Probabilistic Inference with Interval Probabilities

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

MPE Computation in Bayesian Networks Using Mini-Bucket and Probability Trees Approximation

Given a set of uncertain discrete variables with a joint probability distribution and a set of observations for some of them, the most probable explanation is a set or configuration of values for non-observed variables maximizing the conditional probability of these variables given the observations. This is a hard problem which can be solved by a deletion algorithm with max marginalization, having a complexity similar to the one of computing conditional probabilities. When this approach is unfeasible, an alternative is to carry out an approximate deletion algorithm, which can be used to guide the search of the most probable explanation, by using A* or branch and bound (the approximate+search approach). The most common approximation procedure has been the mini-bucket approach. In this paper it is shown that the use of probability trees as representation of potentials with a pruning of branches with similar values can improve the performance of this procedure. This is corroborated with an experimental study in which computation times are compared using randomly generated and benchmark Bayesian networks from UAI competitions.

PROBABILISTIC INFERENCE FOR INTERVAL PROBABILITIES IN DECISION-MAKING PROCESSES

The present paper considers one approach to Bayes’ formula based probabilistic inference under interval values of relevant probabilities; the necessity of it is caused by the impossibility to obtain reliable deterministic values of the required probabilistic evaluations. The paper shows that the approach proves to be the best from the viewpoint of the required amount of calculations and visual representation of the results. The execution of the algorithm of probabilistic inference is illustrated using a classical task of decision making related to oil mining. For visualisation purposes, the state of initial and target information is modelled using probability trees.

Analysis of the Uncertainty in the relationship between Self-Determined Motivation and competitive Anxiety in dual-career students: Application of Information Theory and Bayesian Networks

This study is framed on the Information Theory as a constructive criterion to generate probabilistic distributions –through the elaboration of Bayesian Networks- and to reduce the uncertainty in the occurrence and relationship between two key psychological variables associated with the sports’ performance: Self-Determined Motivation and Competitive Anxiety. We analyzed 674 universitary students/athletes who competed in the 2017 Universitary Games (Universiade) in México, from 44 universities, with an average age of 21 years old (SD = 2.07), and with a sportive experience of 8.61 years of average (SD = 5.15). Methods: Regarding the data analysis, first of all a CHAID algorithm was carried out for to know the independence links among variables, and then two Bayesian networks (BN) were elaborated. The validation of the BN revealed AUC values ranging from 0.5 to 0.92. Subsequently, various instantations were carried out with hypothetical values applied to the “bottom” variables. Results showed two probability trees that have Extrinisic Motivation and Amotivation at the top, while the anxiety/activation due to the worry for performance was at the bottom of probabilities. The instantiations carried out support the existence of these probabilistic relationships, demonstrating the little influence on the competition anxiety generated by the intrinsic motivation. In conclusion, the reduction of the uncertainty made up by the restricted BN may aloe to re-introduce Information Theory principles in psychosocial studies, allowing authors to obtain useful probabilities values upon target psychological variables related with sportive performance.