Browsing by Author "Muller, Peter"

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    Clustering and Prediction With Variable Dimension Covariates
    (2022) Page, Garritt L.; Quintana, Fernando A.; Muller, Peter
    In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a method based on covariate dependent random partition models that seamlessly handles missing covariates while completely avoiding any type of imputation. The method we develop allows in-sample as well as out-of-sample predictions, even if the missing pattern in the new subjects'incomplete covariate vectorwas not seen in the training data. Any data type, including categorical or continuous covariates are permitted. In simulation studies, the proposed method compares favorably. We illustrate themethod in two application examples. Supplementary materials for this article are available here.
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    Semiparametric Bayesian inference for multilevel repeated measurement data
    (WILEY, 2007) Muller, Peter; Quintana, Fernando A.; Rosner, Gary L.
    We discuss inference for data with repeated measurements at multiple levels. The motivating example is data with blood counts from cancer patients undergoing multiple cycles of chemotherapy, with days nested within cycles. Some inference questions relate to repeated measurements over days within cycle, while other questions are concerned with the dependence across cycles. When the desired inference relates to both levels of repetition, it becomes important to reflect the data structure in the model. We develop a semiparametric Bayesian modeling approach, restricting attention to two levels of repeated measurements. For the top-level longitudinal sampling model we use random effects to introduce the desired dependence across repeated measurements. We use a nonparametric prior for the random effects distribution. Inference about dependence across second-level repetition is implemented by the clustering implied in the nonparametric random effects model. Practical use of the model requires that the posterior distribution on the latent random effects be reasonably precise.
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    The Dependent Dirichlet Process and Related Models
    (INST MATHEMATICAL STATISTICS-IMS, 2022) Quintana Quintana, Fernando; Muller, Peter; Jara Vallejos, Alejandro Antonio; MacEachern, Steven N.
    Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate to assume a location/scale representation, where the error distribution has unchanging shape over the predictor space. In fact, it often happens in applied research that the distribution of responses under study changes with predictors in ways that cannot be reasonably represented by a finite dimensional functional form. This can seriously affect the answers to the scientific questions of interest, and therefore more general approaches are indeed needed. This gives rise to the study of fully nonparametric regression models. We review some of the main Bayesian approaches that have been employed to define probability models where the complete response distribution may vary flexibly with predictors. We focus on developments based on modifications of the Dirichlet process, historically termed dependent Dirichlet processes, and some of the extensions that have been proposed to tackle this general problem using nonparametric approaches.