A comparison of numerical approaches for statistical inference with stochastic models

Area of Science:

• Environmental science
• Environmental modeling
• Stochastic processes

Background:

• Complex environmental systems exhibit inherent uncertainty due to limited knowledge of mechanisms and influence factors.
• Accurate prediction and decision-making necessitate quantifying and communicating this uncertainty, often requiring stochastic models.

Purpose of the Study:

• To address the high-dimensional inference challenges in calibrating stochastic models for environmental systems.
• To compare the effectiveness of three numerical approaches for uncertainty quantification in hydrological data analysis.

Main Methods:

• Hamiltonian Monte Carlo (HMC)
• Particle Markov Chain Monte Carlo (PMCMC)
• Conditional Ornstein-Uhlenbeck (COU) Sampling
• Application to a stochastic hydrological model for analyzing hydrological data.

Main Results:

• All three investigated numerical techniques demonstrated comparable performance for the analyzed hydrological system.
• The choice of technique may also depend on generality and practical implementation considerations.

Conclusions:

• Effective uncertainty quantification in environmental systems is achievable with advanced numerical methods.
• The selection of a specific stochastic modeling technique should balance performance with practical applicability.