Transdimensional Sampling Algorithms for Bayesian Variable Selection in Classification Problems With Many More Variables Than Observations

Lamnisos, Demetris; Griffin, Jim E.; Steel, Mark F. J.

doi:10.1198/jcgs.2009.08027

Cited by 37 publications

(31 citation statements)

References 26 publications

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“…To assess the sensitivity of the Bayesian results to the inputs of hyperparameters in the prior distributions, we reanalyzed the data set by using different values of c, π i , h, R 0 , ρ 0 , and τ . For instance, using c = 5 as suggested by Lamnisos et al (2009), π i = 0.007, h = 200, R 0 = 4I, ρ 0 = 6, and τ = 0.005, the identification of the relevant genes and the performance of classification are essentially the same as before.…”

Section: Leukemia Datamentioning

confidence: 64%

“…Sha et al (2004) proposed an algorithm that is based on a multinomial probit model by using adding/deleting and swapping algorithm. According to Lamnisos et al (2009), this kind of algorithm that randomly chooses to either add or delete a single explanatory variable, or to swap two explanatory variables in the model often leads to high model acceptance rates when the number of variables is substantially larger than the sample size. Moreover, the Metropolis random walk suggested by Sha et al (2004) with local proposals and high acceptance rate is often associated with the poor mixing of MCMC chains.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian variable selection in multinomial probit model for classifying high-dimensional data

Yang

Tang

et al. 2014

Comput Stat

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Selecting a small number of relevant genes for classification has received a great deal of attention in microarray data analysis. While the development of methods for microarray data with only two classes is relevant, developing more efficient algorithms for classification with any number of classes is important. In this paper, we propose a Bayesian stochastic search variable selection approach for multi-class classification, which can identify relevant genes by assessing sets of genes jointly. We consider a multinomial probit model with a generalized g-prior for the regresElectronic supplementary material The online version of this article (A. Yang et al.sion coefficients. An efficient algorithm using simulation-based MCMC methods are developed for simulating parameters from the posterior distribution. This algorithm is robust to the choice of initial value, and produces posterior probabilities of relevant genes for biological interpretation. We demonstrate the performance of the approach with two well-known gene expression profiling data: leukemia data, lymphoma data, SRBCTs data and NCI60 data. Compared with other classification approaches, our approach selects smaller numbers of relevant genes and obtains competitive classification accuracy based on obtained results.

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Section: Leukemia Datamentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Bayesian variable selection in multinomial probit model for classifying high-dimensional data

Yang

Tang

et al. 2014

Comput Stat

View full text Add to dashboard Cite

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“…The analytical expression for the marginal density,     M , f Z Y , facilitates the application of adaptive MCMC methods for variable selection proposed by Lamnisos et al (2009Lamnisos et al ( , 2013, which are very efficient when the number of independent variables is large. These algorithms are based on the Random Walk Metropolis sampler with three possible movements: "Addition", "Deletion" and "Swapping" of regressors, which are uniformly chosen at random.…”

Section: Model Selectionmentioning

confidence: 99%

MCMC Bayesian spatial filtering for hedonic models in real estate markets

2017

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The traditional hedonic model postulates that housing prices depend on their characteristics and their location. However, this model assumes a constant relationship between the dependent and the independent variables. This assumption is unrealistic because empirical studies have shown that the regression coefficients depend on the housing location. For this reason, it is necessary to use models with spatially varying coefficients. The approaches proposed in the literature used to estimate this type of models do not incorporate the uncertainty associated with the estimation and selection of models and/or are computationally expensive. To improve these aspects, this paper proposes spatial filtering techniques to parsimoniously model the spatial dependencies of the hedonic coefficients and an adaptive MCMC algorithm of Bayesian variable selection to select the most appropriate filters. The method is illustrated through an application to the real estate market of Zaragoza, and a comparison with alternative procedures is conducted. Our results show that our valuation methodology has better goodness of fit and predictive performance properties than alternative methods. Although our proposal assumes normality and homoscedasticity of the model error distribution, the method is easy to implement and not very computationally demanding, which makes this approach attractive and useful from a practical viewpoint.

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“…For the intercept α, according to Sha et al (2004) and Lamnisos et al (2009), a univariate normal is adopted here…”

Section: Prior Specificationmentioning

confidence: 99%

Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis

Yang

Jiang

Shu³

et al. 2016

Comput Stat

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The main challenge in working with gene expression microarrays is that the sample size is small compared to the large number of variables (genes). In many studies, the main focus is on finding a small subset of the genes, which are the most important ones for differentiating between different types of cancer, for simpler and cheaper diagnostic arrays. In this paper, a sparse Bayesian variable selection method in probit model is proposed for gene selection and classification. We assign a sparse prior for regression parameters and perform variable selection by indexing the covariates of the model with a binary vector. The correlation prior for the binary vector assigned in this paper is able to distinguish models with the same size. The performance of the proposed method is demonstrated with one simulated data and two well known real data sets, and the results show that our method is comparable with other existing methods in variable selection and classification.

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Transdimensional Sampling Algorithms for Bayesian Variable Selection in Classification Problems With Many More Variables Than Observations

Cited by 37 publications

References 26 publications

Bayesian variable selection in multinomial probit model for classifying high-dimensional data

Bayesian variable selection in multinomial probit model for classifying high-dimensional data

MCMC Bayesian spatial filtering for hedonic models in real estate markets

Bayesian variable selection with sparse and correlation priors for high-dimensional data analysis

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