统计计算

This article explores the optimization of variational approximations for posterior covariances of Gaussian multiway arrays. To achieve this, we establish a natural differential geometric optimization framework on the space using the…

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…

It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…

In Fern\'andez-Dur\'an (2004), a new family of circular distributions based on nonnegative trigonometric sums (NNTS models) is developed. Because the parameter space of this family is the surface of the hypersphere, an efficient Newton-like…

We present a randomized Kaczmarz method for linear discriminant analysis (rkLDA), an iterative randomized approach to binary-class Gaussian model linear discriminant analysis (LDA) for very large data. We harness a least squares formulation…

We consider the challenge of estimating the model parameters and latent states of general state-space models within a Bayesian framework. We extend the commonly applied particle Gibbs framework by proposing an efficient particle generation…

Diagnostic classification models (DCMs) offer statistical tools to inspect the fined-grained attribute of respondents' strengths and weaknesses. However, the diagnosis accuracy deteriorates when misspecification occurs in the predefined…

In this paper, we present MCBench, a benchmark suite designed to assess the quality of Monte Carlo (MC) samples. The benchmark suite enables quantitative comparisons of samples by applying different metrics, including basic statistical…

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…

In this paper we address the problem of performing Bayesian inference for the parameters of a nonlinear multi-output model and the covariance matrix of the different output signals. We propose an adaptive importance sampling (AIS) scheme…

The nature of modern data is increasingly real-time, making outlier detection crucial in any data-related field, such as finance for fraud detection and healthcare for monitoring patient vitals. Traditional outlier detection methods, such…

The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…

We develop sampling algorithms to fit Bayesian hierarchical models, the computational complexity of which scales linearly with the number of observations and the number of parameters in the model. We focus on crossed random effect and…

Importance sampling (IS) is a powerful Monte Carlo (MC) technique for approximating intractable integrals, for instance in Bayesian inference. The performance of IS relies heavily on the appropriate choice of the so-called proposal…

Parallel tempering is a meta-algorithm for Markov Chain Monte Carlo that uses multiple chains to sample from tempered versions of the target distribution, enhancing mixing in multi-modal distributions that are challenging for traditional…

Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation…

High-dimensional time series analysis has become increasingly important in fields such as finance, economics, and biology. The two primary tasks for high-dimensional time series analysis are modeling and statistical inference, which aim to…

We describe the R package MOODE and demonstrate its use to find multi-objective optimal experimental designs. Multi-Objective Optimal Design of Experiments (MOODE) targets the experimental objectives directly, ensuring that the full set of…

In this paper we derive a new direct inversion method to simulate squared Bessel processes. Since the transition probability of these processes can be represented by a non-central chi-square distribution, we construct an efficient and…

Generalized additive models (GAMs, Hastie & Tibshirani, 1990; Wood, 2017) are an extension of the generalized linear model that allows the effects of covariates to be modelled as smooth functions. GAMs are increasingly used in many areas of…