Bayesian methods are becoming increasingly popular in sports analytics. Identified advantages of the Bayesian approach include the ability to model complex problems, obtain probabilistic estimates and predictions that account for uncertainty, combine information sources and update learning as new data become available. The volume and variety of data produced in sports activities over recent years and the availability of software packages for Bayesian computation have contributed significantly to this growth. This comprehensive survey reviews and characterizes the latest advances in Bayesian statistics in sports, including methods and applications. We found that a large proportion of these articles focus on modeling/predicting the outcome of sports games and on the development of statistics that provides a better picture of athletes’ performance. We provide a description of some of the advances in basketball, football and baseball. We also summarise the sources of data used for the analysis and the most commonly used software for Bayesian computation. We found a similar number of publications between 2013 and 2018 as compared to those published in the three previous decades, which is an indication of the growing adoption rate of Bayesian methods in sports.

The use of in‐situ digital sensors for water quality monitoring is becoming increasingly common worldwide. While these sensors provide near real‐time data for science, the data are prone to technical anomalies that can undermine the trustworthiness of the data and the accuracy of statistical inferences, particularly in spatial and temporal analyses. Here we propose a framework for detecting anomalies in sensor data recorded in stream networks, which takes advantage of spatial and temporal autocorrelation to improve detection rates. The proposed framework involves the implementation of effective data imputation to handle missing data, alignment of time‐series to address temporal disparities, and the identification of water quality events. We explore the effectiveness of a suite of state‐of‐the‐art statistical methods including posterior predictive distributions, finite mixtures, and Hidden Markov Models (HMM). We showcase the practical implementation of automated anomaly detection in near‐real time by employing a Bayesian recursive approach. This demonstration is conducted through a comprehensive simulation study and a practical application to a substantive case study situated in the Herbert River, located in Queensland, Australia, which flows into the Great Barrier Reef. We found that methods such as posterior predictive distributions and HMM produce the best performance in detecting multiple types of anomalies. Utilizing data from multiple sensors deployed relatively near one another enhances the ability to distinguish between water quality events and technical anomalies, thereby significantly improving the accuracy of anomaly detection. Thus, uncertainty and biases in water quality reporting, interpretation, and modeling are reduced, and the effectiveness of subsequent management actions improved.

Citizen science projects have become increasingly popular in many fields, including ecology. However, the quality of this information is frequently debated within the scientific community. Modern citizen science implementations therefore require measures of the users' proficiency. We introduce a new methodological framework of item response that quantifies a citizen scientist's ability, taking into account the difficulty of the task. We focus on citizen science programs involving the classification of images. Our approach accommodates spatial autocorrelation within the item difficulties, and provides deeper insights and relevant ecological measures of species and site‐related difficulties, discriminatory power and guessing behaviour. The identification of very capable versus less skilled participants can facilitate selective use of data in analyses and more targeted training programs for citizen scientists. This paper also addresses challenges in fitting such models to very large datasets. We found that the suggested methods outperform the traditional item response models in terms of RMSE, accuracy and WAIC, based on leave‐one‐out cross‐validation on simulated and empirical data. We present a comprehensive implementation using a case study of species identification in the Serengeti, Tanzania. The R and Stan codes are provided for full reproducibility. Multiple statistical illustrations and visualizations are given, which allow extrapolation to a wide range of citizen science ecological problems.