An Adaptive Model-Assisted Treatment Strategy for the Management of White-Nose Syndrome in Bats
Nick J. Meyer, Eric B. Laber, Krishna Pacfici, and Brian Reich North Carolina State University
Bats are the primary predator of agricultural pests and insect vectors of human disease in the United States. Consequently, the emergence of white-nose syndrome, a rapidly spreading and 90% fatal fungus a_icting bats, represents a serious threat to agriculture and human health. We propose a model-assisted approximate dynamic programming procedure to minimize the spread of white-nose syndrome. This procedure uses a postulated system dynamics model to solve for an optimal model-based policy for controlling white-nose syndrome. However, because the model-based policy relies on correct speci_cation of the system dynamics model, it may be misspecified. As information accumulates under execution of the model-based policy we estimate the optimal policy nonparametrically. At the time of each treatment intervention we test whether the nonparametric policy is superior to the model-based policy; if the nonparametric policy is deemed superior, then it is used subsequently to control the spread of the disease. The method is demonstrated using simulated experiments informed by real data.
Nonparametric Bayes Estimation of Gap-Time Distribution with Recurrent Event Data
A.K.M. Fazlur Rahmany,University of South Carolina
Nonparametric Bayes estimation of the gap-time survivor function governing the time to occurrence of a recurrent event in the presence of censoring is considered. For the ith among n units, denote the successive gap-times of a recurrent event by Tik, k=1,2,…, and the end of monitoring time by ?i. Assume that Tij, i=1,…,n, and ?i, i=1,…,n, are IID nonnegative random variables with common distribution functions F and G, respectively, and with Tij and ?i mutually independent. In our Bayesian approach, F has a Dirichlet process prior with parameter ?, a non-null finite measure on {R+, ?(R+)}. We derive nonparametric Bayes and empirical Bayes estimators of the survivor function 1-F. The resulting nonparametric Bayes estimator of 1-F extends the Bayes estimator of Susarla and Van Ryzin (1976) based on a single-event right-censored data. The PL-type nonparametric estimator based on recurrent event data presented in Pena et al. (2001) is also a limiting case of the nonparametric Bayes estimator, obtained by letting ?(R+) -> 0. Through simulation studies, we demonstrate that the PL-type estimator has smaller bias but higher root-mean-squared errors (RMSE) than those of the nonparametric Bayes and the empirical Bayes estimators. Even in the case of a misspecfied prior measure parameter ?, the nonparametric Bayes and empirical Bayes estimators have smaller RMSE than the PL-type estimator, indicating robustness of the nonparametric Bayes and empirical Bayes estimators. In addition, the nonparametric Bayes and empirical Bayes estimator is smoother than the PL-type estimator.
