Using Maxwell Distribution to Handle Selector’s Indecisiveness in Choice Data: A New Latent Bayesian Choice Model

This research primarily aims at the development of new pathways to facilitate the resolving of the long debated issue of handling ties or the degree of indecisiveness precipitated in comparative information. The decision chaos is accommodated by the elegant application of the choice axiom ensuring intact utility when imperfect choices are observed. The objectives are facilitated by inducing an additional parameter in the probabilistic set up of Maxwell to retain the extent of indecisiveness prevalent in the choice data. The operational soundness of the proposed model is elucidated through the rigorous employment of Gibbs sampling—a popular approach of the Markov chain Monte Carlo methods. The outcomes of this research clearly substantiate the applicability of the proposed scheme in retaining the advantages of discrete comparative data when the freedom of no indecisiveness is permitted. The legitimacy of the devised mechanism is enumerated on multi-fronts such as the estimation of preference probabilities and assessment of worth parameters, and through the quantification of the significance of choice hierarchy. The outcomes of the research highlight the effects of sample size and the extent of indecisiveness exhibited in the choice data. The estimation efficiency is estimated to be improved with the increase in sample size. For the largest considered sample of size 100, we estimated an average confidence width of 0.0097, which is notably more compact than the contemporary samples of size 25 and 50.

A regularized hidden Markov model for analyzing the ‘hot shoe’ in football

We propose a penalized likelihood approach in hidden Markov models (HMMs) to perform automated variable selection. To account for a potential large number of covariates, which also may be substantially correlated, we consider the elastic net penalty containing LASSO and ridge as special cases. By quadratically approximating the non-differentiable penalty, we ensure that the likelihood can be maximized numerically. The feasibility of our approach is assessed in simulation experiments. As a case study, we examine the ‘hot hand’ effect, whose existence is highly debated in different fields, such as psychology and economics. In the present work, we investigate a potential ‘hot shoe’ effect for the performance of penalty takers in (association) football, where the (latent) states of the HMM serve for the underlying form of a player.