arXiv subjects

Alex Ziyu Jiang

Publications and source records attributed to Alex Ziyu Jiang.

4 recordsLinked to original sources

arXiv2026

AI4BayesCode: From Natural Language Descriptions to Validated Modular Stateful Bayesian Samplers

Coding and computation remain major bottlenecks in Markov chain Monte Carlo (MCMC) workflows, especially as modern sampling algorithms have become increasingly complex and existing probabilistic programming systems remain limited in model support, extensibility, and composability. We introduce \textbf{AI4BayesCode}, an extensible LLM-driven system that translates natural-language Bayesian model descriptions into runnable, validated MCMC samplers. To improve reliability, AI4BayesCode adopts a modular design that decomposes models into modular sampling blocks and maps each block to a built-in sampling component, reducing the need to implement complex sampling algorithms from scratch. Reliability is further improved through pre-generation validation of model specifications and post-generation validation of generated sampler code. AI4BayesCode also introduces a novel recursively stateful coding paradigm for MCMC, allowing modular sampling components, potentially developed by different contributors, to be composed coherently within larger MCMC procedures. We develop a benchmark suite to evaluate AI4BayesCode for sampler-generation. Experiments show that AI4BayesCode can implement a wide range of Bayesian models from natural-language descriptions alone. As an open-ended system, its capability can continue to expand with improvements in the underlying AI agent and the addition of new built-in blocks. The software is available at https://ai4bayescode.com/.

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arXiv2025

Semiparametric estimation for multivariate Hawkes processes using dependent Dirichlet processes: An application to order flow data in financial markets

The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand interplay and price formation. In this work, we propose a semiparametric multivariate Hawkes process model that relies on (mixtures of) dependent Dirichlet processes to analyze order flow data. Such a formulation avoids the kind of strong parametric assumptions about the excitation functions of the Hawkes process that often accompany traditional models and which, as we show, are not justified in the case of order flow data. It also allows us to borrow information across dimensions, improving estimation of the individual excitation functions. To fit the model, we develop two algorithms, one using Markov chain Monte Carlo methods and one using a stochastic variational approximation. In the context of simulation studies, we show that our model outperforms benchmark methods in terms of lower estimation error for both algorithms. In the context of real order flow data, we show that our model can capture features of the excitation functions such as non-monotonicity that cannot be accommodated by standard parametric models.

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arXiv2025

BARTSIMP: flexible spatial covariate modeling and prediction using Bayesian additive regression trees

Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible regression models that allow for nonlinearities and interactions in the covariate specification. Existing machine learning approaches that allow for spatial dependence in the residuals fail to provide reliable uncertainty estimates. In this paper, we investigate the combination of a Gaussian process spatial model with a Bayesian Additive Regression Tree (BART) model. The computational burden of the approach is reduced by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested Laplace Approximation (INLA) technique. We study the performance of the method first via simulation. We then use the model to predict anthropometric responses in Kenya, with the data collected via a complex sampling design. In particular, household survey data are collected via stratified two-stage unequal probability cluster sampling, which requires special care when modeled.

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arXiv2025

Improvements on Scalable Stochastic Bayesian Inference Methods for Multivariate Hawkes Process

Multivariate Hawkes Processes (MHPs) are a class of point processes that can account for complex temporal dynamics among event sequences. In this work, we study the accuracy and computational efficiency of three classes of algorithms which, while widely used in the context of Bayesian inference, have rarely been applied in the context of MHPs: stochastic gradient expectation-maximization, stochastic gradient variational inference and stochastic gradient Langevin Monte Carlo. An important contribution of this paper is a novel approximation to the likelihood function that allows us to retain the computational advantages associated with conjugate settings while reducing approximation errors associated with the boundary effects. The comparisons are based on various simulated scenarios as well as an application to the study the risk dynamics in the Standard & Poor's 500 intraday index prices among its 11 sectors.

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