Generalised Likelihood Profiles

This repository contains reference MATLAB functions and scripts to demonstrate the generalised likelihood profile approach for frequentist style parameter estimation when the likelihood is intractable.

Developers

David Warne$^{1,2}$ (david.warne@qut.edu.au), https://scholar.google.com.au/citations?user=t8l-kuoAAAAJ&hl=en Christopher Drovandi$^{1,2}$ Elliot Carr$^{1}$ Matthew Simpson$^{1}$

1. School of Mathematical Sciences, Faculty of Science, Queensland Univeristy of Technology, Australia
2. Centre for Data Science, Queensland University of Technology, Australia

Citation Information

This code is provided as supplementary information to the paper,

David J Warne, Oliver J. Maclaren, Elliot J. Carr, Matthew J. Simpson, and Christopher Drovandi. Generalised likelihood profiles for models with intractable likelihoods. ArXiv preprint (TBA)

Licensing

This source code is licensed under the GNU General Public License Version 3. Copyright (C) 2023 David J. Warne

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <https://www.gnu.org/licenses/>.

Contents

The directory structure is as follows
|-- init.m                                  Adds all functions to the MATLAB Path
|-- LossFuctions/
    |-- discrete_fisher_divergence.m        
    |-- moments_distance.m
|-- GeneralisedLikelihood/
    |-- generalisedLikelihoodProfiles.m    Main algorithm to calibrate profiles
    |-- compute_coverage.m
|-- Examples/
    |-- ConwayMaxwellPoisson/
        |-- glp_cmp_model.m                Run Conway-Maxwell-Poisson example
        |-- com_rnd.m
        |-- com_pdf_unnorm.m
        |-- com_pdf.m
        |-- com_logpdf.m
        |-- com_cdf.m
    |-- BiasedStochasticDiffusion/
        |-- glp_biased_diffusion.m        Run biased stochastic transport example
        |-- bootstrapMoments.m
        |-- Stochastic_Model.m
        |-- Exact_Moments.m
        |-- Exact_Moments_x0.m
        |-- Numerical_Moments.m
        |-- Numerical_Moments_x0.m

Usage

1. Start MATLAB

2. In MATLAB browse to the repository folder GeneralisedLikelihoodProfiles/

3. In the MATLAB command prompt, run >> init to set up the paths of all the example implementations.

4. Run an example either
   >> glp_cmp_model to generate profiles like Fig 1 for the Conway-Maxwell-Poisson model. or >> glp_biased_diffusion to generate Figs 3 and 4 for th biased stochastic transport model.

5. To obtain coverage plots set validateTF = 1 at line 19 in glp_biased_diffusion.m