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Cross-validation prior choice in Bayesian probit regression with many covariates
2011
Statistics and computing
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This paper examines prior choice in probit regression through a predictive cross-validation criterion. ...
Cross-validation avoids the tendency of such models to fit perfectly. We choose the hyperparameter in the ridge prior, c, as the minimizer of the log predictive score. ...
Conclusions The "ridge" hyperparameter c crucially affects Bayesian variable selection in probit regression with p >> n. ...
doi:10.1007/s11222-011-9228-1
fatcat:trklxopuuzb35bxzrlh2poffdm
Applications of Bayesian Gene Selection and Classification with Mixtures of Generalized Singular -Priors
2013
Computational and Mathematical Methods in Medicine
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In this research, we suggested a reference hyperprior distribution for such uncertainty, outlined the implementation of its computation, and illustrated this fully Bayesian approach with a colon and leukemia ...
Among the latter, Bayesian analysis can further accommodate the correlation between genes through the specification of a multivariate prior distribution and estimate the probabilities of association through ...
. , , and converted the probit model to a Gaussian regression problem with the generalized singular -prior ( -prior). ...
doi:10.1155/2013/420412
pmid:24382981
pmcid:PMC3870637
fatcat:xamsdrsrgfhvram63z47jguhoi
On the marginal likelihood and cross-validation
[article]
2019
arXiv
pre-print
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This offers new insight into the marginal likelihood and cross-validation and highlights the potential sensitivity of the marginal likelihood to the choice of the prior. ...
In contrast, non-Bayesian models are typically compared using cross-validation on held-out data, either through k-fold partitioning or leave-p-out subsampling. ...
A.7 Illustration for the probit model To demonstrate the cumulative cross-validation score in an intractable example, we carry out model selection in the Pima Indian benchmark model with a probit model ...
arXiv:1905.08737v2
fatcat:3ucjbgyu6vfklb7kmyr63zu4lm
A Bayesian Joint Modeling Using Gaussian Linear Latent Variables for Mixed Correlated Outcomes with Possibility of Missing Values
2016
Journal of Statistical Theory and Applications (JSTA)
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This paper proposes a Bayesian approach for the analysis of mixed correlated nominal, ordinal and continuous outcomes with possibility of missing values using a variation of Markov Chain Monte Carlo (MCMC ...
Priors For Bayesian inference, we need to specify priors for parameters in the models described in Section 2.1. ...
A cross validation analysis of simulated data with MAR values shows that the method is reliable regarding parameter estimation and imputations. ...
doi:10.2991/jsta.2016.15.4.5
fatcat:koitshzbarcptfmi7mgqn7bzhy
Bayesian binary kernel probit model for microarray based cancer classification and gene selection
2009
Computational Statistics & Data Analysis
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In this paper we introduce a hierarchical Bayesian probit model for two class cancer classification. ...
We incorporate a Bayesian gene selection scheme with the automatic dimension reduction to adaptively select important genes and classify cancer types under an unified model. ...
In the simulation and case study section in this paper we will show several such cases where simple Bayesian probit regression model performs poorly. ...
doi:10.1016/j.csda.2009.05.007
fatcat:lhuga5vzbrabvmcyfw2vnwy5cy
NIR and mass spectra classification: Bayesian methods for wavelet-based feature selection
2005
Chemometrics and Intelligent Laboratory Systems
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We then use probit models and Bayesian methods that allow the simultaneous classification of the samples as well as the selection of the discriminating features of the spectra. ...
In both examples our method is able to find very small sets of features that lead to good classification results. D ...
For all choices of s in s=14, . . . ,18 LDA achieved an error rate of 4/23 in the validation set. ...
doi:10.1016/j.chemolab.2004.10.009
fatcat:z5lnq4lwovb77ixvgvjvse5lkq
Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo
2000
American Journal of Political Science
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Bayesian multivariate regression model. ...
At this stage prior distributions for the probit coefficients @ are required, reflecting the Bayesian underpinnings of MCMC. ...
doi:10.2307/2669318
fatcat:fn4tyjc3kjcfnm2rsmfmbbly44
Nonparametric binary regression using a Gaussian process prior
2007
Statistical Methodology
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The article describes a nonparametric Bayesian approach to estimating the regression function for binary response data measured with multiple covariates. ...
Such a prior does not require any assumptions like monotonicity or additivity of the covariate effects. ...
The bandwidth parameter in LLE is automatically chosen by locfit() using a cross validation method. ...
doi:10.1016/j.stamet.2006.07.003
fatcat:cnrchf3pzndhhf46pv54pthwxi
A sparse multinomial probit model for classification
2010
Pattern Analysis and Applications
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A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. ...
It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. ...
More comprehensive descriptions of sparse Bayesian learning for both regression and classification can be found in [25] . 5 Figueiredo [24] proposes a sparse Bayesian approach to learn a probit classifier ...
doi:10.1007/s10044-010-0177-7
fatcat:m3duvhd7rjejzcoi4wqovpha5e
Multiple-Shrinkage Multinomial Probit Models with Applications to Simulating Geographies in Public Use Data
2013
Bayesian Analysis
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We propose an approach to modeling multinomial outcomes with many levels based on a Bayesian multinomial probit (MNP) model and a multiple shrinkage prior distribution for the regression parameters. ...
Multinomial outcomes with many levels can be challenging to model. ...
The research was carried out when the first author was a postdoctoral research associate in the Department of Statistical Science at Duke University. ...
doi:10.1214/13-ba816
pmid:24358073
pmcid:PMC3863948
fatcat:wvacaa6cqve5bhm6uhs2lve25a
Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models
[article]
2019
arXiv
pre-print
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2017 pre-print arXiv:1701.01503v1 fatcat:nl4h5r7s6fbutanxcbfzc6kau4
We introduce Bayesian additive regression trees (BART) for log-linear models including multinomial logistic regression and count regression with zero-inflation and overdispersion. ...
But while many useful models are naturally cast in terms of latent Gaussian variables, many others are not -- including models considered in this paper. ...
value as well as a latent covariance matrix, and to cross-validate the choice of reference category in addition to m and the parameters of the covariance matrix prior. ...
arXiv:1701.01503v2
fatcat:ztx3zmxqizejzblo4ma7wq4boi
Easy Variational Inference for Categorical Models via an Independent Binary Approximation
[article]
2022
arXiv
pre-print
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This approximation makes inference straightforward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closed-form variational ...
We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. ...
The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. ...
arXiv:2206.00093v1
fatcat:tj6zr55bcfc4zfo3up4wilr22i
Modeling Complex Phenotypes: Generalized Linear Models Using Spectrogram Predictors of Animal Communication Signals
2009
Biometrics
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In order to accommodate this complexity we propose a Bayesian dimension-reduced spectrogram generalized linear model that directly incorporates representations of the entire phenotype (one-dimensional ...
However, many important evolutionary characteristics of organisms are complex, and have correspondingly complex relationships to fitness. ...
These results are based on the three holdout samples over each of the 500 cross-validation Table 2 Classification results from the "model-averaged" stochastic search variable selection probit regression ...
doi:10.1111/j.1541-0420.2009.01331.x
pmid:19764952
fatcat:okffuyjab5cxtnnsxz5mthovpi
Objective Bayes model selection in probit models
2011
Statistics in Medicine
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We describe a new variable selection procedure for categorical responses where the candidate models are all probit regression models. ...
The procedure uses objective intrinsic priors for the model parameters, which do not depend on tuning parameters, and ranks the models for the different subsets of covariates according to their model posterior ...
Acknowledgement We thank a reviewer for pointing out that, in a spirit similar to (12), Berger and Pericchi [22] used the Cauchy-Binet theorem (which relates the determinant of a matrix product to the ...
doi:10.1002/sim.4406
pmid:22162041
fatcat:hoo2mwpilnhplnd77tmo5gg7de
Clinical Prediction Models to Predict the Risk of Multiple Binary Outcomes: a comparison of approaches
[article]
2020
arXiv
pre-print
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In such a situation, our results suggest that probabilistic classification chains, multinomial logistic regression or the Bayesian probit model are all appropriate choices. ...
, and a Bayesian probit model. ...
For example, many of the methods described below are fit using unpenalised MLE, but methods such as LASSO or fitting through Bayesian inference with penalising priors might be useful in some situations ...
arXiv:2001.07624v1
fatcat:6iksyiresbc4zhy3flb7w3csky
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