John M. Ennis

A neurobiological theory of automaticity in perceptual categorization.

A biologically detailed computational model is described of how categorization judgments become automatic in tasks that depend on procedural learning. The model assumes 2 neural pathways from sensory association cortex to the premotor area that mediates response selection. A longer and slower path projects to the premotor area via the striatum, globus pallidus, and thalamus. A faster, purely cortical path projects directly to the premotor area. The model assumes that the subcortical path has greater neural plasticity because of a dopamine-mediated learning signal from the substantia nigra. In contrast, the cortical-cortical path learns more slowly via (dopamine independent) Hebbian learning. Because of its greater plasticity, early performance is dominated by the subcortical path, but the development of automaticity is characterized by a transfer of control to the faster cortical-cortical projection. The model, called SPEED (Subcortical Pathways Enable Expertise Development), includes differential equations that describe activation in the relevant brain areas and difference equations that describe the 2- and 3-factor learning. A variety of simulations are described, showing that the model accounts for some classic single-cell recording and behavioral results.

THE ROLE OF THE BASAL GANGLIA IN CATEGORY LEARNING

Publisher Summary This chapter discusses the role of the basal ganglia in category learning and provides an overview of the functional neuroanatomy of the basal ganglia, including its relatively unique neural plasticity. It reviews the behavioral neuroscience studies that originally called attention to this brain region as a possible important locus of category learning. The most important category‐learning tasks that are used with human subjects are described. The rule-based and information-integration tasks are more dependent on basal ganglia function. In rule-based tasks, the categories can be learned via some explicit reasoning process. Whereas in information-integration category-learning tasks, accuracy is maximized only if information from two or more stimulus dimensions is integrated at some predecisional stage. The chapter also reviews the relevant neuropsychological patient data, with a focus on patients with basal ganglia disease. The neuroimaging data is also discussed and the COVIS theory is described along with some possible future extensions of the model.

Replicated difference and preference tests: how to account for inter-trial variation☆

Abstract Binomial tests are often used in sensory difference and preference testing. Two assumptions underlie this use: (1) responses are independent and (2) choice probabilities do not vary from trial to trial. In many applications, the latter assumption is violated. In this paper we account for variation in inter-trial choice probabilities using the beta distribution. The result of combining the binomial with the beta distribution is a compound distribution known as the beta-binomial. We show how to use the beta-binomial model for replicated difference and preference tests such as those used to support product claims.

Hypothesis Testing for Equivalence Defined on Symmetric Open Intervals

There are many industrial applications for which it is desirable to know whether one product can act as a substitute for another. Examples include product modifications when ingredients change, substitution of generic drugs for brand-name drugs, and modifications of products in response to government regulations. In addition, some companies develop products that are direct substitutes for those of their competitors and make advertising claims concerning their equivalency. Using an open interval within which to define equivalence, exact and approximate methods for testing a null hypothesis of non equivalence are given. In each case, examples are provided. Comparisons are made between these novel methods and existing methods, including the “two one-sided tests” (TOST) method.

Confidence Bounds for Multiplicative Comparisons

Statements that are inherently multiplicative have historically been justified using ratios of random variables. Although recent work on ratios has extended the classical theory to produce confidence bounds conditioned on a positive denominator, this current article offers a novel perspective that eliminates the need for such a condition. Although seemingly trivial, this new perspective leads to improved lower confidence bounds to support multiplicative statements. This perspective is also more satisfying as it allows comparisons that are inherently multiplicative in nature to be properly analyzed as such.

Confidence Bounds for Positive Ratios of Normal Random Variables

Some applications of ratios of normal random variables require both the numerator and denominator of the ratio to be positive if the ratio is to have a meaningful interpretation. In these applications, there may also be substantial likelihood that the variables will assume negative values. An example of such an application is when comparisons are made in which treatments may have either efficacious or deleterious effects on different trials. Classical theory on ratios of normal variables has focused on the distribution of the ratio and has not formally incorporated this practical consideration. When this issue has arisen, approximations have been used to address it. In this article, we provide an exact method for determining (1 − α) confidence bounds for ratios of normal variables under the constraint that the ratio is composed of positive values and connect this theory to classical work in this area. We then illustrate several practical applications of this method.

A Thurstonian Ranking Model with Rank-Induced Dependencies

A Thurstonian model for ranks is introduced in which rank-induced dependencies are specified through correlation coefficients among ranked objects that are determined by a vector of rank-induced parameters. The ranking model can be expressed in terms of univariate normal distribution functions, thus simplifying a previously computationally intensive problem. A theorem is proven that shows that the specification given in the paper for the dependencies is the only way that this simplification can be achieved under the process assumptions of the model. The model depends on certain conditional probabilities that arise from item orders considered by subjects as they make ranking decisions. Examples involving a complete set of ranks and a set with missing values are used to illustrate recovery of the objects’ scale values and the rank dependency parameters. Application of the model to ranks for gift items presented singly or as composite items is also discussed.

Assignment-minimum clique coverings

The search for minimum clique coverings of graphs appears in many practical guises and with several possible minimization goals. One reasonable goal is to minimize the number of overall cliques in a covering, while a second less well-studied but equally reasonable goal is to minimize the number of individual assignments of vertices to cliques. Both goals constitute NP-hard problems and as such require competitive algorithms for practical progress to be made toward their resolutions. In this article, we introduce a technique for accomplishing the latter goal, using a combination of data reduction and a backtracking algorithm. In addition, we demonstrate that it is not always possible to minimize both the number of cliques and the number of individual vertex-clique assignments simultaneously. This demonstration resolves an open question and underscores the need for techniques that specifically minimize the number of assignments of vertices to cliques. We then illustrate our approach in two practical examples. We follow these examples with a simulation-based comparison of our exact approach with a heuristic based on the state-of-the-art algorithm for minimizing the number of cliques in a clique covering. For this comparison, we consider graphs likely to arise in applied statistics, a category of applications for which minimizing individual vertex-clique assignments is of particular interest.