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Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

James R. Faulkner, Vladimir N. Minin
2018 Bayesian Analysis  
We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian  ...  Gaussian process (GP) regression (Neal, 1998; Rasmussen and Williams, 2006 ) is a popular Bayesian nonparametric approach for functional estimation that places a GP prior on the  ...  Acknowledgments J.R.F, and V.N.M. were supported by the NIH grant R01 AI107034. J.R.F. was supported by the NOAA Advanced Studies Program and V.N.M. was supported by the NIH grant U54 GM111274.  ... 
doi:10.1214/17-ba1050 pmid:29755638 pmcid:PMC5942601 fatcat:at5umjlztrc43igczkaftlmrdi

Locally adaptive smoothing with Markov random fields and shrinkage priors [article]

James R. Faulkner, Vladimir N. Minin
2017 arXiv   pre-print
We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian  ...  We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework.  ...  It is not our goal to compare and characterize properties of Bayesian nonparametric function estimation under all of these priors.  ... 
arXiv:1512.06505v2 fatcat:ix4xrw25ezhqtbb2t6wbunomde

Bayesian curve-fitting with free-knot splines

I. Dimatteo, C. R. Genovese, R. E. Kass
2001 Biometrika  
For nonnormal models, we approximate the integrated likelihood ratios needed to compute acceptance probabilities by using the Bayesian information criterion, , under priors that make this approximation  ...  Our technique is based on a marginalised chain on the knot number and locations, but we provide methods for inference about the regression coefficients, and functions of them, in both normal and nonnormal  ...  (solid line) superimposed on the signal (thin dotted line) for the estimates of the curve using Bayesian adaptive regression splines with Poisson prior in (a) with mean 20, and (b) with mean 3, and using  ... 
doi:10.1093/biomet/88.4.1055 fatcat:2p22dbgtmnh6lj4w5jgtfl674m

Semiparametric Mixed-Scale Models Using Shared Bayesian Forests [article]

Antonio R. Linero, Debajyoti Sinha, Stuart R. Lipsitz
2019 arXiv   pre-print
To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees - a heteroskedastic log-normal hurdle model  ...  with a "shrink-towards-homoskedasticity" prior, and a gamma hurdle model.  ...  Acknowledgements This work was partially supported by National Science Foundation grant DMS-1712870 and by the Department of Defense through the Science of Test research consortium.  ... 
arXiv:1809.08521v4 fatcat:gykhcbkd2ndzxe76mekmsk4g4u

Bayesian Nonparametric Inference for Random Distributions and Related Functions

Stephen G. Walker, Paul Damien, PuruShottam W. Laud, Adrian F. M. Smith
1999 Journal of The Royal Statistical Society Series B-statistical Methodology  
In recent years, Bayesian nonparametric inference, both theoretical and computational, has witnessed considerable advances.  ...  In this paper, we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the Bayesian nonparametric and/or semiparametric framework.  ...  Acknowledgements Research reported here was supported in part by an Engineering and Physical Sciences Research Council`Realising our potential' award and travel grant, a National Science Foundation grant  ... 
doi:10.1111/1467-9868.00190 fatcat:ji4zf5u57vapfkpcupeg6ph3bm

Good, great, or lucky? Screening for firms with sustained superior performance using heavy-tailed priors

Nicholas G. Polson, James G. Scott
2012 Annals of Applied Statistics  
The family is a four-parameter generalization of the normal/inverted-beta prior, and is the natural conjugate prior for shrinkage coefficients in a hierarchical normal model.  ...  These priors are based on the hypergeometric inverted-beta family, and have two main attractive features: heavy tails and computational tractability.  ...  Acknowledgments: The authors would like to thank Mumtaz Ahmed and Michael Raynor of Deloitte Consulting for their insight into the problem described here.  ... 
doi:10.1214/11-aoas512 fatcat:5tokbvkpbvheldybtprahtbqoa

Feature-Preserving MRI Denoising: A Nonparametric Empirical Bayes Approach

Suyash P. Awate, Ross T. Whitaker
2007 IEEE Transactions on Medical Imaging  
The generality and power of nonparametric modeling, coupled with the EB approach for prior estimation, avoids imposing ill-fitting prior models for denoising.  ...  It models the prior in a nonparametric Markov random field (MRF) framework and estimates this prior by optimizing an information-theoretic metric using the expectation-maximization algorithm.  ...  Shamir and Prof. S. Joshi for valuable discussions and feedback, Prof. J. Gee for the DWI data, and H. Zhang for providing the DT-visualization software.  ... 
doi:10.1109/tmi.2007.900319 pmid:17896596 fatcat:fldxvtyiabbfrn2led4h6uwdeu

Qualitative Assumptions and Regularization in High-Dimensional Statistics

Lutz Dümbgen, Jon Wellner
2006 Oberwolfach Reports  
Important and exciting developments are currently underway in nonparametric statistics involving inter-play between qualitative constraints, penalization, and regularization methods.  ...  and approximation theory sides.  ...  Acknowledgment: Cun-Hui Zhang's research is partially supported by the National Science Foundation and National Security Agency.  ... 
doi:10.4171/owr/2006/49 fatcat:3apxa5zhf5fdbmubk2oqgwsxqy

Guaranteed Local Maximum Likelihood Detection of a Change Point in Nonparametric Logistic Regression

A. Vexler, G. Gurevich
2006 Communications in Statistics - Theory and Methods  
We use a local version of 6 unknown likelihood functions and show that under rather common assumptions the asymptotic power of our test is one.  ...  Young Sook Son Kim, Seong W.(2005-24) Bayesian single change point detection in a sequence of multivariate normal observations 16 Abstract: A Bayesian method is used to see whether there are changes of  ...  Normal errors with constant variance are assumed and likelihood ratio statistics are used to test for the presence of two separate regressions.  ... 
doi:10.1080/03610920500498923 fatcat:jxva2knaxvbpbfmovc7yfwwlhu

Nonparametric Bayesian multiple testing for longitudinal performance stratification

James G. Scott
2009 Annals of Applied Statistics  
The modeling approach is Bayesian, though a blend of frequentist and Bayesian reasoning is used to evaluate procedures.  ...  Nonparametric characterizations of both the null and alternative hypotheses will be shown to be the key robustification step necessary to ensure reasonable Type-I error performance.  ...  Dirichlet-process priors for nonparametric Bayesian density estimation were popularized by Ferguson (1973) , Antoniak (1974) , and Escobar and West (1995) .  ... 
doi:10.1214/09-aoas252 fatcat:dz2ezuqkn5a6fbbvi7krfiqpi4

Spike-and-Slab Group Lassos for Grouped Regression and Sparse Generalized Additive Models [article]

Ray Bai, Gemma E. Moran, Joseph Antonelli, Yong Chen, Mary R. Boland
2020 arXiv   pre-print
We introduce the spike-and-slab group lasso (SSGL) for Bayesian estimation and variable selection in linear regression with grouped variables.  ...  We derive posterior concentration rates for both grouped linear regression and sparse GAMs when the number of covariates grows at nearly exponential rate with sample size.  ...  Let n = s 0 log G/n, and suppose that Assumptions (A1)-(A5) hold. Under model (6.1), suppose that we endow (β, σ 2 ) with the prior (6.2).  ... 
arXiv:1903.01979v6 fatcat:z43jzupfbfgnvaa3jmqkshvvrq

Optimal taxation and insurance using machine learning — Sufficient statistics and beyond

Maximilian Kasy
2018 Journal of Public Economics  
using Gaussian process priors.  ...  Available online xxxx JEL classification: H21 C11 C14 Keywords: Optimal policy Gaussian process priors Posterior expected welfare A B S T R A C T How should one use (quasi-)experimental evidence when choosing  ...  Most nonparametric regression estimators are linear in the outcomes Y, and ordinary least squares regressions are commonly fit in settings with non-normal outcomes.  ... 
doi:10.1016/j.jpubeco.2018.09.002 fatcat:x5i3oio6ofbbtgrhfjhg7qghzu

Causal network inference using biochemical kinetics [article]

C. J. Oates, F. Dondelinger, N. Bayani, J. Korola, J. W. Gray, S. Mukherjee
2014 arXiv   pre-print
Inference regarding both parameters and the reaction graph itself is carried out within a fully Bayesian framework.  ...  However, the dynamics of these systems are generally nonlinear, suggesting that suitable nonlinear formulations may offer gains with respect to network inference and associated prediction problems.  ...  Bayesian Inference CheMA 1.0 uses truncated normal priors N T (µ, Σ) with parameters µ, Σ inherited from the corresponding untruncated distribution.  ... 
arXiv:1406.0063v1 fatcat:j5o23k65gbcy5dqyfvoybrs64e

Model-Based Design Analysis and Yield Optimization

Tobias Pfingsten, Daniel J. L. Herrmann, Carl Edward Rasmussen
2006 IEEE transactions on semiconductor manufacturing  
We show how an efficient Bayesian approach, using a Gaussian process prior, can replace the commonly used brute-force Monte Carlo scheme, making it possible to apply the analysis to computationally costly  ...  We show that the Bayesian Monte Carlo scheme can save costly simulation runs and can ensure a reliable accuracy of the analysis.  ...  Under the assumption that the inputs are normally distributed, p(x) = p (x ) = N (x |x , σ 2 ), the output distribution p x (f lin ) is also normal.  ... 
doi:10.1109/tsm.2006.883589 fatcat:zuefrmcdnzekdnby2gqfcvnilu

Bayesian, Likelihood-Free Modelling of Phenotypic Plasticity and Variability in Individuals and Populations

Joao A.N. Filipe, Ilias Kyriazakis
2019 Frontiers in Genetics  
while using fewer assumptions and fewer empirical observations.  ...  about data distribution and correlation, addressed via Approximate Bayesian Computation (a form of nonparametric inference).  ...  We used a uniform prior on B with range [0.5,2].  ... 
doi:10.3389/fgene.2019.00727 pmid:31616460 pmcid:PMC6764410 fatcat:yo5vv3mvqjghhlnghi3fef3phy
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