Simulation based composite likelihood.

Area of Science:

• Statistics
• Computational Biology
• Machine Learning

Background:

• High-dimensional hidden Markov models (HMMs) present significant computational challenges, primarily due to the exponential increase in cost for likelihood calculations.
• Existing methods often struggle with scalability and efficiency when dealing with complex, high-dimensional data.

Purpose of the Study:

• To introduce a novel composite likelihood approach, Simulation Based Composite Likelihood (SimBa-CL), for efficient inference in high-dimensional HMMs.
• To provide a method that overcomes the computational bottlenecks associated with traditional likelihood calculations in complex models.

Main Methods:

• SimBa-CL approximates the model's likelihood by the product of its marginals, estimated via Monte Carlo sampling.
• The approach utilizes automatic differentiation for efficient gradient and Hessian calculation, facilitating parameter optimization.
• It shares similarities with Approximate Bayesian Computation (ABC) by requiring model simulations but differs by providing a guided likelihood approximation.

Main Results:

• Extensive empirical results validate the theoretical underpinnings of SimBa-CL.
• The method demonstrates significant advantages over existing techniques like Sequential Monte Carlo (SMC).
• SimBa-CL was successfully applied to analyze real-world Aphtovirus data, showcasing its practical utility.

Conclusions:

• SimBa-CL offers a computationally efficient and effective solution for inference in high-dimensional hidden Markov models.
• The method's ability to speed up optimization and construct confidence sets makes it a valuable tool for complex statistical modeling.
• Its successful application to biological data highlights its potential impact in various scientific domains.