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In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can…
Functional concurrent, or varying-coefficient, regression models are commonly used in biomedical and clinical settings to investigate how the relation between an outcome and observed covariate varies as a function of another covariate. In…
This paper presents a novel approach to stochastic mortality modelling by using the Conway--Maxwell--Poisson (CMP) distribution to model death counts. Unlike standard Poisson or negative binomial distributions, the CMP is a more adaptable…
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
The extraction of nonstationary signals from blind and semi-blind multivariate observations is a recurrent problem. Numerous algorithms have been developed for this problem, which are based on the exact or approximate joint diagonalization…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
In many applications of Bayesian clustering, posterior sampling on the discrete state space of cluster allocations is achieved via Markov chain Monte Carlo (MCMC) techniques. As it is typically challenging to design transition kernels to…
Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related,…
We develop methods for efficient amortized approximate Bayesian inference over posterior distributions of probabilistic clustering models, such as Dirichlet process mixture models. The approach is based on mapping distributed,…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We propose a new Bayesian tracking and parameter learning algorithm for non-linear non-Gaussian multiple target tracking (MTT) models. We design a Markov chain Monte Carlo (MCMC) algorithm to sample from the posterior distribution of the…
Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…
We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
Analyzing point patterns with linear structures has recently been of interest in e.g. neuroscience and geography. To detect anisotropy in such cases, we introduce a functional summary statistic, called the cylindrical $K$-function, since it…
Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of well separated clusters. The most commonly used…
Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…