25,270 research outputs found
On the Brittleness of Bayesian Inference
With the advent of high-performance computing, Bayesian methods are
increasingly popular tools for the quantification of uncertainty throughout
science and industry. Since these methods impact the making of sometimes
critical decisions in increasingly complicated contexts, the sensitivity of
their posterior conclusions with respect to the underlying models and prior
beliefs is a pressing question for which there currently exist positive and
negative results. We report new results suggesting that, although Bayesian
methods are robust when the number of possible outcomes is finite or when only
a finite number of marginals of the data-generating distribution are unknown,
they could be generically brittle when applied to continuous systems (and their
discretizations) with finite information on the data-generating distribution.
If closeness is defined in terms of the total variation metric or the matching
of a finite system of generalized moments, then (1) two practitioners who use
arbitrarily close models and observe the same (possibly arbitrarily large
amount of) data may reach opposite conclusions; and (2) any given prior and
model can be slightly perturbed to achieve any desired posterior conclusions.
The mechanism causing brittlenss/robustness suggests that learning and
robustness are antagonistic requirements and raises the question of a missing
stability condition for using Bayesian Inference in a continuous world under
finite information.Comment: 20 pages, 2 figures. To appear in SIAM Review (Research Spotlights).
arXiv admin note: text overlap with arXiv:1304.677
Nonparametric Conditional Inference for Regression Coefficients with Application to Configural Polysampling
We consider inference procedures, conditional on an observed ancillary
statistic, for regression coefficients under a linear regression setup where
the unknown error distribution is specified nonparametrically. We establish
conditional asymptotic normality of the regression coefficient estimators under
regularity conditions, and formally justify the approach of plugging in
kernel-type density estimators in conditional inference procedures. Simulation
results show that the approach yields accurate conditional coverage
probabilities when used for constructing confidence intervals. The plug-in
approach can be applied in conjunction with configural polysampling to derive
robust conditional estimators adaptive to a confrontation of contrasting
scenarios. We demonstrate this by investigating the conditional mean squared
error of location estimators under various confrontations in a simulation
study, which successfully extends configural polysampling to a nonparametric
context
Justifying Inference to the Best Explanation as a Practical Meta-Syllogism on Dialectical Structures
This article discusses how inference to the best explanation (IBE) can be justified as a practical meta-argument. It is, firstly, justified as a *practical* argument insofar as accepting the best explanation as true can be shown to further a specific aim. And because this aim is a discursive one which proponents can rationally pursue in--and relative to--a complex controversy, namely maximising the robustness of one's position, IBE can be conceived, secondly, as a *meta*-argument. My analysis thus bears a certain analogy to Sellars' well-known justification of inductive reasoning (Sellars 1969); it is based on recently developed theories of complex argumentation (Betz 2010, 2011)
RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs
Power and reproducibility are key to enabling refined scientific discoveries
in contemporary big data applications with general high-dimensional nonlinear
models. In this paper, we provide theoretical foundations on the power and
robustness for the model-free knockoffs procedure introduced recently in
Cand\`{e}s, Fan, Janson and Lv (2016) in high-dimensional setting when the
covariate distribution is characterized by Gaussian graphical model. We
establish that under mild regularity conditions, the power of the oracle
knockoffs procedure with known covariate distribution in high-dimensional
linear models is asymptotically one as sample size goes to infinity. When
moving away from the ideal case, we suggest the modified model-free knockoffs
method called graphical nonlinear knockoffs (RANK) to accommodate the unknown
covariate distribution. We provide theoretical justifications on the robustness
of our modified procedure by showing that the false discovery rate (FDR) is
asymptotically controlled at the target level and the power is asymptotically
one with the estimated covariate distribution. To the best of our knowledge,
this is the first formal theoretical result on the power for the knockoffs
procedure. Simulation results demonstrate that compared to existing approaches,
our method performs competitively in both FDR control and power. A real data
set is analyzed to further assess the performance of the suggested knockoffs
procedure.Comment: 37 pages, 6 tables, 9 pages supplementary materia
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