Bayesian Inference for Skew-Symmetric Distributions

Skew-symmetric distributions are a popular family of flexible distributions that conveniently model non-normal features such as skewness, kurtosis and multimodality. Unfortunately, their frequentist inference poses several difficulties, which may be adequately addressed by means of a Bayesian approach. This paper reviews the main prior distributions proposed for the parameters of skew-symmetric distributions, with special emphasis on the skew-normal and the skew-t distributions which are the most prominent skew-symmetric models. The paper focuses on the univariate case in the absence of covariates, but more general models are also discussed.

Five Bayesian Intuitions for the Stopping Rule Principle

Is it statistically appropriate to monitor evidence for or against a hypothesis as the data accumulate, and stop whenever this evidence is deemed sufficiently compelling Researchers raised in the tradition of frequentist inference may intuit that such a practice will bias the results and may even lead to "sampling to a foregone conclusion". In contrast, the Bayesian formalism entails that the decision on whether or not to terminate data collection is irrelevant for the assessment of the strength of the evidence. Here we provide five Bayesian intuitions for why the rational updating of beliefs ought not to depend on the decision when to stop data collection, that is, for the Stopping Rule Principle.

FREQUENTIST INFERENCE IN INSURANCE RATEMAKING MODELS ADJUSTING FOR MISREPRESENTATION

In insurance underwriting, misrepresentation represents the type of insurance fraud when an applicant purposely makes a false statement on a risk factor that may lower his or her cost of insurance. Under the insurance ratemaking context, we propose to use the expectation-maximization (EM) algorithm to perform maximum likelihood estimation of the regression effects and the prevalence of misrepresentation for the misrepresentation model proposed by Xia and Gustafson [(2016) The Canadian Journal of Statistics, 44, 198–218]. For applying the EM algorithm, the unobserved status of misrepresentation is treated as a latent variable in the complete-data likelihood function. We derive the iterative formulas for the EM algorithm and obtain the analytical form of the Fisher information matrix for frequentist inference on the parameters of interest for lognormal losses. We implement the algorithm and demonstrate that valid inference can be obtained on the risk effect despite the unobserved status of misrepresentation. Applying the proposed algorithm, we perform a loss severity analysis with the Medical Expenditure Panel Survey data. The analysis reveals not only the potential impact misrepresentation may have on the risk effect but also statistical evidence on the presence of misrepresentation in the self-reported insurance status.