arXiv subjects

Jiezhong Wu

Publications and source records attributed to Jiezhong Wu.

4 recordsLinked to original sources

arXiv2026

Stopping Rules for Monte Carlo Methods: A Review

Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many more are currently being refined and developed. This article aims to deliver an up-to-date review of recent developments in sequential stopping rules, with a deliberate emphasis on Monte Carlo methods for estimating an unknown expectation, including binomial proportions, primarily under standard iid sampling and also under certain lightly generalized settings. These methodologies have long served and likely will continue to serve, as fundamental bases for both theoretical and practical developments in stopping rules for general statistical inference, advanced Monte Carlo techniques, and their modern applications. Building upon over a hundred references and empirical studies, we explore the essential aspects of these methods, such as core assumptions, numerical algorithms, convergence properties, and practical trade-offs to guide further developments, particularly at the intersection of sequential stopping rules and related areas of research.

stat.ME↗

arXiv2026

Bootstrapped Control Limits for Score-Based Concept Drift Control Charts

Monitoring for changes in a predictive relationship represented by a fitted supervised learning model (i.e., concept drift detection) is a widespread problem in modern data-driven applications. A general and powerful Fisher score-based concept drift approach was recently proposed, in which detecting concept drift reduces to detecting changes in the mean of the model's score vector using a multivariate exponentially weighted moving average (MEWMA). To implement the approach, the initial data must be split into two subsets. The first subset serves as the training sample to which the model is fit, and the second subset serves as an out-of-sample test set from which the MEWMA control limit (CL) is determined. In this paper, we retain the same score-based MEWMA monitoring statistic as the existing method and focus instead on improving the computation of the control limit. We develop a novel nested bootstrap procedure for calibrating the CL that allows the entire initial sample to be used for model fitting, thereby yielding a more accurate baseline model while eliminating the need for a large holdout set. The outer bootstrap loop is fully parallelizable, making the method computationally practical, with CL setup times comparable to or faster than the existing method. We show that a standard nested bootstrap substantially underestimates the variability of the monitoring statistic and develop a 0.632-like correction that appropriately accounts for this. We demonstrate the advantages with numerical examples.

stat.ME↗

arXiv2026

SELDON: Supernova Explosions Learned by Deep ODE Networks

The discovery rate of optical transients will explode to 10 million public alerts per night once the Vera C. Rubin Observatory's Legacy Survey of Space and Time comes online, overwhelming the traditional physics-based inference pipelines. A continuous-time forecasting AI model is of interest because it can deliver millisecond-scale inference for thousands of objects per day, whereas legacy MCMC codes need hours per object. In this paper, we propose SELDON, a new continuous-time variational autoencoder for panels of sparse and irregularly time-sampled (gappy) astrophysical light curves that are nonstationary, heteroscedastic, and inherently dependent. SELDON combines a masked GRU-ODE encoder with a latent neural ODE propagator and an interpretable Gaussian-basis decoder. The encoder learns to summarize panels of imbalanced and correlated data even when only a handful of points are observed. The neural ODE then integrates this hidden state forward in continuous time, extrapolating to future unseen epochs. This extrapolated time series is further encoded by deep sets to a latent distribution that is decoded to a weighted sum of Gaussian basis functions, the parameters of which are physically meaningful. Such parameters (e.g., rise time, decay rate, peak flux) directly drive downstream prioritization of spectroscopic follow-up for astrophysical surveys. Beyond astronomy, the architecture of SELDON offers a generic recipe for interpretable and continuous-time sequence modeling in any time domain where data are multivariate, sparse, heteroscedastic, and irregularly spaced.

astro-ph.IM↗

arXiv2025

Stopping Rules for Monte Carlo Methods of Martingale Difference Type

We establish a practical and easy-to-implement sequential stopping rule for the martingale central limit theorem, focusing on Monte Carlo methods for estimating the mean of a non-iid sequence of martingale difference type. Starting with an impractical scheme based on the standard martingale central limit theorem, we progressively address its limitations from implementation perspectives in the non-asymptotic regime. Along the way, we compare the proposed schemes with their counterparts in the asymptotic regime. The developed framework has potential applications in various domains. Numerical results are provided to demonstrate the effectiveness of the developed stopping rules in terms of reliability and complexity.

math.ST↗