统计计算
Non-Gaussian spatial and spatio-temporal data are becoming increasingly prevalent, and their analysis is needed in a variety of disciplines. FRK is an R package for spatial/spatio-temporal modelling and prediction with very large data sets…
A new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper…
In several applied fields, multimodality assessment is a crucial task as a previous exploratory tool or for determining the suitability of certain distributions. The goal of this paper is to present the utilities of the R package multimode,…
In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile…
Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many…
The theory and computational methods for custom-made Gauss quadrature have been described in Gautschi's 2004 monograph. Gautschi has also provided Fortran and MATLAB code for the implementation and illustration of these methods. We have…
There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there…
Data depth, introduced by Tukey (1975), is an important tool in data science, robust statistics, and computational geometry. One chief barrier to its broader practical utility is that many common measures of depth are computationally…
In the last few decades, uncertainty quantification (UQ) methods have been used widely to ensure the robustness of engineering designs. This chapter aims to detail recent advances in popular uncertainty quantification methods used in…
This paper examines the problem of computing a canonical smallest covering region for an arbitrary discrete probability distribution. This optimisation problem is similar to the classical 0-1 knapsack problem, but it involves optimisation…
We examine the problem of computing the highest density region (HDR) in a computational context where the user has access to a density function and quantile function for the distribution (e.g., in the statistical language R). We examine…
Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but…
The Gaussian Process (GP)-based surrogate model has the inherent capability of capturing the anomaly arising from limited data, lack of data, missing data, and data inconsistencies (noisy/erroneous data) present in the modeling and…
In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC)…
Inferring how an epidemic will progress and what actions to take when presented with limited information is of critical importance for epidemiologists and health professionals. In real world settings, epidemiology data can be scarce or…
In this document I aim to give an informal treatment of automatic Backward Filtering Forward Guiding, a general algorithm for conditional sampling from a Markov process on a directed acyclic graph. I'll show that the underlying ideas can be…
Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…
We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et…
Dynamic heterogeneous networks describe the temporal evolution of interactions among nodes and edges of different types. While there is a rich literature on finding communities in dynamic networks, the application of these methods to…
This work considers variational Bayesian inference as an inexpensive and scalable alternative to a fully Bayesian approach in the context of sparsity-promoting priors. In particular, the priors considered arise from scale mixtures of Normal…