# mathpsych.org

 Invited Symposia

# Contextualized Probability Theories

### Jerome R. Busemeyer1 Zheng (Joyce) Wang2

1Indiana University  2The Ohio State University

Contextualized probability theories concern the problem of joining together in a coherent manner a set of unrelated probability distributions. These unrelated distributions occur under different experimental conditions (contexts).  This issue often arises in "big data" problems. Consider the following very simple example. Suppose we have four binary valued questions and each condition is formed by asking about the probability of  the conjunction of the two questions. There are six conditions formed by the six ways to combine two pairs of questions from a set of 4 questions.  Each of these six conditions produces a two-way joint probability distribution.  How can we join together these six two-way tables into one coherent probability theory? One answer might be to derive each of these 6 two-way tables from a single 4-way joint distribution, but this might turn out to be impossible! In the latter case, what can one do?  What is needed for to address these issues is a contextualized theory of probability.

# Symmetry: Theory and Applications

### Zygmunt Pizlo1 Manish Singh2

1Purdue University   2Rutgers University

Symmetry has a solid foundation in mathematics where it refers to invariance with respect to a group of transformations. When viewed from an information-theoretic standpoint, symmetry is thus a form of redundancy. For years, symmetry has played a central role in art, esthetics, architecture, physics, and computer science. It has recently started playing a similar role in human and computer vision as well. Symmetry is widely prevalent in the natural environment; and symmetric structures are inherently simpler. For both reasons, symmetry can serve as a powerful “prior” that perceptual systems can use to infer invariant 3D structure from 2D images. Moreover various forms of symmetry can be used to represent the shape of complex objects in a compact manner. This symposium will explore various types of symmetry and their role in perception and cognition.

# The "same"-"Different" task: Things are the same 50 years later

### Denis Cousineau

University of Ottawa

The "same"-"different" task, also commonly called the matching task or the comparison task, is a classic paradigm in cognitive psychology, explored by Bamber, Nickerson, and Egeth, among others. One salient aspect of the results was the "fast-same phenomenon" where "same" responses were sometimes considerably faster than any of the fastest "different" responses, despite the fact that logic suggests that "same" must be exhaustive whereas "different" doesn't have to be. The early research culminated in reviews and syntheses in the 1980's (e.g., Proctor, 1980, Farell, 1985, and Sternberg, 1998). Afterwards, research on this paradigm came to a near stop and since then, few newer contributions have been proposed. Considering the vast amount of research conducted on close topics, such as priming, short term memory, feature extraction, redundant target detection, novelty detection, sampling models, etc., the near absence of new propositions regarding the "same"-"different" task is rather surprising. In this symposium, I invite researchers to propose new leads on the comparison task. Their perspectives on priming, attention, and memory should provide fruitful new approaches to understand the processes underlying performances in this task.