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The tenets of indirect inference in Bayesian models

Perepolkin, Dmytro LU orcid ; Goodrich, Benjamin and Sahlin, Ullrika LU orcid (2021)
Abstract
This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips... (More)
This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful. (Less)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Other contribution
publication status
epub
subject
keywords
Bayesian Inference, Quantile function, quantile distribution
pages
36 pages
publisher
OSF
DOI
10.31219/osf.io/enzgs
language
English
LU publication?
yes
id
e6903446-6f67-4f71-80f0-43873cc8d504
date added to LUP
2021-09-10 14:06:21
date last changed
2025-04-04 15:17:41
@misc{e6903446-6f67-4f71-80f0-43873cc8d504,
  abstract     = {{This paper extends the application of Bayesian inference to probability distributions defined in terms of its quantile function. We describe the method of *indirect likelihood* to be used in the Bayesian models with sampling distributions which lack an explicit cumulative distribution function. We provide examples and demonstrate the equivalence of the "quantile-based" (indirect) likelihood to the conventional "density-defined" (direct) likelihood. We consider practical aspects of the numerical inversion of quantile function by root-finding required by the indirect likelihood method. In particular, we consider a problem of ensuring the validity of an arbitrary quantile function with the help of Chebyshev polynomials and provide useful tips and implementation of these algorithms in Stan and R. We also extend the same method to propose the definition of an *indirect prior* and discuss the situations where it can be useful.}},
  author       = {{Perepolkin, Dmytro and Goodrich, Benjamin and Sahlin, Ullrika}},
  keywords     = {{Bayesian Inference; Quantile function; quantile distribution}},
  language     = {{eng}},
  month        = {{09}},
  publisher    = {{OSF}},
  title        = {{The tenets of indirect inference in Bayesian models}},
  url          = {{http://dx.doi.org/10.31219/osf.io/enzgs}},
  doi          = {{10.31219/osf.io/enzgs}},
  year         = {{2021}},
}