
Dmytro Perepolkin
Doctoral student

The tenets of indirect inference in Bayesian models
Author
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.
Department/s
- Centre for Environmental and Climate Science (CEC)
- BECC: Biodiversity and Ecosystem services in a Changing Climate
- MERGE: ModElling the Regional and Global Earth system
Publishing year
2021-09-10
Language
English
Document type
Other
Publisher
OSF
Topic
- Probability Theory and Statistics
Keywords
- Bayesian Inference
- Quantile function
- quantile distribution
Status
Epub