A tutorial on Bayes factor estimation with the product space method

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial to implement. In this tutorial, we explain and illustrate the use of one such procedure, known as the product space method (Carlin & Chib, 1995). This is a transdimensional Markov chain Monte Carlo method requiring the construction of a “supermodel” encompassing the models under consideration. A model index measures the proportion of times that either model is visited to account for the observed data. This proportion can then be transformed to yield a Bayes factor. We discuss the theory behind the product space method and illustrate, by means of applied examples from psychological research, how the method can be implemented in practice.     

Exploring Directional Consistency in Offending: The Case of Residential Burglary in The Hague

Many aspects of human behaviour are remarkably stable across times, places and situations. Repetition and predictability also characterises our geographical behaviour. Prior research has confirmed that criminal behaviour is no exception. Offenders tend to recidivate, and recidivists tend to be behaviourally consistent in many aspects, including geographical ones. The present study assesses directional consistency in offending. It reviews the literature on directional consistency. It proposes an improved measure of directional consistency, and empirically uses this measure to explore directional consistency amongst a set of 268 burglars in The Hague. Copyright © 2012 John Wiley & Sons, Ltd.     

An application of Carnapian inductive logic to an argument in the philosophy of statistics

I claim that an argument from the philosophy of statistics can be improved by using Carnapian inductive logic. Gelman and Shalizi [9] criticise a philosophical account of how statisticians ought to choose statistical models which they call ‘the received view of Bayesian inference’ and propose a different account inspired by falsificationist philosophy of science. I introduce another philosophical account inspired by Carnapian inductive logic and argue that it is even better than Gelman and Shalizi's falsificationist account.     

Outline of a Physico-Mathematical Theory of the Brain

The author comments on the (mis?)portrayal of her research in an article by Brand and Bradley (2012).     

Episodes of momentary resilience in daily life are associated with HRV reductions to stressful operations in firefighters: an ambulatory assessment approach using bayesian multilevel modeling

ABSTRACT

Background: Resilience is discussed to constitute a protective buffer against stress, thus fostering health. Methods: This study aimed to assess resilience both via traditional questionnaire and in everyday life on a momentary basis, and to relate these measures to autonomic functioning (heart rate variability, HRV) in 38 male firefighters during a weekday. Stressful operations, non-stressful operations and routine work at the firestation were coded during 24 hours. Momentary negative affect, feelings of resilience, and HRV were recorded via ecological momentary assessment. Findings: Questionnaire-assessed resilience was significantly positively associated with aggregated momentary resilience (r = .58, p < .001), but unrelated to HRV. However, controlling for multiple confounders (e.g., age, smoking, bodily movement, waist-to-height ratio) momentary resilience was associated with attenuated HRV and lower negative affect during stressful encounters only. Discussion: The findings suggest that momentary feelings of resilience are accompanied by vagal withdrawal to stress, possibly indicating psychological flexibility and adaptive responding to stress.     

Apes are intuitive statisticians

Inductive learning and reasoning, as we use it both in everyday life and in science, is characterized by flexible inferences based on statistical information: inferences from populations to samples and vice versa. Many forms of such statistical reasoning have been found to develop late in human ontogeny, depending on formal education and language, and to be fragile even in adults. New revolutionary research, however, suggests that even preverbal human infants make use of intuitive statistics. Here, we conducted the first investigation of such intuitive statistical reasoning with non-human primates. In a series of 7 experiments, Bonobos, Chimpanzees, Gorillas and Orangutans drew flexible statistical inferences from populations to samples. These inferences, furthermore, were truly based on statistical information regarding the relative frequency distributions in a population, and not on absolute frequencies. Intuitive statistics in its most basic form is thus an evolutionarily more ancient rather than a uniquely human capacity.     

Model based clustering of large data sets: Tracing the development of spelling ability

There are two main theories with respect to the development of spelling ability: the stage model and the model of overlapping waves. In this paper exploratory model based clustering will be used to analyze the responses of more than 3500 pupils to subsets of 245 items. To evaluate the two theories, the resulting clusters will be ordered along a developmental dimension using an external criterion. Solutions for three statistical problems will be given: (1) an algorithm that can handle large data sets and only renders non-degenerate clusters; (2) a goodness of fit test that is not affected by the fact that the number of possible response vectors by far out-weights the number of observed response vectors; and (3) a new technique,data expunction, that can be used to evaluate goodness-of-fit tests if the missing data mechanism is known. Research supported by a grant (NWO 411-21-006) of the Dutch Organization for Scientific Research.     

‘Peer review’ culture

A relatively high incidence of unsatisfactory review decisions is widely recognised and acknowledged as ‘the peer review problem’. Factors contributing to this problem are identified and examined. Specific examples of unreasonable rejection are considered. It is concluded that weaknesses of the ‘peer review’ system are significant and that they are well known or readily recognisable but that necessary counter-measures are not always enforced. Careful management is necessary to discount hollow opinion or error in review comment. Review and referee functions should be quite separate.     

Factor analysis and Psychometrika: Major developments

Papers on factor analysis appearing inPsychometrika reflect the initial efforts of the Thurstonians to reformulate psychology as a quantitative science. The Thurstonians' emphasis on the development of factor analysis as an exploratory methodology was not new with them but was taken from British statisticians and psychologists who preceded them, whose literature the Thurstonians otherwise tended to ignore. The Thurstonians' rejection of general factors and focus on rotation to simple structure reflected an attempt to avoid statistical artifact and to identify factors with psychological substance. Much of the literature on factor analysis inPsychometrika concerned solving technical problems in the exploratory factor analysis method. Factor analysis took a major shift in direction in the 1970's with the development of confirmatory methodologies, many of which now receive greater attention than the method of exploratory factor analysis, most of the problems of which are now resolved.     

A note on Roy's largest root

The name Roy's largest root and similar names are used in practice to label two different but functionally related statistics—one proportional to anF, and the other, a squared canonical correlation. This note presents the logic that leads to the two formulations, states which statistic some popular statistical packages use, and shows the possible source of this inconsistency in the original work of Roy (1953) and Heck (1960).