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Ullrika Sahlin. Foto.

Ullrika Sahlin

Universitetslektor

Ullrika Sahlin. Foto.

The tenets of indirect inference in Bayesian models

Författare

  • Dmytro Perepolkin
  • Benjamin Goodrich
  • Ullrika Sahlin

Summary, in English

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.

Avdelning/ar

  • Centrum för miljö- och klimatvetenskap (CEC)
  • BECC: Biodiversity and Ecosystem services in a Changing Climate
  • MERGE: ModElling the Regional and Global Earth system

Publiceringsår

2021-09-10

Språk

Engelska

Dokumenttyp

Övrigt

Förlag

OSF

Ämne

  • Probability Theory and Statistics

Nyckelord

  • Bayesian Inference
  • Quantile function
  • quantile distribution

Aktiv

Epub