AABC: approximate approximate Bayesian computation for inference in population-genetic models.

Area of Science:

• Computational Biology
• Statistical Inference
• Population Genetics

Background:

• Approximate Bayesian computation (ABC) methods are vital for parameter inference in complex models where likelihood evaluation is intractable.
• The success of ABC relies on computationally inexpensive data simulation from the model of interest.
• Challenges arise when simulating data is computationally prohibitive, hindering standard ABC application.

Purpose of the Study:

• To introduce "approximate approximate Bayesian computation" (AABC), a novel class of computationally fast inference methods.
• To extend ABC to models with computationally expensive data simulation processes.
• To provide a viable alternative for parameter inference when standard ABC is infeasible.

Main Methods:

• AABC involves initial simulation of a limited number of data sets from the true model.
• A statistical approximation model is then employed, conditioned on the initial data, for efficient large-scale data simulation.
• This approach approximates the target model to overcome computational bottlenecks.

Main Results:

• AABC is shown to converge to the true posterior distribution obtained by ABC under mild assumptions.
• Convergence is demonstrated as the number of simulated data sets and observed data sample size increase.
• The method's performance is validated on population genetics models, including natural selection and admixture history.

Conclusions:

• AABC offers a computationally efficient solution for Bayesian inference in models with expensive simulation costs.
• This method significantly broadens the applicability of ABC, particularly in fields like population genetics.
• AABC is particularly useful for complex forward-in-time simulations in population genetics research.