A Multiresolution Method for Parameter Estimation of Diffusion Processes.

Area of Science:

• Computational Science
• Statistical Modeling
• Financial Mathematics

Background:

• Diffusion processes are crucial in various scientific fields but are often observed at discrete time points.
• Analytic likelihood forms for discretely observed diffusion data are rare, complicating parametric inference.
• Existing methods often rely on discrete-time approximations, which can lack accuracy.

Purpose of the Study:

• To develop a more accurate and efficient Bayesian framework for inferring parameters of diffusion processes from discretely observed data.
• To address the challenge of non-existent analytic likelihoods in practical data analysis.
• To improve upon existing computational strategies for diffusion model inference.

Main Methods:

• A novel multiresolution Bayesian framework is proposed.
• The methodology employs multiple approximations and extrapolation techniques.
• The approach is benchmarked against traditional Gibbs sampling strategies.

Main Results:

• The multiresolution framework demonstrates significantly improved speed and accuracy.
• Successful application to diverse inference problems in biophysics and finance.
• Effectiveness shown even for multivariate diffusion models with unobserved components.

Conclusions:

• The proposed multiresolution Bayesian framework provides a powerful tool for diffusion process inference.
• This method overcomes limitations of existing techniques for discretely observed data.
• The approach offers practical advantages for complex real-world applications.