arXiv subjects

Roland Langrock

Publications and source records attributed to Roland Langrock.

At least 19 recordsLinked to original sources

arXiv2026

Betting Against Integrity: Identifying Match-Fixing Through In-Play Market Dynamics

Match-fixing undermines the integrity of sport by eroding public trust and threatening the financial sustainability of clubs and leagues. The global expansion of sports betting markets has created new incentives and opportunities for manipulation, calling for rigorous, data-driven monitoring tools. Football, which accounts for the largest share of global betting turnover, remains particularly exposed: integrity reports continue to flag several suspicious matches, with past scandals in Italy and Turkey underlining the problem's persistence. This study uses high-frequency live-betting data from the Italian Serie B (2018/19-2020/21) to explore statistical approaches for detecting abnormal betting behaviour. A state-space modelling framework is employed to describe standard betting market dynamics and to predict expected betting volumes conditional on match characteristics. Deviations from these expectations can then be analysed using outlier detection techniques to identify potentially suspicious periods. The results demonstrate how statistical modelling can contribute to the early identification of irregular betting patterns, thereby supporting integrity assurance in live sports betting markets.

econ.GN↗

arXiv2025

Inference on state occupancy in covariate-driven hidden Markov models

Hidden Markov models (HMMs) are popular tools for analysing animal behaviour based on movement, acceleration and other sensor data. In particular, these models allow to infer how the animal's decision-making process interacts with internal and external drivers, by relating the probabilities of switching between distinct behavioural states to covariates. A key challenge arising in the statistical analysis of behavioural data using covariate-driven HMMs is the models' interpretation, especially when there are more than two states, as then several functional relationships between state-switching probabilities and covariates need to be jointly interpreted. The model-implied probabilities of occupying the different states, as a function of a covariate of interest, constitute a much simpler summary statistic. A pragmatic approximation of the state occupancy distribution, namely the hypothetical stationary distribution of the model's underlying Markov chain for fixed covariate values, has in fact routinely been reported in HMM-based analyses of ecological data. However, for stochastically varying covariates with relatively little persistence, we show that this approximation can be severely biased, potentially invalidating ecological inference. We develop two alternative approaches for obtaining the state occupancy distribution as a function of a covariate of interest - one based on resampling of the covariate process, the other obtained by regression analysis of the empirical state probabilities. The practical application of these approaches is demonstrated in simulations and a case study on Galápagos tortoise (Chelonoidis niger) movement data. Our methods enable practitioners to conduct unbiased inference on the relationship between animal behaviour and general types of covariates, thus allowing to uncover the factors influencing behavioural decisions made by animals.

stat.ME↗

arXiv2025

Inference on the state process of periodically inhomogeneous hidden Markov models for animal behavior

Over the last decade, hidden Markov models (HMMs) have become increasingly popular in statistical ecology, where they constitute natural tools for studying animal behavior based on complex sensor data. Corresponding analyses sometimes explicitly focus on - and in any case need to take into account - periodic variation, for example by quantifying the activity distribution over the daily cycle or seasonal variation such as migratory behavior. For HMMs including periodic components, we establish important mathematical properties that allow for comprehensive statistical inference related to periodic variation, thereby also providing guidance for model building and model checking. Specifically, we derive the periodically varying unconditional state distribution as well as the time-varying and overall state dwell-time distributions - all of which are of key interest when the inferential focus lies on the dynamics of the state process. We use the associated novel inference and model-checking tools to investigate changes in the diel activity patterns of fruit flies in response to changing light conditions.

stat.ME↗

arXiv2025

How to build your latent Markov model -- the role of time and space

Statistical models that involve latent Markovian state processes have become immensely popular tools for analysing time series and other sequential data. However, the plethora of model formulations, the inconsistent use of terminology, and the various inferential approaches and software packages can be overwhelming to practitioners, especially when they are new to this area. With this review-like paper, we thus aim to provide guidance for both statisticians and practitioners working with latent Markov models by offering a unifying view on what otherwise are often considered separate model classes, from hidden Markov models over state-space models to Markov-modulated Poisson processes. In particular, we provide a roadmap for identifying a suitable latent Markov model formulation given the data to be analysed. Furthermore, we emphasise that it is key to applied work with any of these model classes to understand how recursive techniques exploiting the models' dependence structure can be used for inference. The R package LaMa adapts this unified view and provides an easy-to-use framework for very fast (C++ based) numerical maximum likelihood estimation of any of the models discussed in this paper, allowing users to tailor a latent Markov model to their data using a Lego-type approach.

stat.ME↗

arXiv2024

Autoregressive hidden Markov models for high-resolution animal movement data

New types of high-resolution animal movement data allow for increasingly comprehensive biological inference, but method development to meet the statistical challenges associated with such data is lagging behind. In this contribution, we extend the commonly applied hidden Markov models for step lengths and turning angles to address the specific requirements posed by high-resolution movement data, in particular the very strong within-state correlation induced by the momentum in the movement. The models feature autoregressive components of general order in both the step length and the turning angle variable, with the possibility to automate the selection of the autoregressive degree using a lasso approach. In a simulation study, we identify potential for improved inference when using the new model instead of the commonly applied basic hidden Markov model in cases where there is strong within-state autocorrelation. The practical use of the model is illustrated using high-resolution movement tracks of terns foraging near an anthropogenic structure causing turbulent water flow features.

stat.ME↗

arXiv2024

Dynamic Stochastic Inventory Management in E-Grocery Retailing

E-grocery retailing enables ordering products online to be delivered at a future time slot chosen by the customer. This emerging field of business provides retailers with large and comprehensive new data sets, yet creates several challenges for the inventory management process. For example, the risk of a single item's stock-out leading to a complete cancellation of the shopping process is higher in e-grocery than in traditional store retailing. As a consequence, retailers aim at very high service level targets to provide satisfactory customer service and to ensure long-term business growth. When determining replenishment order quantities, it is of crucial importance to precisely account for the full uncertainty in the inventory process. This requires predictive and prescriptive analytics to (1) estimate suitable underlying probability distributions to represent the uncertainty caused by non-stationary customer demand, shelf lives, and supply, and to (2) integrate those forecasts into a comprehensive multi-period optimisation framework. In this paper, we model this stochastic dynamic problem by a sequential decision process that allows us to avoid simplifying assumptions commonly made in the literature, such as the focus on a single demand period. As the resulting problem will typically be analytically intractable, we propose a stochastic lookahead policy incorporating Monte Carlo techniques to fully propagate the associated uncertainties in order to derive replenishment order quantities. This policy naturally integrates probabilistic forecasts and allows us to explicitly derive the value of accounting for probabilistic information compared to myopic or deterministic approaches in a simulation-based setting. In addition, we evaluate our policy in a case study based on real-world data where underlying probability distributions are estimated from historical data and explanatory variables.

econ.GN↗

arXiv2023

Nonparametric estimation of multivariate hidden Markov models using tensor-product B-splines

For multivariate time series driven by underlying states, hidden Markov models (HMMs) constitute a powerful framework which can be flexibly tailored to the situation at hand. However, in practice it can be challenging to choose an adequate emission distribution for multivariate observation vectors. For example, the marginal data distribution may not immediately reveal the within-state distributional form, and also the different data streams may operate on different supports, rendering the common approach of using a multivariate normal distribution inadequate. Here we explore a nonparametric estimation of the emission distributions within a multivariate HMM based on tensor-product B-splines. In two simulation studies, we show the feasibility of our modelling approach and demonstrate potential pitfalls of inappropriate choices of parametric distributions. To illustrate the practical applicability, we present a case study where we use an HMM to model the bivariate time series comprising the lengths and angles of goalkeeper passes during the UEFA EURO 2020, investigating the effect of match dynamics on the teams' tactics.

stat.ME↗

arXiv2022

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.

stat.AP↗

arXiv2022

The reaction to news in live betting

Sports betting markets have grown very rapidly recently, with the total European gambling market worth 98.6 billion euro in 2019. Considering a high-resolution (1 Hz) data set provided by a large European bookmaker, we investigate the effect of news on the dynamics of live betting. In particular, we consider stakes placed in a live betting market during football matches. Accounting for the general market activity level within a state-space modelling framework, we focus on the market's response to events such as goals (i.e. major news), but also to the general situation within a match such as the uncertainty about the outcome. Our results indicate that markets might overreact to recent news, confirming cognitive biases known from psychology and behavioural economics.

physics.soc-ph↗

arXiv2020

Maximum approximate likelihood estimation of general continuous-time state-space models

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions concerning linearity and Gaussianity to facilitate inference on the model parameters via the Kalman filter. In this contribution, we provide a general continuous-time SSM framework, allowing both the observation and the state process to be non-linear and non-Gaussian. Statistical inference is carried out by maximum approximate likelihood estimation, where multiple numerical integration within the likelihood evaluation is performed via a fine discretisation of the state process. The corresponding reframing of the SSM as a continuous-time hidden Markov model, with structured state transitions, enables us to apply the associated efficient algorithms for parameter estimation and state decoding. We illustrate the modelling approach in a case study using data from a longitudinal study on delinquent behaviour of adolescents in Germany, revealing temporal persistence in the deviation of an individual's delinquency level from the population mean.

stat.ME↗

arXiv2020

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.

stat.AP↗

arXiv2020

Uncovering ecological state dynamics with hidden Markov models

Ecological systems can often be characterised by changes among a finite set of underlying states pertaining to individuals, populations, communities, or entire ecosystems through time. Owing to the inherent difficulty of empirical field studies, ecological state dynamics operating at any level of this hierarchy can often be unobservable or "hidden". Ecologists must therefore often contend with incomplete or indirect observations that are somehow related to these underlying processes. By formally disentangling state and observation processes based on simple yet powerful mathematical properties that can be used to describe many ecological phenomena, hidden Markov models (HMMs) can facilitate inferences about complex system state dynamics that might otherwise be intractable. However, while HMMs are routinely applied in other disciplines, they have only recently begun to gain traction within the broader ecological community. We provide a gentle introduction to HMMs, establish some common terminology, and review the immense scope of HMMs for applied ecological research. We also provide a supplemental tutorial on some of the more technical aspects of HMM implementation and interpretation. By illustrating how practitioners can use a simple conceptual template to customise HMMs for their specific systems of interest, revealing methodological links between existing applications, and highlighting some practical considerations and limitations of these approaches, our goal is to help establish HMMs as a fundamental inferential tool for ecologists.

q-bio.QM↗

arXiv2020

A primer on coupled state-switching models for multiple interacting time series

State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend these approaches to address the case of multiple observation sequences whose underlying state variables interact. In this paper, we provide an overview of the modelling techniques related to coupling in state-switching models, thereby forming a rich and flexible statistical framework particularly useful for modelling correlated time series. Simulation experiments demonstrate the relevance of being able to account for an asynchronous evolution as well as interactions between the underlying latent processes. The models are further illustrated using two case studies related to a) interactions between a dolphin mother and her calf as inferred from movement data; and b) electronic health record data collected on 696 patients within an intensive care unit.

stat.ME↗

arXiv2020

Continuous-time multi-state capture-recapture models

Multi-state capture-recapture data comprise individual-specific sighting histories together with information on individuals' states related, for example, to breeding status, infection level, or geographical location. Such data are often analysed using the Arnason-Schwarz model, where transitions between states are modelled using a discrete-time Markov chain, making the model most easily applicable to regular time series. When time intervals between capture occasions are not of equal length, more complex time-dependent constructions may be required, increasing the number of parameters to estimate, decreasing interpretability, and potentially leading to reduced precision. Here we develop a novel continuous-time multi-state model that can be regarded as an analogue of the Arnason-Schwarz model for irregularly sampled data. Statistical inference is carried out by regarding the capture-recapture data as realisations from a continuous-time hidden Markov model, which allows the associated efficient algorithms to be used for maximum likelihood estimation and state decoding. To illustrate the feasibility of the modelling framework, we use a long-term survey of bottlenose dolphins where capture occasion are not regularly spaced through time. Here we are particularly interested in seasonal effects on the movement rates of the dolphins along the Scottish east coast. The results reveal seasonal movement patterns between two core areas of their range, providing information that will inform conservation management.

stat.AP↗

arXiv2019

Penalized estimation of flexible hidden Markov models for time series of counts

Hidden Markov models are versatile tools for modeling sequential observations, where it is assumed that a hidden state process selects which of finitely many distributions generates any given observation. Specifically for time series of counts, the Poisson family often provides a natural choice for the state-dependent distributions, though more flexible distributions such as the negative binomial or distributions with a bounded range can also be used. However, in practice, choosing an adequate class of (parametric) distributions is often anything but straightforward, and an inadequate choice can have severe negative consequences on the model's predictive performance, on state classification, and generally on inference related to the system considered. To address this issue, we propose an effectively nonparametric approach to fitting hidden Markov models to time series of counts, where the state-dependent distributions are estimated in a completely data-driven way without the need to select a distributional family. To avoid overfitting, we add a roughness penalty based on higher-order differences between adjacent count probabilities to the likelihood, which is demonstrated to produce smooth probability mass functions of the state-dependent distributions. The feasibility of the suggested approach is assessed in a simulation experiment, and illustrated in two real-data applications, where we model the distribution of i) major earthquake counts and ii) acceleration counts of an oceanic whitetip shark (Carcharhinus longimanus) over time.

stat.ME↗

arXiv2018

Very Highly Skilled Individuals Do Not Choke Under Pressure: Evidence from Professional Darts

Understanding and predicting how individuals perform in high-pressure situations is of importance in designing and managing workplaces, but also in other areas of society such as disaster management or professional sports. For simple effort tasks, an increase in the pressure experienced by an individual, e.g. due to incentive schemes in a workplace, will increase the effort put into the task and hence in most cases also the performance. For the more complex and usually harder to capture case of skill tasks, there exists a substantial body of literature that fairly consistently reports a choking phenomenon under pressure. However, we argue that many of the corresponding studies have crucial limitations, such as neglected interaction effects or insufficient numbers of observations to allow within-individual analysis. Here, 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. We analyze almost one year of tournament data covering 23,192 dart throws, hence a data set that is very much larger than those used in most previous studies. Contrary to what would be expected given the evidence in favor of a choking phenomenon, we find strong evidence for an overall improved performance under pressure, for nearly all 83 players in the sample. These results could have important consequences for our understanding of how highly skilled individuals deal with high-pressure situations.

stat.AP↗

arXiv2018

The Hot Hand in Professional Darts

We investigate the hot hand hypothesis in professional darts in a near-ideal setting with minimal to no interaction between players. Considering almost one year of tournament data, corresponding to 167,492 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 ability, and we use autoregressive processes to model how this process evolves over time. We find a strong but short-lived serial dependence in the latent state process, thus providing evidence for the existence of the hot hand.

stat.AP↗

arXiv2017

Estimation and simulation of foraging trips in land-based marine predators

The behaviour of colony-based marine predators is the focus of much research globally. Large telemetry and tracking data sets have been collected for this group of animals, and are accompanied by many theoretical studies of optimal foraging strategies. However, relatively few studies have detailed statistical methods for inferring behaviours in central place foraging trips. In this paper we describe an approach based on hidden Markov models, which splits foraging trips into segments labelled as "outbound", "search", "forage", and "inbound". By structuring the hidden Markov model transition matrix appropriately, the model naturally handles the sequence of behaviours within a foraging trip. Additionally, by structuring the model in this way, we are able to develop realistic simulations from the fitted model. We demonstrate our approach on data from southern elephant seals (Mirounga leonina) tagged on Kerguelen Island in the Southern Ocean. We discuss the differences between our 4-state model and the widely used 2-state model, and the advantages and disadvantages of employing a more complex model.

q-bio.QM↗