameters of interest. The methodology is used for a constrained multivariate t-test using the JZS Bayes factor and a constrained hypothesis test under the multinomial model.

KW - BAYES FACTORS

KW - Bayes factors

KW - Constrained hypotheses

KW - Constrained multinomial models

KW - Constrained multivariate Bayesiant-test

KW - INEQUALITY

UR - https://app-eu.readspeaker.com/cgi-bin/rsent?customerid=10118&lang=en_us&readclass=rs_readArea&url=https%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Ffull%2F10.1080%2F00031305.2020.1799861&dict=math&rule=math&xslrule=math

UR - http://www.scopus.com/inward/record.url?scp=85089908586&partnerID=8YFLogxK

U2 - 10.1080/00031305.2020.1799861

DO - 10.1080/00031305.2020.1799861

M3 - Article

SN - 0003-1305

VL - 76

SP - 102

EP - 109

JO - The American Statistician

JF - The American Statistician

IS - 2

ER -