Likelihood-Free Inference in High-Dimensional Models.

Area of Science:

• Statistical inference
• Computational biology
• Evolutionary genetics

Background:

• Likelihood-free methods are crucial for statistical inference but are limited to low-dimensional models due to reliance on summary statistics and manageable acceptance rates.
• Existing methods struggle with high-dimensional models where likelihood evaluation is computationally intensive.

Purpose of the Study:

• To develop a novel likelihood-free Markov chain Monte Carlo (MCMC) method that overcomes the limitations of existing approaches.
• To enable statistical inference in very high-dimensional models, expanding the applicability of likelihood-free methods.

Main Methods:

• Introduced a new MCMC method that updates one parameter per iteration.
• Accepts or rejects parameter updates based on subsets of statistics that are approximately sufficient for that parameter.
• Derived that a one-dimensional combination of statistics per parameter is sufficient for linear models and can be found empirically.

Main Results:

• The novel method significantly increases acceptance rates, making it suitable for high-dimensional models.
• Demonstrated scalability to very high-dimensional models using toy examples.
• Successfully applied the method to jointly infer population size, distribution of fitness effects (DFE), and selection coefficients from influenza drug resistance data.

Conclusions:

• The proposed likelihood-free MCMC method offers a powerful and scalable solution for statistical inference in complex, high-dimensional models.
• This advancement has broad implications for various scientific fields, including evolutionary genetics and computational biology.
• The method's ability to handle high dimensionality and complex inference tasks opens new avenues for data analysis in biological systems.