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Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

We use Generalized Beta Prime distribution, also known as GB2, for fitting response time distributions. This distribution, characterized by one scale and three shape parameters, is incredibly flexible in that it can mimic behavior of many…

A new method called "variational sampling" is proposed to estimate integrals under probability distributions that can be evaluated up to a normalizing constant. The key idea is to fit the target distribution with an exponential family model…

We characterise the convergence of the Gibbs sampler which samples from the joint posterior distribution of parameters and missing data in hierarchical linear models with arbitrary symmetric error distributions. We show that the convergence…

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…

Data compression often subtracts prediction and encodes the difference (residue) e.g. assuming Laplace distribution, for example for images, videos, audio, or numerical data. Its performance is strongly dependent on the proper choice of…

In this paper, a generalization for the Birnbaum Saunders distribution, which has been applied to the modelling of fatigue failure times and reliability studies, is considered. The maximum likelihood estimators and statistical inference for…

We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

Flexible distributions for modelling angular data have received considerable attention in recent years, with ongoing work extending existing circular models to provide greater flexibility in capturing diverse angular behaviours. In this…

We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

This paper explores improvements in prediction accuracy and inference capability when allowing for potential correlation in team-level random effects across multiple game-level responses from different assumed distributions. First-order and…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for…

Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions.…

Parametric copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to…

Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai…

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time…

Irregularly sampled time series data arise naturally in many application domains including biology, ecology, climate science, astronomy, and health. Such data represent fundamental challenges to many classical models from machine learning…