Approximate knowledge of rationality and correlated equilibria

We extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. Wereplace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probability p or more. We show that behavior in this case constitutes a kind of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one,with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interimtypes, to games of incomplete information, as well as to the case of non-common priors.

Survey on batch-to-batch variation in spray paints: a collaborative study

This study represents the most extensive analysis of batch-to-batch variations in spray paint samples to date. The survey was performed as a collaborative project of the ENFSI (European Network of Forensic Science Institutes) Paint and Glass Working Group (EPG) and involved 11 laboratories. Several studies have already shown that paint samples of similar color but from different manufacturers can usually be differentiated using an appropriate analytical sequence. The discrimination of paints from the same manufacturer and color (batch-to-batch variations) is of great interest and these data are seldom found in the literature. This survey concerns the analysis of batches from different color groups (white, papaya (special shade of orange), red and black) with a wide range of analytical techniques and leads to the following conclusions. Colored batch samples are more likely to be differentiated since their pigment composition is more complex (pigment mixtures, added pigments) and therefore subject to variations. These variations may occur during the paint production but may also occur when checking the paint shade in quality control processes. For these samples, techniques aimed at color/pigment(s) characterization (optical microscopy, microspectrophotometry (MSP), Raman spectroscopy) provide better discrimination than techniques aimed at the organic (binder) or inorganic composition (fourier transform infrared spectroscopy (FTIR) or elemental analysis (SEM - scanning electron microscopy and XRF - X-ray fluorescence)). White samples contain mainly titanium dioxide as a pigment and the main differentiation is based on the binder composition (Csingle bondH stretches) detected either by FTIR or Raman. The inorganic composition (elemental analysis) also provides some discrimination. Black samples contain mainly carbon black as a pigment and are problematic with most of the spectroscopic techniques. In this case, pyrolysis-GC/MS represents the best technique to detect differences. Globally, Py-GC/MS may show a high potential of discrimination on all samples but the results are highly dependent on the specific instrumental conditions used. Finally, the discrimination of samples when data was interpreted visually as compared to statistically using principal component analysis (PCA) yielded very similar results. PCA increases sensitivity and could perform better on specific samples, but one first has to ensure that all non-informative variation (baseline deviation) is eliminated by applying correct pre-treatments. Statistical treatments can be used on a large data set and, when combined with an expert's opinion, will provide more objective criteria for decision making.

Estimating vadose zone hydraulic properties using ground penetrating radar: The impact of prior information

A number of geophysical methods, such as ground-penetrating radar (GPR), have the potential to provide valuable information on hydrological properties in the unsaturated zone. In particular, the stochastic inversion of such data within a coupled geophysical-hydrological framework may allow for the effective estimation of vadose zone hydraulic parameters and their corresponding uncertainties. A critical issue in stochastic inversion is choosing prior parameter probability distributions from which potential model configurations are drawn and tested against observed data. A well chosen prior should reflect as honestly as possible the initial state of knowledge regarding the parameters and be neither overly specific nor too conservative. In a Bayesian context, combining the prior with available data yields a posterior state of knowledge about the parameters, which can then be used statistically for predictions and risk assessment. Here we investigate the influence of prior information regarding the van Genuchten-Mualem (VGM) parameters, which describe vadose zone hydraulic properties, on the stochastic inversion of crosshole GPR data collected under steady state, natural-loading conditions. We do this using a Bayesian Markov chain Monte Carlo (MCMC) inversion approach, considering first noninformative uniform prior distributions and then more informative priors derived from soil property databases. For the informative priors, we further explore the effect of including information regarding parameter correlation. Analysis of both synthetic and field data indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when we combine these data with a realistic, informative prior.

Candidate SNPs for carcass and meat traits in Nelore animals and in their crosses with Bos taurus

The objective of this work was to evaluate the effects of single-nucleotide polymorphisms (SNPs) in the genes IGF1 (AF_017143.1:g.198C>T), MSTN (AF_320998.1:g.433C>A), MYOD1 (NC_007313:g.1274A>G) and MYF5 (NC_007303:g.1911A>G) on carcass and meat traits in Nelore (Bos indicus) and Nelore x B. taurus. A total of 300 animals were genotyped and phenotyped for rib eye area (REA), backfat thickness (BT), intramuscular fat (IF), shear force (SF) and myofibrillar fragmentation index (MFI). The effects of allele substitution for each SNP were estimated by regression of the evaluated phenotypes on the number of copies of a particular allele using the general linear model. The polymorphism at IGF1 was non-informative in Nelore animals. In crossbred animals, the IGF1 C allele was associated with greater REA. However, this relation was not significant after Bonferroni correction for multiple testing. The A allele of the MSTN polymorphism was absent in Nelore cattle and was only found in two crossbred animals. The polymorphisms of MYOD1 and MYF5 were little informative in Nelore animals with G allele frequency of 0.097 and A allele frequency of 0.031, respectively. These markers show no association with the analyzed traits in the total sample of evaluated animals.

A comparison of Bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk.

We present the most comprehensive comparison to date of the predictive benefit of genetics in addition to currently used clinical variables, using genotype data for 33 single-nucleotide polymorphisms (SNPs) in 1,547 Caucasian men from the placebo arm of the REduction by DUtasteride of prostate Cancer Events (REDUCE®) trial. Moreover, we conducted a detailed comparison of three techniques for incorporating genetics into clinical risk prediction. The first method was a standard logistic regression model, which included separate terms for the clinical covariates and for each of the genetic markers. This approach ignores a substantial amount of external information concerning effect sizes for these Genome Wide Association Study (GWAS)-replicated SNPs. The second and third methods investigated two possible approaches to incorporating meta-analysed external SNP effect estimates - one via a weighted PCa 'risk' score based solely on the meta analysis estimates, and the other incorporating both the current and prior data via informative priors in a Bayesian logistic regression model. All methods demonstrated a slight improvement in predictive performance upon incorporation of genetics. The two methods that incorporated external information showed the greatest receiver-operating-characteristic AUCs increase from 0.61 to 0.64. The value of our methods comparison is likely to lie in observations of performance similarities, rather than difference, between three approaches of very different resource requirements. The two methods that included external information performed best, but only marginally despite substantial differences in complexity.

Inhibition of return, gap effect and saccadic reaction time to a visual target

Simple manual reaction time (MRT) to a visual target (S2) is shortened when a non-informative cue (S1) is flashed at the S2 location shortly before the onset of S2 (early facilitation). Afterwards, MRT to S2 appearing at the S1 location is lengthened (inhibition of return - IOR). Similar results have been obtained for saccadic reaction time (SRT). Moreover, when there is a temporal gap between offset of the fixation point (FP) and onset of a target (gap paradigm), SRT is shorter than SRT in an overlap paradigm (FP remains on). In the present study, we determined SRT to S2 (10º) after presenting S1 at the same eccentricity (10º) or at a parafoveal position (2º) in the same or in the opposite hemifield. In addition, we employed both gap and overlap paradigms. Twelve subjects were asked not to respond to S1 (2º or 10º) to the right or to the left of FP, but to respond by making a saccadic movement in response to S2. We obtained the following results: 1) a 40-ms gap effect, 2) an interaction between gap effect and IOR, 3) a 39-ms delay (IOR) when S2 appeared at the cued (S1) position, and 4) a smaller (17 ms) but significant inhibition when S1 occurred at 2º in the ipsilateral hemifield. Thus, a parafoveal (2º) S1 elicits an inhibition of SRT towards ipsilateral peripheral targets. Since an inhibition of the ipsilateral hemifield by a 1º eccentric cue has been reported to occur when manual responses are employed, we suggest that the postulated functional link between covert and overt orienting of attention is also valid for parafoveal cues.

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry as an alternate and complementary tool to classical shape analysis, especially when size is non-informative. Shapes are typically described by the location of user-chosen landmarks. However the shape – considered as invariant under scaling, translation, mirroring and rotation – does not uniquely define the location of landmarks. A simple approach is to use distances of landmarks instead of the locations of landmarks them self. Distances are positive numbers defined up to joint scaling, a mathematical structure quite similar to compositions. The shape fixes only ratios of distances. Perturbations correspond to relative changes of the size of subshapes and of aspect ratios. The power transform increases the expression of the shape by increasing distance ratios. In analogy to the subcompositional consistency, results should not depend too much on the choice of distances, because different subsets of the pairwise distances of landmarks uniquely define the shape. Various compositional analysis tools can be applied to sets of distances directly or after minor modifications concerning the singularity of the covariance matrix and yield results with direct interpretations in terms of shape changes. The remaining problem is that not all sets of distances correspond to a valid shape. Nevertheless interpolated or predicted shapes can be backtransformated by multidimensional scaling (when all pairwise distances are used) or free geodetic adjustment (when sufficiently many distances are used)

Viewing the body modulates tactile receptive fields

Tactile discrimination performance depends on the receptive field (RF) size of somatosensory cortical (SI) neurons. Psychophysical masking effects can reveal the RF of an idealized "virtual" somatosensory neuron. Previous studies show that top-down factors strongly affect tactile discrimination performance. Here, we show that non-informative vision of the touched body part influences tactile discrimination by modulating tactile RFs. Ten subjects performed spatial discrimination between touch locations on the forearm. Performance was improved when subjects saw their forearm compared to viewing a neutral object in the same location. The extent of visual information was relevant, since restricted view of the forearm did not have this enhancing effect. Vibrotactile maskers were placed symmetrically on either side of the tactile target locations, at two different distances. Overall, masking significantly impaired discrimination performance, but the spatial gradient of masking depended on what subjects viewed. Viewing the body reduced the effect of distant maskers, but enhanced the effect of close maskers, as compared to viewing a neutral object. We propose that viewing the body improves functional touch by sharpening tactile RFs in an early somatosensory map. Top-down modulation of lateral inhibition could underlie these effects.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (C) 2007 John Wiley & Sons, Ltd.

Vision of the body and the differentiation of perceived body side in touch

Although tactile representations of the two body sides are initially segregated into opposite hemispheres of the brain, behavioural interactions between body sides exist and can be revealed under conditions of tactile double simultaneous stimulation (DSS) at the hands. Here we examined to what extent vision can affect body side segregation in touch. To this aim, we changed hand-related visual input while participants performed a go/no-go task to detect a tactile stimulus delivered to one target finger (e.g., right index), stimulated alone or with a concurrent non-target finger either on the same hand (e.g., right middle finger) or on the other hand (e.g., left index finger = homologous; left middle finger = non-homologous). Across experiments, the two hands were visible or occluded from view (Experiment 1), images of the two hands were either merged using a morphing technique (Experiment 2), or were shown in a compatible vs incompatible position with respect to the actual posture (Experiment 3). Overall, the results showed reliable interference effects of DSS, as compared to target-only stimulation. This interference varied as a function of which non-target finger was stimulated, and emerged both within and between hands. These results imply that the competition between tactile events is not clearly segregated across body sides. Crucially, non-informative vision of the hand affected overall tactile performance only when a visual/proprioceptive conflict was present, while neither congruent nor morphed hand vision affected tactile DSS interference. This suggests that DSS operates at a tactile processing stage in which interactions between body sides can occur regardless of the available visual input from the body.

Bayesian estimation of regression parameters in elliptical measurement error models

The main object of this paper is to discuss the Bayes estimation of the regression coefficients in the elliptically distributed simple regression model with measurement errors. The posterior distribution for the line parameters is obtained in a closed form, considering the following: the ratio of the error variances is known, informative prior distribution for the error variance, and non-informative prior distributions for the regression coefficients and for the incidental parameters. We proved that the posterior distribution of the regression coefficients has at most two real modes. Situations with a single mode are more likely than those with two modes, especially in large samples. The precision of the modal estimators is studied by deriving the Hessian matrix, which although complicated can be computed numerically. The posterior mean is estimated by using the Gibbs sampling algorithm and approximations by normal distributions. The results are applied to a real data set and connections with results in the literature are reported. (C) 2011 Elsevier B.V. All rights reserved.

Bayesian Analysis for the Generalized Lognormal Distribution Applied to Failure Time Analysis

There are several versions of the lognormal distribution in the statistical literature, one is based in the exponential transformation of generalized normal distribution (GN). This paper presents the Bayesian analysis for the generalized lognormal distribution (logGN) considering independent non-informative Jeffreys distributions for the parameters as well as the procedure for implementing the Gibbs sampler to obtain the posterior distributions of parameters. The results are used to analyze failure time models with right-censored and uncensored data. The proposed method is illustrated using actual failure time data of computers.

Uncertainty aversion and the optmal choice of portfolio

In this paper we apply the theory of declsion making with expected utility and non-additive priors to the choice of optimal portfolio. This theory describes the behavior of a rational agent who i5 averse to pure 'uncertainty' (as well as, possibly, to 'risk'). We study the agent's optimal allocation of wealth between a safe and an uncertain asset. We show that there is a range of prices at which the agent neither buys not sells short the uncertain asset. In contrast the standard theory of expected utility predicts that there is exactly one such price. We also provide a definition of an increase in uncertainty aversion and show that it causes the range of prices to increase.

Openability of soft drinks PET packagings

Studies on packaging accessibility are still incipient in Brazil. Many of these packagings can represent a challenge to users, whether due to non-informative labels, tricky tabs or seals, or even those that need strength to open. This paper brings a simple test to determine the necessary torque force to open PET bottles, and to predict the amount of users that could not open it. The findings suggest that a considerable amount of users could not open it or would have some difficulties to exert the necessary force.