This is a repo with code examples for simulating and performing Bayesian estimation of single and double Pareto log normal distributions using Pigeons.jl. This class of distributions is quite hard to fit in general, and the default samplers in Stan do a poor job. This is also the case for most of the samplers in Pigeons.jl, with the exception of variational parallel tempering, so if you want to use these methods, please use doubleparetolognormal.jl for Double Pareto Log Normal or singleparetolognormalvariational.jl for Single Pareto Log Normal for one collection of settings that work, or the alternative parameterization in soft_asym_laplace.stan accessed from soft_asym_laplace.jl, which may work better for well-identified cases.

This code is provided as is and will have to be modified to apply to your applications. For installation of the Julia packages, simply activate the project. BridgeStan, which requires an active Stan installation, can be installed following these instructions. To call your installation of BridgeStan, replace the variable bridgestan_path in .env with the location of the directory in which it is installed.

The models and Stan code are taken mostly from from a Stan forums post, with minor modifications. See their discussion for context and references. Credit to Rachael Meager, Michael Betancourt, Ben Goodrich, and Sean Pinkney for the code snippets that became the .stan files, and all R code. Any added mistakes are my own.

Also, see Alexis Toda's site for theory and applications of double pareto log normal distributions in economics.