Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale...

Area of Science:

• Computational Statistics
• Data-driven Modeling
• Applied Mathematics

Background:

• Parameter inference is crucial for understanding data-driven models.
• Stochastic models, essential for incorporating uncertainty, complicate parameter inference.
• Bayesian statistics provides a framework for learning from data and quantifying uncertainty.

Purpose of the Study:

• To develop a novel, exact, and efficient method for generating posterior parameter distributions.
• To apply this method to stochastic differential equation models calibrated with time series data.

Main Methods:

• Reinterpreting posterior distributions as statistical mechanics partition functions.
• Employing Hamiltonian Monte Carlo with multiple time-scale integration.
• Analytically solving fast dynamics in one-dimensional problems.

Main Results:

• A highly efficient and parallelizable algorithm for posterior distribution sampling.
• Successful application to stochastic differential equation models.
• Demonstrated applicability to a broad range of inference problems.

Conclusions:

• The proposed method offers a significant advancement in parameter inference for stochastic models.
• It enables accurate probabilistic predictions by generating posterior parameter distributions.
• The approach is versatile and computationally efficient.