Model fitting and inference under Latent Equilibrium Processes.

Area of Science:

• Statistics
• Computational Biology
• Population Genetics

Background:

• Bayesian models with latent stationary stochastic processes are common in population genetics.
• The equilibrium distribution of these processes is often intractable, posing challenges for model fitting.
• Latent Equilibrium Process (LEP) models are used when data is observed at equilibrium.

Purpose of the Study:

• To develop a methodology for model fitting and inference in Bayesian Latent Equilibrium Process (LEP) models.
• To provide a practical implementation of Markov chain Monte Carlo (MCMC) for LEP models.
• To address the computational challenges associated with fitting these complex models.

Main Methods:

• Development of a novel methodology for implementing Markov chain Monte Carlo (MCMC) for Latent Equilibrium Process (LEP) models.
• Application of the methodology to Bayesian inference problems in population genetics.
• Demonstration using both simulated and real population genetics data sets.

Main Results:

• Successfully implemented MCMC for Bayesian inference in LEP models, overcoming previous implementation difficulties.
• The methodology is demonstrated to be effective for problems in population genetics, including parameter estimation (mutation rates, migration rates, population sizes).
• Computational intensity was noted, leading to a discussion on parallel implementation strategies.

Conclusions:

• The proposed methodology provides a viable approach for fitting and performing Bayesian inference on Latent Equilibrium Process (LEP) models.
• This work facilitates the analysis of complex population genetics data where underlying allele frequencies are unobserved.
• The study highlights the computational demands and suggests parallel computing as a solution for intensive model fitting.