Related papers: Bayesian mortality forecasting with a Conway--Maxw…
Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…
We investigate the class of $\sigma$-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular…
An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or…
Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
This paper introduces posterior mean matching (PMM), a new method for generative modeling that is grounded in Bayesian inference. PMM uses conjugate pairs of distributions to model complex data of various modalities like images and text,…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties…
Divergence is not only an important mathematical concept in information theory, but also applied to machine learning problems such as low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection. We…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework…
This paper introduces a novel family of geostatistical models designed to capture complex features beyond the reach of traditional Gaussian processes. The proposed family, termed the Poisson-Gaussian Mixture Process (POGAMP), is…
Recent developments in big data and analytics research have produced an abundance of large data sets that are too big to be analyzed in their entirety, due to limits on computer memory or storage capacity. To address these issues,…
Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…
A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…
Based on the recent paper by Delong et al. (2021), two distributions for the total claims amount (loss cost) are considered: Compound Poisson-gamma (CPG) and Tweedie. Each is used as an underlying distribution in the Bonus-Malus Scale (BMS)…
In this paper, we propose a nonparametric Bayesian approach for Lindsey and penalized Gaussian mixtures methods. We compare these methods with the Dirichlet process mixture model. Our approach is a Bayesian nonparametric method not based…
From a practical perspective, proposals are one of the main bottleneck for any Markov Chain Monte Carlo (MCMC) algorithm. This paper suggests a novel data driven or informed proposal for reversible jump MCMC for Bayesian variable selection…
Reliable mortality estimates at the subnational level are essential in the study of health inequalities within a country. One of the difficulties in producing such estimates is the presence of small populations, where the stochastic…