统计计算
Importance sampling (IS) is commonly used for cross validation (CV) in Bayesian models, because it only involves reweighting existing posterior draws without needing to re-estimate the model by re-running Markov chain Monte Carlo (MCMC).…
We prove that the true underlying directed acyclic graph (DAG) in Gaussian linear structural equation models is identifiable as the minimum-trace DAG when the error variances are weakly increasing with respect to the true causal ordering.…
Conducting research often involves managing multiple disconnected tools for survey design, data collection, response analysis, and report generation, leading to inefficiencies, increased error risks, and challenges in ensuring…
Linear mixed models (LMM) are widely adopted in genome-wide association studies (GWAS) to account for population stratification and cryptic relatedness. However, the parameter estimation of LMMs imposes substantial computational burdens due…
Robust estimators for linear regression require non-convex objective functions to shield against adverse affects of outliers. This non-convexity brings challenges, particularly when combined with penalization in high-dimensional settings.…
The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but a naive sequential implementation becomes impractical online due to high…
Errors in variables (Deming) regression of measurements spanning a wide range of values requires appropriate weighting to reflect nonconstant variance. Precision profile models, mathematical relationships between measurement variance and…
For random-walk Metropolis (RWM) and parallel tempering (PT) algorithms, an asymptotic acceptance rate of around 0.234 is known to be optimal in certain high-dimensional limits. However, its practical relevance is uncertain due to…
We introduce methodology for real-time inference in general-state-space hidden Markov models. Specifically, we extend recent advances in controlled sequential Monte Carlo (CSMC) methods-originally proposed for offline smoothing-to the…
Estimating rare events in complex systems is a key challenge in reliability analysis. The challenge grows in multimodal problems, where traditional methods often rely on a small set of design points and risk overlooking critical failure…
Piecewise deterministic Markov processes provide scalable methods for sampling from the posterior distributions in big data settings by admitting principled sub-sampling strategies that do not bias the output. An important example is the…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
We consider the branch-length estimation problem on a bifurcating tree: a character evolves along the edges of a binary tree according to a two-state symmetric Markov process, and we seek to recover the edge transition probabilities from…
Hamiltonian Monte Carlo (HMC) is widely used for sampling from high dimensional target distributions with densities known up to proportionality. While HMC exhibits favorable scaling properties in high dimensions, it struggles with strongly…
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…
In this study, we present a method for predicting the representativity of the phase fraction observed in a single image (2D or 3D) of a material. Traditional approaches often require large datasets and extensive statistical analysis to…
Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by…
We consider a bivariate, possibly non-homogeneous, finite-state Markov chain $(X,U)=\{(X_t,U_t)\}_{t=1}^n$. We are interested in the marginal process $X$, which typically is not a Markov chain. The goal is to find a realization (path)…
This study introduces the SH-MBS-GARCH model, a hysteretic multivariate Bayesian structural GARCH framework that integrates hard and soft information to capture the joint dynamics of multiple financial time series, incorporating hysteretic…