arXiv subjects

Cici Chen Gu

Publications and source records attributed to Cici Chen Gu.

2 recordsLinked to original sources

arXiv2026

The MCMC convergence graph: a diagnostic for multimodal posteriors

Multimodality is common in many scientific and engineering applications. However, standard Markov chain Monte Carlo (MCMC) convergence diagnostics often penalise multimodality in practice by conflating overall poor mixing with groups of chains that have mixed well within distinct modes. To diagnose multimodality rather than flag it as a sampling failure, we introduce the MCMC convergence graph: a graph-based diagnostic that computes pairwise R-hat values between chains and summarises them in a graph, revealing sets of chains that explore the same posterior mode. We implement the method in the probabilistic programming framework Stan and demonstrate its use on worked examples ranging from regression models with inherent multimodality in the data, to a pharmacokinetic model for which multimodality reflects non-identifiability. The graph-based diagnostic, which we make freely available in the R package mcmcConvergenceGraph and which accepts MCMC output from any sampler, provides both graphical and numerical summaries of MCMC behaviour for diagnosing multimodality.

stat.ME↗

arXiv2026

A practical introduction to ODE modelling in Stan for biological systems

Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these purposes. One such tool is Stan, a freely available and open-source probabilistic programming framework that provides efficient methods for estimating model parameters from data using computational Bayesian inference algorithms. Stan includes built-in mechanisms for working with ordinary differential equation (ODE) models, which are widely used in mathematical biology and related fields to study simulated, experimental, and real-world systems that change over time. Through step-by-step worked examples, including both pedagogical toy models and applications with real data, this article provides a practical, self-contained introduction to performing parameter estimation and model evaluation for first-order linear and nonlinear ODE models in Stan. The article also explains key statistical methods that underpin Stan and discusses computational Bayesian modelling in the context of biological applications.

stat.CO↗