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.     

Constructing informative model priors using hierarchical methods

Despite their negative reputation, informative priors are very useful in inference. Priors that express psychologically meaningful intuitions damp out random fluctuations in the data due to sampling variability, without sacrificing flexibility. This article focuses on how an intuitively satisfying informative prior distribution can be constructed. In particular, it demonstrates how the hierarchical introduction of a parameterized generative account of the set of models under consideration naturally imposes a non-uniform prior distribution over the models, encoding existing intuitions about the models. The hierarchical approach for constructing informative model priors is made concrete using a worked example, the Varying Abstraction Model (VAM), a family of categorization models including and expanding the exemplar and prototype models. It is shown how psychological intuitions about the relative plausibilities of the models in the VAM can be formally captured in an informative prior distribution over these models, by specifying a theoretically informed process for generating the models in the VAM. The smoothing effect of the informative prior in estimation is demonstrated by considering ten previously published data sets from the category learning literature.     

Hierarchical single- and dual-process models of recognition memory

Recognition memory is commonly modeled as either a single, continuous process within the theory of signal detection, or with two-process models such as Yonelinas’ dual-process model. Previous attempts to determine which model provides a better account of the data have relied on fitting the models to data that are averaged over items. Because such averaging distorts conclusions, we develop and compare hierarchical versions of competing single and dual-process models that account for item variability. The dual-process model provides a superior account of a typical data set when models are compared with the deviance information criterion. Parameters of the dual-process model are highly correlated, however, suggesting that a single-process model may exist that can provide a better account of the data.     

Reflexivity in pigeons

A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was trained in this fashion; a second group was trained similarly but with successive oddity (rather than identity). Subsequently, comparison-response rates on novel matching versus mismatching sequences with the remaining symbolic matching stimuli were measured on nonreinforced probe trials. Higher rates were observed on matching than on mismatching probes in the former group. The opposite effect--higher rates on mismatching than matching probes--was mostly absent in the latter group, despite being predicted by the theory. Nevertheless, the ostensible reflexivity effect observed in former group may be the first time this phenomenon has been demonstrated in any animal.     

Children's Production of Unfamiliar Word Sequences Is Predicted by Positional Variability and Latent Classes in a Large Sample of Child-Directed Speech

We explore whether children's willingness to produce unfamiliar sequences of words reflects their experience with similar lexical patterns. We asked children to repeat unfamiliar sequences that were identical to familiar phrases (e.g., A piece of toast) but for one word (e.g., a novel instantiation of A piece of X, like A piece of brick). We explore two predictions-motivated by findings in the statistical learning literature-that children are likely to have detected an opportunity to substitute alternative words into the final position of a four-word sequence if (a) it is difficult to predict the fourth word given the first three words and (b) the words observed in the final position are distributionally similar. Twenty-eight 2-year-olds and thirty-one 3-year-olds were significantly more likely to correctly repeat unfamiliar variants of patterns for which these properties held. The results illustrate how children's developing language is shaped by linguistic experience.     

Contextualizing neuroticism in the Hierarchical Taxonomy of Psychopathology

Neuroticism is the personality trait most consistently and strongly connected to psychopathology. The majority of research on the relationship between traits and mental illness has focused on neuroticism’s connection with broad psychopathology spectra or discrete disorders. However, both personality and psychopathology are hierarchically-organized domains that may be examined at multiple levels of fidelity and bandwidth from very specific thoughts, feelings, and behaviors (i.e., nuance traits or symptoms) to very broad patterns indexing many interrelated tendencies (i.e., general factors). The Hierarchical Taxonomy of Psychopathology (HiTOP) is a recently proposed nosologic framework for psychopathology symptoms and domains that accounts for this tiered organization. Here, we illustrate how neuroticism-psychopathology relationships—both what is known and unknown—may be elucidated through the HiTOP system.     

Comparing hierarchical models of personality pathology

Two dimensional, hierarchical classification models of personality pathology have emerged as alternatives to traditional categorical systems: multi-tiered models with increasing numbers of factors and models that distinguish between a general factor of severity and specific factors reflecting style. Using a large sample (N = 840) with a range of psychopathology, we conducted exploratory factor analyses of individual personality disorder criteria to evaluate the validity of these conceptual structures. We estimated an oblique, “unfolding” hierarchy and a bifactor model, then examined correlations between these and multi-method functioning measures to enrich interpretation. Four-factor solutions for each model, reflecting rotations of each other, fit well and equivalently. The resulting structures are consistent with previous empirical work and provide support for each theoretical model.     

Biased belief in the Bayesian brain: A deeper look at the evidence

A recent critique of hierarchical Bayesian models of delusion argues that, contrary to a key assumption of these models, belief formation in the healthy (i.e., neurotypical) mind is manifestly non-Bayesian. Here we provide a deeper examination of the empirical evidence underlying this critique. We argue that this evidence does not convincingly refute the assumption that belief formation in the neurotypical mind approximates Bayesian inference. Our argument rests on two key points. First, evidence that purports to reveal the most damning violation of Bayesian updating in human belief formation is counterweighted by substantial evidence that indicates such violations are the rare exception—not a common occurrence. Second, the remaining evidence does not demonstrate convincing violations of Bayesian inference in human belief updating; primarily because this evidence derives from study designs that produce results that are not obviously inconsistent with Bayesian principles.     

SEAT-DSR: Spatial and energy aware trusted dynamic distance source routing algorithm for secure data communications in wireless sensor networks

This paper propose a novel secure routing mechanism called Spatial and Energy Aware Trusted Dynamic Distance Source Routing (SEAT-DSR) algorithm for enhancing the network life time of wireless sensor networks. Here, the spatial information, energy level, and the effectiveness of data quality are equalized by the Quality of Service (QoS) based energy aware routing algorithms. In addition to this approach, a standard clustering algorithm is also incorporates for grouping the wireless sensor nodes based on the trust score, spatial information, energy level and the distance between the nodes. In this SEAT-DSR is also capable of making decision over the evaluation metrics that are decided and expressed the QoS. Moreover, a new hierarchical trust mechanism is also introduced in this model which adopts multi-attributes of many wireless sensor nodes according to the data communication speed, data size, energy consumption, and the recommendation. This new hierarchical trust method relies over an improved the sliding window time by considering the presence of various attacks frequency to identify the attackers by discovering their anomalous behaviour. The proposed SEAT-DSR is evaluated by conducting many experiments in a simulation environment that creates by using Network Simulator-2 (NS2). The experimental results of the proposed algorithm are proved that the average packet transfer rate is increased drastically than the existing secure routing methodologies.     

Cognitive capacities for behavioural flexibility in wild chimpanzees (Pan troglodytes): the effect of snare injury on complex manual food processing

In chimpanzees, it is only in the restricted context of tool use that manual and cognitive skills have been described, comparable to those that gorillas and orang-utans display in obtaining plant foods. We report the complex food preparation skills used to eat, without tools, the leaves of the tree Broussonettia papyrifera in the Sonso community of chimpanzees at Budongo Forest, Uganda. Able-bodied individuals used multi-stage techniques that required bimanual role differentiation at several stages, and were hierarchical in organisation. A total repertoire of 14 techniques was found, with strong preference in all individuals for either of two of these; 6 additional techniques were found when flowers and leaves were eaten together. However, in this community over 20% of individuals suffer from some form of upper- or lower-limb injury as a result of snares. We investigated the manner of compensation for upper-limb injury. Only the most severely injured showed reduced feeding efficiency. Injured individuals were found to use the same repertoire of techniques as able-bodied chimpanzees. We found no evidence to suggest that injured individuals were able to develop wholly novel techniques optimal for their specific injuries, although shifts in preference for particular techniques did occur. Rather, injured individuals used novel ways of achieving particular steps in the process; by "working around" their impairments; in this way, they managed to use the same techniques as the able-bodied. Since snare injuries generally befall young animals, these results suggest that chimpanzees learn techniques partly through observational learning (of, necessarily, able-bodied individuals). Accepted after revision: 8 February 2001 Electronic Publication