Journal of Data Science

Abstract: Clustered binary samples arise often in biomedical investigations. An important feature of such samples is that the binary responses within clusters tend to be correlated. The Beta-Binomial model is commonly applied to account for the intra-cluster correlation – the correlation between responses within the clusters – among dichotomous outcomes in cluster sampling. The intracluster correlation coefficient (ICC) quantifies this correlation or level of similarity. In this paper, we propose Bayesian point and interval estimators for the ICC under the Beta-Binomial model. Using Laplace’s method, the asymptotic posterior distribution of the ICC is approximated by a normal distribution. The posterior mean of this normal density is used as a central point estimator for the ICC, and 95% credible sets are calculated. A Monte Carlo simulation is used to evaluate the coverage probability and average length of the credible set of the proposed interval estimator. The simulations indicate that for the situation when the number of clusters is above 40, the underlying mean response probability falls in the range of [0.3;0.7], and the underlying ICC values are ≤ 0.4, the proposed interval estimator performs quite well and attains the correct coverage level. Even for number of clusters as small as 20, the proposed interval estimator may still be useful in the case of small ICC (≤ 0.2).

Abstract: For many years actuaries and demographers have been doing curve fitting of age-specific mortality data. We use the eight-parameter Heligman Pollard (HP) empirical law to fit the mortality curve. It consists of three nonlinear curves, child mortality, mid-life mortality and adult mortality. It is now well-known that the eight unknown parameters in the HP law are difficult to estimate because numerical algorithms generally do not converge when model fitting is done. We consider a novel idea to fit the three curves (nonlinear splines) separately, and then connect them smoothly at the two knots. To connect the curves smoothly, we express uncertainty about the knots because these curves do not have turning points. We have important prior information about the location of the knots, and this helps in the es timation convergence problem. Thus, the Bayesian paradigm is particularly attractive. We show the theory, method and application of our approach. We discuss estimation of the curve for English and Welsh mortality data. We also make comparisons with the recent Bayesian method.