Description: A method is presented which uses Bayes Lemma in an elementary way to construct posterior probabilities to be attached to each of several alternative prior distributions, given a few observations. The availability of efficient computer programs to numerically perform discrete convolutions for producing prior distributions makes this a practical method. From the Actuarial Research Clearing House 1978, Vol.2.

Description: This paper presents Bayesian models for analysis of claim lag data. The analysis of claim runoff patterns investigate the extraction of information on trend and seasonal patterns in incurred claims. This is investigated on the basis of individual group data, and also relative to a larger aggregation of pooled experience. The models are implemented based on Markov chain Monte Carlo methods. The models are applied to examples using simulated claim lag data. From Actuarial Research Clearing House, 2003, Vol. 1.

Description: Poisson regression models are commonly used in actuarial science to model count data e.g., the number of claims and covariates. The standard parametric formulation assumes that the response to covariates is constant across the population under study. Additionally, the shape of the posterior distribution is rather inflexible. In practice, however, the response to covariates may depend on a latent class and the posterior distribution may be highly nonparametric. This paper proposes a Bayesian nonparametric model in which a Dirichlet process prior on the regression coefficients leads to a clustering of observations into groups having the same response to covariates. This paper illustrates the utility of this approach with an example dataset of diabetes deaths.

Description: This paper addresses various modifications of the Kimeldorf-Jones Bayesian graduation method. These enhancements entail the use of time series and eigenvalue decomposition. By augmenting the existing method one can empirically smooth the Kimeldorf-Jones technique. From Actuarial Research Clearing House 1991, VOL. 1.

Description: In this paper the ad-hoc Bayesian derivation of the Whittaker method is replaced with a formal Bayesian specification, and then it is shown that with this specification it is possible to complete the graduation without making an arbitrary selection of the smoothing parameter. From Actuarial Research Clearing House 1992, VOL. 1.

Description: This paper presents an additional view of estimating parameters of the force of mortality using Bayesian methods. Some examples are provided. From Actuarial Research Clearing House 1993 VOL. 1.

Description: This paper examines the compatibility of the two models, in the hope that this exploration will prompt a greater cross-fertilization of ideas between the life actuarial branch which favors Bayesian models and the casualty branch which favors Hans Buhlmann models.

Description: This paper shows how a graduation method may be developed as straight forward statistical estimation within a statistical theory based upon personal probability, that is, so-called Bayesian statistics. The method discussed is applicable to a broad range of graduation situations, but does assume the more specific property of the graduator's prior opinion with respect to mortality rates.

Description: The objective of this paper is to present a technical exposition of the rudiments of Bayesian statistics.

Description: In this paper, the Bayesian model of collective risk theory is extended in the sense that a large class of distributions is used instead of a single one. The authors then investigate the sensitivity of variance premium principle when the structure function belongs to that class. According to robust Bayesian methodology, the uncertainty in the prior can be modeled by specifying a class of priors instead of a single one. The authors examine the ranges of the Bayesian premium, also called experience rated premium, when the priors belong to that class. Most of the robust Bayesian procedures developed measures of sensitivity of quantities which can be expressed in terms of posterior expectation [e.g., mean, variance and probability of given sets]. Nevertheless, relatively few papers have been related to measure Bayesian sensitivity of quantities which can be expressed in terms of ratio of two posterior expectations, as occurs in the variance premium principle. Appropriate techniques to solve this situation are considered. Unimodality turns out to be very convenient for modelling subjective beliefs about the risk parameter. The very common Poisson-Gamma model is developed in depth using this paper's methodology.