Construction of weakly CUD sequences for MCMC sampling

In Markov chain Monte Carlo (MCMC) sampling considerable thought goes into constructing random transitions. But those transitions are almost always driven by a simulated IID sequence. Recently it has been shown that replacing an IID sequence by a weakly completely uniformly distributed (WCUD) sequence leads to consistent estimation in finite state spaces. Unfortunately, few WCUD sequences are known. This paper gives general methods for proving that a sequence is WCUD, shows that some specific sequences are WCUD, and shows that certain operations on WCUD sequences yield new WCUD sequences. A numerical example on a 42 dimensional continuous Gibbs sampler found that some WCUD inputs sequences produced variance reductions ranging from tens to hundreds for posterior means of the parameters, compared to IID inputs.Comment: Published in at http://dx.doi.org/10.1214/07-EJS162 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measures of metacognition on signal-detection theoretic models

Analysing metacognition, specifically knowledge of accuracy of internal perceptual, memorial or other knowledge states, is vital for many strands of psychology, including determining the accuracy of feelings of knowing, and discriminating conscious from unconscious cognition. Quantifying metacognitive sensitivity is however more challenging than quantifying basic stimulus sensitivity. Under popular signal detection theory (SDT) models for stimulus classification tasks, approaches based on type II receiver-operator characteristic (ROC) curves or type II d-prime risk confounding metacognition with response biases in either the type I (classification) or type II (metacognitive) tasks. A new approach introduces meta-d′: the type I d-prime that would have led to the observed type II data had the subject used all the type I information. Here we (i) further establish the inconsistency of the type II d-prime and ROC approaches with new explicit analyses of the standard SDT model, and (ii) analyse, for the first time, the behaviour of meta-d′ under non-trivial scenarios, such as when metacognitive judgments utilize enhanced or degraded versions of the type I evidence. Analytically, meta-d′ values typically reflect the underlying model well, and are stable under changes in decision criteria; however, in relatively extreme cases meta-d′ can become unstable. We explore bias and variance of in-sample measurements of meta-d′ and supply MATLAB code for estimation in general cases. Our results support meta-d′ as a useful measure of metacognition, and provide rigorous methodology for its application. Our recommendations are useful for any researchers interested in assessing metacognitive accuracy

The role of visual and mechanosensory cues in structuring forward flight in Drosophila melanogaster

It has long been known that many flying insects use visual cues to orient with respect to the wind and to control their groundspeed in the face of varying wind conditions. Much less explored has been the role of mechanosensory cues in orienting insects relative to the ambient air. Here we show that Drosophila melanogaster, magnetically tethered so as to be able to rotate about their yaw axis, are able to detect and orient into a wind, as would be experienced during forward flight. Further, this behavior is velocity dependent and is likely subserved, at least in part, by the Johnston's organs, chordotonal organs in the antennae also involved in near-field sound detection. These wind-mediated responses may help to explain how flies are able to fly forward despite visual responses that might otherwise inhibit this behavior. Expanding visual stimuli, such as are encountered during forward flight, are the most potent aversive visual cues known for D. melanogaster flying in a tethered paradigm. Accordingly, tethered flies strongly orient towards a focus of contraction, a problematic situation for any animal attempting to fly forward. We show in this study that wind stimuli, transduced via mechanosensory means, can compensate for the aversion to visual expansion and thus may help to explain how these animals are indeed able to maintain forward flight

Acoustic positioning and orientation prediction

A method is described for use with an acoustic positioner, which enables a determination of the equilibrium position and orientation which an object assumes in a zero gravity environment, as well as restoring forces and torques of an object in an acoustic standing wave field. An acoustic standing wave field is established in the chamber, and the object is held at several different positions near the expected equilibrium position. While the object is held at each position, the center resonant frequency of the chamber is determined, by noting which frequency results in the greatest pressure of the acoustic field. The object position which results in the lowest center resonant frequency is the equilibrium position. The orientation of a nonspherical object is similarly determined, by holding the object in a plurality of different orientations at its equilibrium position, and noting the center resonant frequency for each orientation. The orientation which results in the lowest center resonant frequency is the equilibrium orientation. Where the acoustic frequency is constant, but the chamber length is variable, the equilibrium position or orientation is that which results in the greatest chamber length at the center resonant frequency

Blind insight: metacognitive discrimination despite chance task performance

Blindsight and other examples of unconscious knowledge and perception demonstrate dissociations between judgment accuracy and metacognition: Studies reveal that participants’ judgment accuracy can be above chance while their confidence ratings fail to discriminate right from wrong answers. Here, we demonstrated the opposite dissociation: a reliable relationship between confidence and judgment accuracy (demonstrating metacognition) despite judgment accuracy being no better than chance. We evaluated the judgments of 450 participants who completed an AGL task. For each trial, participants decided whether a stimulus conformed to a given set of rules and rated their confidence in that judgment. We identified participants who performed at chance on the discrimination task, utilizing a subset of their responses, and then assessed the accuracy and the confidence-accuracy relationship of their remaining responses. Analyses revealed above-chance metacognition among participants who did not exhibit decision accuracy. This important new phenomenon, which we term blind insight, poses critical challenges to prevailing models of metacognition grounded in signal detection theory

The Impact of Property Assessment Standards on Property Tax Burden: An Examination of Systematic Bias in a Market Value versus a Non-Market Value Assessment Standard

Property tax is a tax on estimated values rather than on transactions—an important distinction from other taxes. Another distinction is that each state develops its own system for administering the property tax, including how properties are assessed. The consensus among scholars is that current market value assessment is the standard for achieving the most fair and equitable property tax burden. This study compares two disparate assessment standards in one urban county, analyzing potential determinants of systematic bias. The findings indicate that less systematic bias exists under the market value standard, but that the overall equity is only marginally better horizontally and tended toward a more regressive tax structure. A market value assessment standard may mitigate the inherent inequity (i.e., systematic bias) in a nonmarket value system. However, the inequities in the market value system, which may be less predictable, still must be monitored and addressed