| Bayesian modeling and its applications are discussed in two settings. The first involves Bayesian approach in a study in which researchers investigated the effect of bomb tests conducted in the 1950s from the Nevada test site (NTS). This approach models a flexible regression function when the predictor variable is assumed to be measured with the Berkson error for binary regression. The regression function is modeled with regression P-splines. We employ a fully Bayesian analysis and use the recent Markov Chain Monte Carlo (MCMC) techniques to generate observations from the joint posterior distribution. An advantage of the MCMC approach is that we can obtain credible interval estimates that directly model and adjust for the measurement error. We present a small simulation study, followed by the analysis of the NTS data.; The second problem is set in a biological framework. The data set consists of the level of DNA damage (X) and the level of DNA damage after exposure to FPG (Y). We have the biological constraint that, overall, the mean of X is less than the mean of Y. A hierarchical Bayesian analysis is proposed for this problem and the goal is to provide a more efficient analysis when taking the constraint into account. |
