International Journal of Psychological Studies; Vol. 10, No. 4; 2018 ISSN 1918-7211 E-ISSN 1918-722X Published by Canadian Center of Science and Education 53 Bayesian Modeling of Working Memory and Inhibitory Control Héctor A. Cepeda-Freyre 1 , Gregorio Garcia-Aguilar 1 & J. Jacobo Oliveros-Oliveros 2 1 Benemerita Universidad Autonoma de Puebla, Faculty of Psychology, Mexico. 2 Benemerita Universidad Autonoma de Puebla, Faculty of Physics and Mathematic Sciences, Mexico Correspondence: Gregorio Garcia-Aguilar, Benemerita Universidad Autonoma de Puebla, Faculty of Psychology, Mexico. E-mail: gregorio.garcia@correo.buap.mx Received: October 9, 2018 Accepted: October 30, 2018 Online Published: November 7, 2018 doi:10.5539/ijps.v10n4p53 URL: https://doi.org/10.5539/ijps.v10n4p53 Abstract In cognitive science, working memory is a core cognitive ability that might be functionally related to other capacities, such as perceptual processes, inhibitory control, memory and attention processes and executive functions. The mathematical study of working memory has been explored before. However, there is not enough research aiming to study the relationship between working memory and inhibitory control. This is the objective of the present report. Bayesian hypothesis testing is often more robust than traditional p-value null hypothesis testing. Yet, the number of studies using this approach is still limited. A secondary objective of this paper is to contribute to fill that gap, as well as provide an empirical application of Bayesian hypothesis testing using cognitive and behavioral data. A within-subjects design was used to measure working memory function for three types of visual stimuli that varied in the degree of attentional interference they were designed to elicit. Data collected was contrasted with measurements of inhibitory control and analyzed using Bayes’ theorem. Our results provide evidence against the theoretical relationship of working memory and inhibitory control. This outcome is analyzed in light of related cognitive research. Keywords: working memory, inhibitory control, bayesian analysis 1. Introduction Working memory is a cognitive process that has received the attention of a multitude of thinkers and researchers through the years (Cassel, Cassel, & Manning, 2013). Working memory involves the capacity for maintaining and storing information for short periods of time. The information to maintain may come from visual and auditive sensory modalities mainly, but cognitive psychologist have interested in other forms of information (Baddeley, 2003). The concept of working memory has been invented by Miller, Galanter and Pribram, but the leading theorist is A. Baddeley (Baddeley, 2017). Working memory is a type of memory used to process several cognitive operations. One of the models most used to describe it is the one proposed by Baddeley and Hitch in 1974 (Baddeley & Hitch, 1974). The authors use empirical evidence to create a model that sees working memory as a dynamic system, a special kind of temporal buffer that both stores and processes information. In this model, there exist three components: a visuospatial sketchpad, dealing with visual information; a phonological loop in charge of the linguistic information; these two components are for storing information. A central executive component, working as a control system complete the model. Recently, a forth component, called episodic buffer has been added, as an interface between long term and working memory (Baddeley, 2003) . The working memory (WM from now on) research has been driven by theory. At first, scientific discussion regarding memory focused on whether it was a single capacity or multiple ones; the first position saw memory as an unitary capacity that handled all tasks related to retention and retrieval of information, the second point of view theorized the existence of several types of memory, which were independent to each other and were divided according to the type of functions they carried out; evidence obtained through the years has supported this last posture (Atkinson & Shiffrin, 1968; Repovš & Baddeley, 2006) However, because memory is a double storing and processing function cognitive capacity, it is not clear at the present how much of these functions, or in what degree memory works together with other cognitive capacities, hence facilitating the processing; or if memory is an independent and unrelated process, coming along with different cognitive processes, as attention or inhibitory control. For this reason, two different approximations