Related papers: Experience Rating with Poisson Mixtures

This paper provides a review of model selection and model averaging methods for multinomial probit models estimated using the MACML approach. The proposed approaches are partitioned into test based methods (mostly derived from the…

We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…

The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…

A new method for the computation of the posterior distribution of the number k of components in a finite mixture is presented. Two aspects of prior specification are also studied: an argument is made for the use of a Poisson(1) distribution…

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive…

We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cram\'er-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…

Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the…

This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…

There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…

In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general…

The prediction of future insurance claims based on observed risk factors, or covariates, help the actuary set insurance premiums. Typically, actuaries use parametric regression models to predict claims based on the covariate information.…

Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson…

A non-homogeneous Poisson cluster model is studied, motivated by insurance applications. The Poisson center process which expresses arrival times of claims, triggers off cluster member processes which correspond to number or amount of…

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)…