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The generalized Poisson distribution is well known to be a compound Poisson distribution with Borel summands. As a generalization we present closed formulas for compound Bartlett and Delaporte distributions with Borel summands and a…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

At the core of insurance business lies classification between risky and non-risky insureds, actuarial fairness meaning that risky insureds should contribute more and pay a higher premium than non-risky or less-risky ones. Actuaries,…

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…

Standard count models such as the Poisson and Negative Binomial models often fail to capture the large proportion of zero claims commonly observed in insurance data. To address such issue of excessive zeros, zero-inflated and hurdle models…

Predicting the price of used vehicles is a more interesting and needed problem by many users. Vehicle price prediction can be a challenging task due to the high number of attributes that should be considered for accurate prediction. The…

Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…

A transformation group approach to the prior for the parameters of the beta distribution is suggested which accounts for finite sets of data by imposing a limit to the range of parameter values under consideration. The relationship between…

To date, we have seen the emergence of a large literature on multivariate disease mapping. That is, incidence of (or mortality from) multiple diseases is recorded at the scale of areal units where incidence (mortality) across the diseases…

Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often…

We consider the insurance company as a physical system which is immersed in its environment (the financial market). The insurer company interacts with the market by exchanging the money through the payments for loss claims and receiving the…

We consider event-driven clinical trials, where the analysis is performed once a pre-determined number of clinical events has been reached. For example, these events could be progression in oncology or a stroke in cardiovascular trials. At…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…

This paper develops a dynamic insurance market model comprising two competing insurance companies and a continuum of insureds, and examines the interaction between strategic underreporting by the insureds and competitive pricing between the…

The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a…

Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate…

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the…