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Optimal Weighted Wilcoxon–Mann–Whitney Test for Prioritized Outcomes Read chapter Read first chapter

2018 | OriginalPaper | Chapter

4. Bayesian Nonparametric Spatially Smoothed Density Estimation

Authors : Timothy Hanson, Haiming Zhou, Vanda Inácio de Carvalho

Published in: New Frontiers of Biostatistics and Bioinformatics

Publisher: Springer International Publishing

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Abstract

A Bayesian nonparametric density estimator that changes smoothly in space is developed. The estimator is built using the predictive rule from a marginalized Polya tree, modified so that observations are spatially weighted by their distance from the location of interest. A simple refinement is proposed to accommodate arbitrarily censored data and a test for whether the density is spatially varying is also developed. The method is illustrated on two real datasets, and an R function SpatDensReg is provided for general use.

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Literature
Chen, Y., & Hanson, T. (2014). Bayesian nonparametric k-sample tests for censored and uncensored data. Computational Statistics and Data Analysis, 71, 335–346.MathSciNetCrossRef
Chung, Y., & Dunson, D. B. (2011). The local Dirichlet process. Annals of the Institute of Statistical Mathematics, 63, 59–80.MathSciNetCrossRef
Dahl, D. B., Day, R., & Tsai, J. W. (2017). Random partition distribution indexed by pairwise information. Journal of the American Statistical Association, 112, 721–732.MathSciNetCrossRef
De Iorio, M., Johnson, W. O., Müller, P., & Rosner, G. L. (2009). Bayesian Nonparametric nonproportional hazards survival modeling. Biometrics, 65, 762–771.MathSciNetCrossRef
Duan, J., Guindani, M., & Gelfand, A. E. (2007). Generalized spatial Dirichlet process models. Biometrika, 94, 809–825.MathSciNetCrossRef
Dunson, D. B., Pillai, N. S., & Park, J-H. (2007). Bayesian density regression. Journal of the Royal Statistical Society, Series B, 69, 163–183.MathSciNetCrossRef
Escobar, M. D., & West, M. (1995). Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association, 90, 577–588.MathSciNetCrossRef
Fisher, R. (1935). The design of experiments. Edinburgh: Oliver & Boyd.
Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: The analysis of spatially varying relationships, Hoboken: Wiley.MATH
Fuentes, M., & Reich, B. (2013). Multivariate spatial nonparametric modeling via kernel process mixing. Statistica Sinica, 23, 75–97.MathSciNetMATH
Gelfand A. E., Diggle, P. J., Fuentes, M., & Guttorp, P. (Eds.) (2010). Handbook of spatial statistics. Chapman&Hall/CRC handbooks of modern statistical methods. Boca Raton: CRC Press.
Gelfand, A. E., Kottas, A., & Maceachern, S. N. (2005). Bayesian nonparametric spatial modelling with Dirichlet process mixing. Journal of the American Statistical Association, 100, 1021–1035.MathSciNetCrossRef
Griffin, J. E., & Steel, M. F. J. (2006). Order based dependent Dirichlet processes. Journal of the American Statistical Association, 101, 179–194.MathSciNetCrossRef
Hanson, T. (2006). Inference for mixtures of finite Polya tree models. Journal of the American Statistical Association, 101, 1548–1565.MathSciNetCrossRef
Hanson, T., Branscum, A., & Gardner, I. (2008). Multivariate mixtures of Polya trees for modelling ROC data. Statistical Modelling, 8, 81–96.MathSciNetCrossRef
Jo, S., Lee, J., Müller, P., Quintana, F., & Trippa, L. (2017). Dependent species sampling model for spatial density estimation. Bayesian Analysis, 12, 379–406.MathSciNetCrossRef
MacEachern, S. N. (2001). Decision theoretic aspects of dependent nonparametric processes. In E. George (Ed.), Bayesian methods with applications to science, policy and official statistics (pp. 551–560). Luxembourg City: Eurostat.
Newton, M. A., & Zhang, Y. (1999). A recursive algorithm for nonparametric analysis with missing data. Biometrika, 86, 15–26.MathSciNetCrossRef
Petrone, S., Guindani, M., & Gelfand, A. E. (2009). Hybrid Dirichlet mixture models for functional data. Journal of the Royal Statistical Society, Series B, 71, 755–782.MathSciNetCrossRef
Reich, B., & Fuentes, M. (2007). A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields. Annals of Applied Statistics, 1, 249–264.MathSciNetCrossRef
Rodríguez, A., Dunson, D., & Gelfand, A. (2010). Latent stick-breaking processes. Journal of the American Statistical Association, 105, 647–659.MathSciNetCrossRef
Schörgendorfer, A., & Branscum, A. J. (2013). Regression analysis using dependent Polya trees. Statistics in Medicine, 32, 4679–4695.MathSciNetCrossRef
Tansey, W., Athey, A., Reinhart, A., & Scott, J. G. (2017). Multiscale spatial density smoothing: An application to large-scale radiological survey and anomaly detection. Journal of the American Statistical Association, 112, 1047–1063.MathSciNetCrossRef
Zhao, L., & Hanson, T. (2011). Spatially dependent Polya tree modeling for survival data. Biometrics, 67, 391–403.MathSciNetCrossRef
Zhou, H., Hanson, T., & Knapp, R. (2015). Marginal Bayesian nonparametric model for time to disease arrival of threatened amphibian populations. Biometrics, 71, 1101–1110.MathSciNetCrossRef
Zhou, H., Hanson, T., & Zhang, J. (2017). Generalized accelerated failure time spatial frailty model for arbitrarily censored data. Lifetime Data Analysis, 23, 495–515.MathSciNetCrossRef
Metadata
Title
Bayesian Nonparametric Spatially Smoothed Density Estimation
Authors
Timothy Hanson
Haiming Zhou
Vanda Inácio de Carvalho
Copyright Year
2018
Book
New Frontiers of Biostatistics and Bioinformatics

Print ISBN: 978-3-319-99388-1

Electronic ISBN: 978-3-319-99389-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-99389-8_4

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