Browsing by Author "Hanson, Timothy E."
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- ItemA Bayesian Semiparametric Temporally-Stratified Proportional Hazards Model with Spatial Frailties(INT SOC BAYESIAN ANALYSIS, 2012) Hanson, Timothy E.; Jara, Alejandro; Zhao, LupingIncorporating temporal and spatial variation could potentially enhance information gathered from survival data. This paper proposes a Bayesian semiparametric model for capturing spatio-temporal heterogeneity within the proportional hazards framework. The spatial correlation is introduced in the form of county level frailties. The temporal effect is introduced by considering the stratification of the proportional hazards model, where the time dependent hazards are indirectly modeled using a probability model for related probability distributions. With this aim, an autoregressive dependent tailfree process is introduced. The full Kullback-Leibler support of the proposed process is provided. The approach is illustrated using simulated data and data from the Surveillance Epidemiology and End Results database of the National Cancer Institute on patients in Iowa diagnosed with breast cancer.
- ItemBayesian nonparametric ROC regression modeling(2013) Calhau Fernandes Inacio de Carvalho, Vanda; Jara, Alejandro; Hanson, Timothy E.; Bras De Carvalho, Miguel
- ItemDPpackage: Bayesian Semi- and Nonparametric Modeling in R(JOURNAL STATISTICAL SOFTWARE, 2011) Jara, Alejandro; Hanson, Timothy E.; Quintana, Fernando A.; Mueller, Peter; Rosner, Gary L.Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility and robustness against mis-specification of the probability model. In the Bayesian context, this is accomplished by placing a prior distribution on a function space, such as the space of all probability distributions or the space of all regression functions. Unfortunately, posterior distributions ranging over function spaces are highly complex and hence sampling methods play a key role. This paper provides an introduction to a simple, yet comprehensive, set of programs for the implementation of some Bayesian nonparametric and semiparametric models in R, DPpackage. Currently, DPpackage includes models for marginal and conditional density estimation, receiver operating characteristic curve analysis, interval-censored data, binary regression data, item response data, longitudinal and clustered data using generalized linear mixed models, and regression data using generalized additive models. The package also contains functions to compute pseudo-Bayes factors for model comparison and for eliciting the precision parameter of the Dirichlet process prior, and a general purpose Metropolis sampling algorithm. To maximize computational efficiency, the actual sampling for each model is carried out using compiled C, C++ or Fortran code.
- ItemSurviving fully Bayesian nonparametric regression models(Oxford University Press, 2013) Hanson, Timothy E.; Jara Vallejos, Alejandro AntonioThis chapter compares two Bayesian nonparametric models that generalize the accelerated failure time model, based on recent work on probability models for predictor-dependent probability distributions. It begins by reviewing commonly used semiparametric survival models. It then discusses the Bayesian nonparametric priors used in the generalizations of the accelerated failure time (AFT) model. Next, the two generalizations of the accelerated failure time model are introduced and compared by means of real-life data analyses. The models correspond to generalizations of AFT models based on dependent extensions of the Dirichlet process (DP) and Polya tree (PT) priors. Advantages of the induced survival regression models include ease of interpretability and computational tractability.
- ItemThe Polya Tree Sampler: Toward Efficient and Automatic Independent Metropolis-Hastings Proposals(AMER STATISTICAL ASSOC, 2011) Hanson, Timothy E.; Monteiro, Joao V. D.; Jara, AlejandroWe present a simple, efficient, and computationally cheap sampling method for exploring an unnormalized multivariate density on R-d, such as a posterior density, called the Polya tree sampler. The algorithm constructs an independent proposal based on an approximation of the target density. The approximation is built from a set of (initial) support points data that act as parameters for the approximation and the predictive density of a finite multivariate Polya tree. In an initial "warming-up" phase, the support points are iteratively relocated to regions of higher support under the target distribution to minimize the distance between the target distribution and the Polya tree predictive distribution. In the "sampling" phase, samples from the final approximating mixture of finite Polya trees are used as candidates which are accepted with a standard Metropolis Hastings acceptance probability. Several illustrations are presented, including comparisons of the proposed approach to Metropolis-within-Gibbs and delayed rejection adaptive Metropolis algorithm. This article has supplementary material online.