Markov-switching generalized additive models

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation and further illustrated by modelling how energy price in Spain depends on the Euro/Dollar exchange rate

A copula-based multivariate hidden Markov model for modelling momentum in football

We investigate the potential occurrence of change points - commonly referred to as "momentum shifts" - in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state correlation of the variables considered, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans

A copula-based multivariate hidden Markov model for modelling momentum in football

We investigate the potential occurrence of change points—commonly referred to as “momentum shifts”—in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state dependence of the variables, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.publishedVersio

Bettors' reaction to match dynamics -- Evidence from in-game betting

It is still largely unclear to what extent bettors update their prior assumptions about the strength and form of competing teams considering the dynamics during the match. This is of interest not only from the psychological perspective, but also as the pricing of live odds ideally should be driven both by the (objective) outcome probabilities and also the bettors' behaviour. Using state-space models (SSMs) to account for the dynamically evolving latent sentiment of the betting market, we analyse a unique high-frequency data set on stakes placed during the match. We find that stakes in the live-betting market are driven both by perceived pre-game strength and by in-game strength, the latter as measured by the Valuing Actions by Estimating Probabilities (VAEP) approach. Both effects vary over the course of the match

The hot hand in professional darts

Ötting M, Langrock R, Deutscher C, Leos-Barajas V. The hot hand in professional darts. Journal of the Royal Statistical Society. Series A. 2020;183(2):565-580.We investigate the hot hand hypothesis in professional darts in a nearly ideal setting with minimal to no interaction between players. Considering almost 1 year of tournament data, corresponding to 167492 dart throws in total, we use state space models to investigate serial dependence in throwing performance. In our models, a latent state process serves as a proxy for a player's underlying form, and we use auto-regressive processes to model how this process evolves over time. Our results regarding the persistence of the latent process indicate a weak hot hand effect, but the evidence is inconclusive

Dynamic Stochastic Inventory Management in E-Grocery Retailing: The Value of Probabilistic Information

Inventory management optimisation in a multi-period setting with dependent demand periods requires the determination of replenishment order quantities in a dynamic stochastic environment. Retailers are faced with uncertainty in demand and supply for each demand period. In grocery retailing, perishable goods without best-before-dates further amplify the degree of uncertainty due to stochastic spoilage. Assuming a lead time of multiple days, the inventory at the beginning of each demand period is determined jointly by the realisations of these stochastic variables. While existing contributions in the literature focus on the role of single components only, we propose to integrate all of them into a joint framework, explicitly modelling demand, supply shortages, and spoilage using suitable probability distributions learned from historic data. As the resulting optimisation problem is analytically intractable in general, we use a stochastic lookahead policy incorporating Monte Carlo techniques to fully propagate the associated uncertainties in order to derive replenishment order quantities. We develop a general inventory management framework and analyse the benefit of modelling each source of uncertainty with an appropriate probability distribution. Additionally, we conduct a sensitivity analysis with respect to location and dispersion of these distributions. We illustrate the practical feasibility of our framework using a case study on data from a European e-grocery retailer. Our findings illustrate the importance of properly modelling stochastic variables using suitable probability distributions for a cost-effective inventory management process

Performance under pressure in skill tasks: An analysis of professional darts

Ötting M, Deutscher C, Schneemann S, Langrock R, Gehrmann S, Scholten H. Performance under pressure in skill tasks: An analysis of professional darts. PLOS ONE. 2020;15(2): e0228870.Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces. We investigate performance under pressure in professional darts as a near-ideal setting with no direct interaction between players and a high number of observations per subject. Analyzing almost one year of tournament data covering 32,274 dart throws, we find no evidence in favor of either choking or excelling under pressure

Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges

With the influx of complex and detailed tracking data gathered from electronic tracking devices, the analysis of animal movement data has recently emerged as a cottage industry among biostatisticians. New approaches of ever greater complexity are continue to be added to the literature. In this paper, we review what we believe to be some of the most popular and most useful classes of statistical models used to analyse individual animal movement data. Specifically, we consider discrete-time hidden Markov models, more general state-space models and diffusion processes. We argue that these models should be core components in the toolbox for quantitative researchers working on stochastic modelling of individual animal movement. The paper concludes by offering some general observations on the direction of statistical analysis of animal movement. There is a trend in movement ecology towards what are arguably overly complex modelling approaches which are inaccessible to ecologists, unwieldy with large data sets or not based on mainstream statistical practice. Additionally, some analysis methods developed within the ecological community ignore fundamental properties of movement data, potentially leading to misleading conclusions about animal movement. Corresponding approaches, e.g. based on Lévy walk-type models, continue to be popular despite having been largely discredited. We contend that there is a need for an appropriate balance between the extremes of either being overly complex or being overly simplistic, whereby the discipline relies on models of intermediate complexity that are usable by general ecologists, but grounded in well-developed statistical practice and efficient to fit to large data sets