arXiv subjects

Johannes Bracher

Publications and source records attributed to Johannes Bracher.

13 recordsLinked to original sources

arXiv2026

Information leakage from data revisions in retrospective forecasts

Aygün et al (2026, https://doi.org/10.1038/s41586-026-10658-6) claim that their AI-driven Empirical Research Assistance (ERA) system produces COVID-19 hospitalisation forecasts which outperform the state-of-the-art CDC ensemble by a considerable margin for the 2024/25 season. We demonstrate that the observed performance gain is attributable to information leakage in the retrospective forecasting setup, which resulted because data revisions were not taken into account. As similar mechanisms are at play in many other forecasting fields, our cautionary tale applies not just to epidemic forecasting, but is relevant to the entire emerging field of AI-assisted predictive modelling.

stat.AP↗

arXiv2025

Shift-Dispersion Decompositions of Wasserstein and Cramér Distances

Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cramér distances$-$which compare two distributions by integrating over their differences in distribution or quantile functions$-$into directed shift and dispersion components. These components are obtained by dividing the differences between the quantile functions into contributions arising from shift and dispersion, respectively. Our decompositions add information on how the distributions differ in a condensed form and consequently enhance the interpretability of the underlying divergences. We show that our decompositions satisfy a number of natural properties and are unique in doing so in location-scale families. The decompositions allow to derive sensitivities of the divergence measures to changes in location and dispersion, and they give rise to weak stochastic order relations that are linked to the usual stochastic and the dispersive order. Our theoretical developments are illustrated in two applications, where we focus on forecast evaluation of temperature extremes and on the design of probabilistic surveys in economics.

stat.ME↗

arXiv2024

A class of count time series models uniting compound Poisson INAR and INGARCH models

INAR (integer-valued autoregressive) and INGARCH (integer-valued GARCH) models are among the most commonly employed approaches for count time series modelling, but have been studied in largely distinct strands of literature. In this paper, a new class of generalized integer-valued ARMA (GINARMA) models is introduced which unifies a large number of compound Poisson INAR and INGARCH processes. Its stochastic properties, including stationarity and geometric ergodicity, are studied. Particular attention is given to a generalization of the INAR($p$) model which parallels the extension of the INARCH(p) to the INGARCH(p, q) model. For inference, we consider moment-based estimation and a maximum likelihood inference scheme inspired by the forward algorithm. Models from the proposed class have a natural interpretation as stochastic epidemic processes, which throughout the article is used to illustrate our arguments. In a case study, different instances of the class, including both established and newly introduced models, are applied to weekly case numbers of measles and mumps in Bavaria, Germany.

math.PR↗

arXiv2023

Direction Augmentation in the Evaluation of Armed Conflict Predictions

In many forecasting settings, there is a specific interest in predicting the sign of an outcome variable correctly in addition to its magnitude. For instance, when forecasting armed conflicts, positive and negative log-changes in monthly fatalities represent escalation and de-escalation, respectively, and have very different implications. In the ViEWS forecasting challenge, a prediction competition on state-based violence, a novel evaluation score called targeted absolute deviation with direction augmentation (TADDA) has therefore been suggested, which accounts for both for the sign and magnitude of log-changes. While it has a straightforward intuitive motivation, the empirical results of the challenge show that a no-change model always predicting a log-change of zero outperforms all submitted forecasting models under the TADDA score. We provide a statistical explanation for this phenomenon. Analyzing the properties of TADDA, we find that in order to achieve good scores, forecasters often have an incentive to predict no or only modest log-changes. In particular, there is often an incentive to report conservative point predictions considerably closer to zero than the forecaster's actual predictive median or mean. In an empirical application, we demonstrate that a no-change model can be improved upon by tailoring predictions to the particularities of the TADDA score. We conclude by outlining some alternative scoring concepts.

stat.AP↗

arXiv2023

Learning to forecast: The probabilistic time series forecasting challenge

We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse set of skills in data science and applied statistics. We describe the context and aims of the course, and discuss design parameters like the selection of target variables, the forecast submission process, the evaluation of forecast performance, and the feedback provided to students. Furthermore, we describe empirical properties of students' probabilistic forecasts, as well as some lessons learned on our part.

stat.OT↗

arXiv2022

Comparing trained and untrained probabilistic ensemble forecasts of COVID-19 cases and deaths in the United States

The U.S. COVID-19 Forecast Hub aggregates forecasts of the short-term burden of COVID-19 in the United States from many contributing teams. We study methods for building an ensemble that combines forecasts from these teams. These experiments have informed the ensemble methods used by the Hub. To be most useful to policy makers, ensemble forecasts must have stable performance in the presence of two key characteristics of the component forecasts: (1) occasional misalignment with the reported data, and (2) instability in the relative performance of component forecasters over time. Our results indicate that in the presence of these challenges, an untrained and robust approach to ensembling using an equally weighted median of all component forecasts is a good choice to support public health decision makers. In settings where some contributing forecasters have a stable record of good performance, trained ensembles that give those forecasters higher weight can also be helpful.

stat.ME↗

arXiv2021

Evaluating epidemic forecasts in an interval format

For practical reasons, many forecasts of case, hospitalization and death counts in the context of the current COVID-19 pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation of quantile and interval forecasts can be applied to epidemic forecasts in this format. Specifically, we discuss the computation and interpretation of the weighted interval score, which is a proper score that approximates the continuous ranked probability score. It can be interpreted as a generalization of the absolute error to probabilistic forecasts and allows for a decomposition into a measure of sharpness and penalties for over- and underprediction.

stat.AP↗

arXiv2020

A marginal moment matching approach for fitting endemic-epidemic models to underreported disease surveillance counts

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic-epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analysed. Notably, we show that this leads to a downward bias in model-based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time-varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany.

stat.ME↗

arXiv2020

Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction

Multivariate count time series models are an important tool for the analysis and prediction of infectious disease spread. We consider the endemic-epidemic framework, an autoregressive model class for infectious disease surveillance counts, and replace the default autoregression on counts from the previous time period with more flexible weighting schemes inspired by discrete-time serial interval distributions. We employ three different parametric formulations, each with an additional unknown weighting parameter estimated via a profile likelihood approach, and compare them to an unrestricted nonparametric approach. The new methods are illustrated in a univariate analysis of dengue fever incidence in San Juan, Puerto Rico, and a spatio-temporal study of viral gastroenteritis in the twelve districts of Berlin. We assess the predictive performance of the suggested models and several reference models at various forecast horizons. In both applications, the performance of the endemic-epidemic models is considerably improved by the proposed weighting schemes.

stat.AP↗

arXiv2019

A new INARMA(1, 1) model with Poisson marginals

We suggest an INARMA(1, 1) model with Poisson marginals which extends the INAR(1) in a similar way as the INGARCH(1, 1) does for the INARCH(1) model. The new model is equivalent to a binomially thinned INAR(1) process. This allows us to obtain some of its stochastic properties and use inference methods for hidden Markov models. The model is compared to various other models in two case studies.

stat.ME↗

arXiv2019

An extended note on the multibin logarithmic score used in the FluSight competitions

In recent years the Centers for Disease Control and Prevention (CDC) have organized FluSight influenza forecasting competitions. To evaluate the participants' forecasts a multibin logarithmic score has been created, which is a non-standard variant of the established logarithmic score. Unlike the original log score, the multibin version is not proper and may thus encourage dishonest forecasting. We explore the practical consequences this may have, using forecasts from the 2016/17 FluSight competition for illustration.

stat.AP↗

arXiv2019

Comment on "Under-reported data analysis with INAR-hidden Markov chains"

In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model with time-homogeneous underreporting can be expressed equivalently as a completely observed INAR(inf) model with a geometric lag structure. This implies that estimated reporting probabilities depend on the assumed lag structure of the latent process.

stat.ME↗

arXiv2017

Periodically stationary multivariate autoregressive models

A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the framework, including the negative binomial, gamma and Gaussian distributions. We develop an iterative algorithm to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags. Analytical solutions are given for the univariate model with lag one and multivariate models with linear mean-variance relationship. A special case of the model class is an established framework for modelling multivariate time series of counts from routine surveillance of infectious diseases. We extend this model class to allow for distributed lags and apply it to a dataset on norovirus gastroenteritis in two German states. The availability of unconditional moments and auto/cross-correlations enhances model assessment and interpretation.

stat.ME↗