A Bayesian hidden Markov model for assessing the hot hand phenomenon in basketball shooting performance

Sports data analytics is a relevant topic in applied statistics that has been growing in importance in recent years. In basketball, a player or team has a hot hand when their performance during a match is better than expected or they are on a streak of making consecutive shots. This phenomenon has generated a great deal of controversy with detractors claiming its non-existence while other authors indicate its evidence. In this work, we present a Bayesian longitudinal hidden Markov model that analyses the hot hand phenomenon in consecutive basketball shots, each of which can be either missed or made. Two possible states (cold or hot) are assumed in the hidden Markov chains of events, and the probability of success for each throw is modelled by considering both the corresponding hidden state and the distance to the basket. This model is applied to a real data set, the Miami Heat team in the season 2005-2006 of the USA National Basketball Association. We show that this model is a powerful tool for assessing the overall performance of a team during a match or a season, and, in particular, for quantifying the magnitude of the team streaks in probabilistic terms

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes

2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.We study the problem of the global regularity for linear partial differential operators with polynomial coefficients. In particular for multi-quasi-elliptic operators we prove global regularity in generalized Gelfand-Shilov classes. We also provide counterexamples of globally regular operators which are not multi-quasi-elliptic

Methodological matters on an Alzheimer's dementia trial: is a double-blind randomized controlled study design sufficient to draw strong conclusions on treatment?

Letter to Edito

Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems

One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. For example, it is well known that classical symplectic methods can only exactly preserve, at most, quadratic Hamiltonians. In this paper, a new family of methods, called "Hamiltonian Boundary Value Methods (HBVMs)", is introduced and analyzed. HBVMs are able to exactly preserve, in the discrete solution, Hamiltonian functions of polynomial type of arbitrarily high degree. These methods turn out to be symmetric, precisely A-stable, and can have arbitrarily high order. A few numerical tests confirm the theoretical results.Comment: 25 pages, 8 figures, revised versio

International differences in treatment effect: do they really exist and why?

With the increasing globalization of clinical trials, the opportunity exists to explore potential geographic differences in treatment effect within any major trial. Such geographic differences may arise because of international differences in patient selection, medical practice, or evaluation of outcomes, and such international variations need better documentation in trial reports. Appropriate pre-defined statistical analyses, including statistical tests of interaction regarding geographic heterogeneity in treatment effect, are important. Geographic variations are a particularly tricky form of subgroup analysis: they lack statistical power, are at best hypothesis-generating and can generate more confusion than insight. Referring to key examples, e.g. the PLATO and MERIT-HF, we emphasize the need for caution in interpreting evidence of potential geographic inconsistencies in treatment effect. Although it is appropriate to explore any biological or practical reasons for apparent geographic anomalies in treatment effect, the play of chance is often the most plausible and wise interpretation