Nonparametric Applications of Bayesian Inference

By Gary Chamberlain, Guido W. Imbens. 2003

121 citations recorded by the source corpus.

This article evaluates the usefulness of a nonparametric approach to Bayesian inference by presenting two applications. Our first application considers an educational choice problem. We focus on obtaining a predictive distribution for earnings corresponding to various levels of schooling. This predictive distribution incorporates the parameter uncertainty, so that it is relevant for decision making under uncertainty in the expected utility framework of microeconomics. The second application is to quantile regression. Our point here is to examine the potential of the nonparametric framework to provide inferences without relying on asymptotic approximations. Unlike in the first application, the standard asymptotic normal approximation turns out not to be a good guide.

Subfields: Artificial Intelligence, Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9d8c63d0043cb96e3423cef18b42be996ec8e52c

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Citations in the corpus

A Bayesian Nonparametric Approach to Inference for Quantile Regression (2010, methodology): “Moreover, Chamberlain and Imbens (2003) and Dunson and Taylor (2005) propose semi-Bayesian inference methods for linear quantile regression, which, in contrast to the work discussed above, do not involve probabilistic modeling for the response distribution. A practical limitation of the Bayesian sem”
Conditional quantile processes based on series or many regressors (2011, methodology): “Præstgaard and Wellner [72], Hahn [41], Chamberlain and Imbens [17], and Chen and Pouzo [23] previously used this method in the point-wise case, where the set U is a singleton.”
Program evaluation and causal inference with high-dimensional data (2013, methodology): “, where Nis standard normal random variable, and (c) ξ= N/ √ 2 + (N2 −1)/2, where Nis standard normal random variable.8 Method (a), (b), and (c) correspond respectively to a Bayesian bootstrap (e.g., Chamberlain and Imbens (2003)), a Gaussian multiplier method (e.g, van der Vaart and Wellner (1996))”
A Bayesian view of doubly robust causal inference (2016, methodology): “This approach of creating a mapping between the non-parametric specification and a parametrization relevant to inferences is analogous to Chamberlain and Imbens (2003), but adds the importance sampling weights to the Dirichlet weights in order to make inferences across the observational and…”
Heterogeneous Treatment Effects in Digital Experimentation (2014, methodology): “As a closing point, we note that the classical Ferguson (1973) nonparametric setup, and especially the standard model of Chamberlain and Imbens (2003) that uses observed support to approximate population support, is a useful theoretical framework for Big data problems where sample n is larger than,…”
Bayesian quantile regression methods (2010, methodology): “Chamberlain and Imbens (2003) note that it is straightforward to compute the Bayesian bootstrap posterior density in quantile regression by repeatedly solving the problem βτ = arg min t n∑ i=1 ρτ (viui), (3) where the {vi} are iid unit exponential variates and ui = Yi − X ′it.”
An MCMC approach to classical estimation (2003, unknown): “Hahn (1997), Chamberlain and Imbens (1997), Kottas and Gelfand (2001).”
A Nonparametric Bayesian Analysis of Heterogenous Treatment Effects in Digital Experimentation (2014, background): “Indeed, it is the foundation for the Bayesian bootstrap of Rubin (1981), and Chamberlain and Imbens (2003) provided a nice survey of some econometric applications.”
Program evaluation with high-dimensional data (2013, methodology): “, Chamberlain and Imbens (2003)), a Gaussian multiplier method (e.g, van der Vaart and Wellner (1996)), and a wild bootstrap method (Mammen, 1993).”
General Bayesian updating and the loss-likelihood bootstrap (2017, background): “The Bayesian bootstrap can produce posterior samples for a much larger family of parameters than just those that maximize expected log likelihoods, see for example Chamberlain and Imbens (2003). Of interest to us is the family of parameters than minimize an expected loss, as in (1).”
Nonparametric identification in panels using quantiles (2013, methodology): “Following Praestgaard and Wellner (1993), Hahn (1995), and Chamberlain and Imbens (2003), we use weighted bootstrap for inference.1 To describe this method, let (w1, . . . , wn) be an i.i.d. sequence of nonnegative random variables from a distribution with mean and variance equal to one (e.g., the…”
Bayesian and Empirical Bayesian Forests (2015, background): “Chamberlain & Imbens (2003) provide an overview in the context of econometric problems.”
Smoothly mixing regressions (2007, methodology): “(1996) and Chamberlain and Imbens (2003), the latter with an application related to the example in Section 3.”