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

Single camera pose estimation using Bayesian filtering and Kinect motion priors

Traditional approaches to upper body pose estimation using monocular vision rely on complex body models and a large variety of geometric constraints. We argue that this is not ideal and somewhat inelegant as it results in large processing burdens, and instead attempt to incorporate these constraints through priors obtained directly from training data. A prior distribution covering the probability of a human pose occurring is used to incorporate likely human poses. This distribution is obtained offline, by fitting a Gaussian mixture model to a large dataset of recorded human body poses, tracked using a Kinect sensor. We combine this prior information with a random walk transition model to obtain an upper body model, suitable for use within a recursive Bayesian filtering framework. Our model can be viewed as a mixture of discrete Ornstein-Uhlenbeck processes, in that states behave as random walks, but drift towards a set of typically observed poses. This model is combined with measurements of the human head and hand positions, using recursive Bayesian estimation to incorporate temporal information. Measurements are obtained using face detection and a simple skin colour hand detector, trained using the detected face. The suggested model is designed with analytical tractability in mind and we show that the pose tracking can be Rao-Blackwellised using the mixture Kalman filter, allowing for computational efficiency while still incorporating bio-mechanical properties of the upper body. In addition, the use of the proposed upper body model allows reliable three-dimensional pose estimates to be obtained indirectly for a number of joints that are often difficult to detect using traditional object recognition strategies. Comparisons with Kinect sensor results and the state of the art in 2D pose estimation highlight the efficacy of the proposed approach.Comment: 25 pages, Technical report, related to Burke and Lasenby, AMDO 2014 conference paper. Code sample: https://github.com/mgb45/SignerBodyPose Video: https://www.youtube.com/watch?v=dJMTSo7-uF

Persistence of political partisanship : evidence from 9/11

This paper empirically examines whether the act of deciding to support a political party can impact partisan leanings years later. We use the discontinuity in the probability of being registered to vote around the 18th birthday to look at the impact of registration after the 9/11/01 attacks on party of registration. We first show that 9/11 increased Republican registration by approximately 2%. Surprisingly, these di¤erences in registration patterns fully persist over the two year period from 2006 to 2008, even for a group of registrants who moved and changed their registration address. We find full persistence for those registered in zip codes within two miles of a four year university, suggesting that persistence is unlikely to be explained by lack of easy access to or inability to process information. Instead, we suggest an interpretation of our findings based upon either cognitive or social biases