Description: Premium computation in a Bayesian context requires the use of a prior distribution [structure function] that the risk parameter follows in the heterogeneous portfolio. This paper contributes to the analysis of credibility theory by identifying the unique relationship between the prior distribution and credibility formula. The latter corresponds to a suggestive form of expressing the premium to be charged to a policyholder as a weighted sum of the sample mean and collective premium. Results for net premium principle and Poisson and negative binomial likelihood functions are shown.

Description: The problem of estimation of a tabular survival model from complete samples is considered from a Bayesian approach. If a life test involves a large cohort group, then data is typically given as a grouped data set. The survival function St is usually estimated by the moment estimator. We approximate the joint prior distribution of the unknown unconditional failure probabilities by a Dirichlet distribution, and then use a linear relationship between St and the conditional survival probabilities to obtain a Bayes estimator of St.

Description: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.

Description: This is a presentation from the Actuarial Research Conference in August 2006 in Montreal. It is on Bayesian Inference Resistant to Outliers. Presented by Alain Desgagne.

Description: An in-depth look at how actuarial skills and competencies picked up in the field can be applied to topics that aren't traditionally actuarial - with this article focusing on card counting in the casino game blackjack.

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 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: This abstract describes a paper that assesses the optimal manner to collapse a factor with many levels into one with a smaller number of levels.

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 work describes a study undertaken to determine whether the Federal Housing Administration's 'FHA' single-family-home mortgage insurance program for investor 'non-occupant' loans should be modified. The sample data were analyzed using both Bayesian and sample reuse procedures. A commentary on the paper is included.