Nonparametric binary regression using a Gaussian process prior

Choudhuri, Nidhan; Ghosal, Subhashis

doi:10.1016/j.stamet.2006.07.003

Cited by 38 publications

(53 citation statements)

References 26 publications

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“…A Gaussian process prior was assumed by Choudhuri et al (2003). Their approach requires a prior distribution ong, which is specified hierarchically through a polynomial function of the covariate value, and a prior distribution for the covariance matrix.…”

Section: Prior On the Unknown Functionsmentioning

confidence: 99%

“…As we show in this article, Bayesian methods in conjunction with the approach of Albert and Chib (1993) are very convenient for dealing with these models. Our work is Downloaded by [Australian National University] at 20:29 05 June 2016 thus a contribution to both the Bayesian literature on IV models (e.g., Chib 2003) and the nonparametric Bayesian literature (e.g., Wood and Kohn 1998;Choudhuri, Ghosal, and Roy 2003).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Semiparametric Modeling and Estimation of Instrumental Variable Models

Chib

Greenberg

2007

Journal of Computational and Graphical Statistics

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We apply Bayesian methods to a model involving a binary nonrandom treatment intake variable and an instrumental variable in which the functional forms of some of the covariates in both the treatment intake and outcome distributions are unknown. Continuous and binary response variables are considered. Under the assumption that the functional form is additive in the covariates, we develop efficient Markov chain Monte Carlo-based approaches for summarizing the posterior distribution and for comparing various alternative models via marginal likelihoods and Bayes factors. We show in a simulation experiment that the methods are capable of recovering the unknown functions and are sensitive neither to the sample size nor to the degree of confounding as measured by the correlation between the errors in the treatment and response equations. In the binary response case, however, estimation of the average treatment effect requires larger sample sizes, especially when the degree of confounding is high. The methods are applied to an example dealing with the effect on wages of more than 12 years of education.

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Section: Prior On the Unknown Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semiparametric Modeling and Estimation of Instrumental Variable Models

Chib

Greenberg

2007

Journal of Computational and Graphical Statistics

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“…linear or polynomial) whose parameters will then be optimized by minimizing a combination of a misfit function and a regularizer. In contrast, the approach described in the following, realizes a non-parametric model by using a Gaussian Process 10,11 to represent a prior probability over the underlying function () fr  . The regularization of () fr  is directly controlled by the properties of this Gaussian Process prior.…”

Section: Introductionmentioning

confidence: 99%

Bayesian soft X-ray tomography using non-stationary Gaussian Processes

Liu

Svensson

Thomsen

et al. 2013

Review of Scientific Instruments

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In this study, a Bayesian based non-stationary Gaussian Process method for the inference of soft X-ray emissivity distribution along with its associated uncertainties, has been developed. For the investigation of equilibrium condition and fast magnetohydrodynamic (MHD) behaviors in nuclear fusion plasmas, it is of importance to infer, especially in the plasma center, spatially resolved soft X-ray profiles from a limited number of noisy line integral measurements. For this ill-posed inversion problem, Bayesian probability theory can provide a posterior probability distribution over all possible solutions under given model assumptions. Specifically, the use of a non-stationary Gaussian Process to model the emission allows the model to adapt to the varying length scales of the underlying diffusion process. In contrast to other conventional methods, the prior regularization is realized in a probability form which enhances the capability of uncertainty analysis, in consequence, scientists who concern the reliability of their results will benefit from it. Under the assumption of normally distributed noise, the posterior distribution evaluated at a discrete number of points becomes a multivariate normal distribution whose mean and covariance are analytically available, making inversions and calculation of uncertainty fast. Additionally, the hyper-parameters embedded in the model assumption can be optimized through a Bayesian Occam"s Razor formalism and thereby automatically adjust the model complexity. This method is shown to produce convincing reconstructions and good agreements with independently calculated results from the Maximum Entropy (MaxEnt) and Equilibrium-Based Iterative Tomography Algorithm (EBITA) methods.

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“…For an account on Bayesian methods for function estimation, see Choudhuri et al (2005) and the references therein. Only in recent years large-sample properties like consistency and rates of convergence of posterior distributions for Bayesian nonparametric regression problems have been studied, see Shen and Wasserman (2001), Amewou-Atisso et al (2003), Ghosal and Roy (2006), Kleijn and van der Vaart (2006), Choudhuri et al (2007). In all these articles as well as in the present note, the frequentist or "what if" approach for studying Bayesian asymptotics is adopted.…”

Section: Introductionmentioning

confidence: 99%