Simulation-Based Inference of Bayesian Hierarchical Models While Checking for Model Misspecification †
Abstract
:1. Introduction
2. Method
2.1. Bayesian Hierarchical Models with a Latent Function
2.2. Latent Function Inference with SELFI
2.3. Check for Model Misspecification
2.4. Score Compression and Simulation-Based Inference
3. Lotka–Volterra BHM
3.1. Lotka–Volterra Solver
3.2. Lotka–Volterra Observer
3.2.1. Full Data Model
- Demographic Gaussian noise with zero mean and variance proportional to the true underlying population, i.e., and . The parameter r gives the strength of demographic noise.
- Observational Gaussian noise that accounts for observer efficiency, coupling prey and predators such thatThe parameter s gives the overall amplitude of observational noise, and the parameter t controls the strength of the non-diagonal component (it should be chosen such that the covariance matrix appearing in Equation (18) is positive semi-definite).
3.2.2. Simplified Data Model
4. Results
4.1. Inference of Population Functions with SELFI
4.2. Check for Model Misspecification
4.3. Score Compression
4.4. Inference of Parameters Using Likelihood-Free Rejection Sampling
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Leclercq, F. Simulation-Based Inference of Bayesian Hierarchical Models While Checking for Model Misspecification. Phys. Sci. Forum 2022, 5, 4. https://doi.org/10.3390/psf2022005004
Leclercq F. Simulation-Based Inference of Bayesian Hierarchical Models While Checking for Model Misspecification. Physical Sciences Forum. 2022; 5(1):4. https://doi.org/10.3390/psf2022005004
Chicago/Turabian StyleLeclercq, Florent. 2022. "Simulation-Based Inference of Bayesian Hierarchical Models While Checking for Model Misspecification" Physical Sciences Forum 5, no. 1: 4. https://doi.org/10.3390/psf2022005004
APA StyleLeclercq, F. (2022). Simulation-Based Inference of Bayesian Hierarchical Models While Checking for Model Misspecification. Physical Sciences Forum, 5(1), 4. https://doi.org/10.3390/psf2022005004