Description: A presentation of a mathematics/statistics based approach for determining credibility factors for possible use in group health insurance premium rate setting and experience refund setting. Includes supporting mathematical proofs of approach. Followed by discussions submitted by several people

Description: In this Chapter we present a novel way for estimating aggregated EC figures based on Bayesian copula estimation. Contrary to the classic approach of using a single inter-risk- correlation matrix we derive a probability distribution of possible correlation matrices that enables us to tackle the important issue of parameter uncertainty. Presented at 2010 Enterprise Risk Management Symposium, Society of Actuaries, April 12-15, 2010.

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: 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 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: 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 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.

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: 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.