Yau-YauAL: A computer tool for solving nonlinear filtering problems

TL;DR

YauYauAL is an R-based software package that simplifies the implementation of the Yau-Yau nonlinear filter, enabling real-time visualization and application to complex stochastic systems across various scientific fields.

Contribution

It introduces a user-friendly, open-source software tool combining R and C++ for efficient nonlinear filtering, making advanced methods accessible to practitioners without specialized programming skills.

Findings

Provides real-time parameter adjustment and visualization

Employs finite difference methods for stable solutions

Facilitates broader application of nonlinear filtering

Abstract

The Yau-Yau nonlinear filter has increasingly emerged as a powerful tool to study stochastic complex systems. To leverage it to a wider spectrum of application scenarios, we pack the Yau-Yau filtering ALgorithms (YauYauAL) into a package of computer software. Yau-YauAL was written in R, designed to simplify the implementation of the Yau-Yau filter for solving nonlinear filtering problems. Combining R's accessibility with C++ (via Rcpp) for computational efficiency, YauYauAL provides an intuitive Shiny-based interface that enables real-time parameter adjustment and result visualization. At its core, YauYauAL employs finite difference methods to numerically solve the Kolmogorov forward equation, ensuring a stable and accurate solution even for complex systems. YauYauAL's modular design and open-source framework further encourage customization and community-driven development. YauYauAL aims to bridge the gap between theoretical nonlinear filtering methods and practical applications, without requiring expertise in differential equation solving or programming, fostering its broader impact on various scientific fields, such as signal processing, finance, medicine, and biology among a long list.