Hierarchical Absorbing Markov Chain Models for Pooling Sparse Combat Sequence Data

Music City Center 

Combat dynamics in no-gi Brazilian jiu-jitsu (NGJJ) can be organized as sequences of discrete events. Absorbing Markov chains have been used to model sequence data with success. The individual sequences can have an attached label corresponding to a certain subgroups, such as weight categories for NGJJ. We aim to estimate the transition probabilities of the tactic progression in NGJJ, whilst simultaneously exploring the effects of weight categories on this progression and the underlying groupings of these weight categories. To model such probabilities we use a hierarchical absorbing Markov chain model with a random partition using the Ewens-Pitman attraction of Dahl, Day and Tsai. With this model we can cluster the weight categories to borrow strength and estimate the variation between them even with sparse data. The hierarchical structure gives us the ability to obtain an overall mean estimate to which we can compare the individual estimates of the weight categories. We cover the literature associated with combat sports, Markov chains, and similar hierarchical models, the methodology used, and discussion of the application.

Sparse count data

dependent random partition models

Markov chain Monte Carlo

partial pooling

slice sampler

no-gi Brazilian jiu-jitsu