Work

Bayesian estimation of discretely observed diffusion processes using Wiener chaos expansion

Year: 2025

Type: article

Abstract: We employ a Bayesian inference technique for discretely observed diffusion processes that arise as solutions of stochastic differential equations. Our aim is to estimate the parameters of the stochastic differential equation. To achieve this, we frame the estimation procedure as a missing data problem. In this framework, the complete dataset includes the theoretically continuous-time path between observed points. We propose augmenting the dataset and using a Gibbs sampler to derive Bayesian estimators for the parameters in cases where the diffusion process is observed discretely. The Gibbs sampler is integrated with a diffusion bridge simulation technique based on the Wiener chaos expansion. The methodology and its implementation are demonstrated through examples and simulation studies. We also present an application to actual data.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100644

Authors: Fernando Baltazar-Larios, Gabriel Adrián Salcedo-Varela, Francisco Delgado-Vences

Institution: Universidad Nacional Autónoma de México

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funder: Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México