arXiv subjects

Göran Kauermann

Publications and source records attributed to Göran Kauermann.

At least 37 records · Page 2Linked to original sources

arXiv2023

The Skellam Distribution revisited -Estimating the unobserved incoming and outgoing ICU COVID-19 patients on a regional level in Germany

With the beginning of the COVID-19 pandemic, we became aware of the need for comprehensive data collection and its provision to scientists and experts for proper data analyses. In Germany, the Robert Koch Institute (RKI) has tried to keep up with this demand for data on COVID-19, but there were (and still are) relevant data missing that are needed to understand the whole picture of the pandemic. In this paper, we take a closer look at the severity of the course of COVID-19 in Germany, for which ideal information would be the number of incoming patients to ICU units. This information was (and still is) not available. Instead, the current occupancy of ICU units on the district level was reported daily. We demonstrate how this information can be used to predict the number of incoming as well as released COVID-19 patients using a stochastic version of the Expectation Maximisation algorithm (SEM). This in turn, allows for estimating the influence of district-specific and age-specific infection rates as well as further covariates, including spatial effects, on the number of incoming patients. The paper demonstrates that even if relevant data are not recorded or provided officially, statistical modelling allows for reconstructing them. This also includes the quantification of uncertainty which naturally results from the application of the SEM algorithm.

stat.AP↗

arXiv2023

Weighted high dimensional data reduction of finite Element Features -- An Application on High Pressure of an Abdominal Aortic Aneurysm

In this work we propose a low rank approximation of high fidelity finite element simulations by utilizing weights corresponding to areas of high stress levels for an abdominal aortic aneurysm, i.e. a deformed blood vessel. We focus on the van Mises stress, which corresponds to the rupture risk of the aorta. This is modeled as a Gaussian Markov random field and we define our approximation as a basis of vectors that solve a series of optimization problems. Each of these problems describes the minimization of an expected weighted quadratic loss. The weights, which encapsulate the importance of each grid point of the finite elements, can be chosen freely - either data driven or by incorporating domain knowledge. Along with a more general discussion of mathematical properties we provide an effective numerical heuristic to compute the basis under general conditions. We explicitly explore two such bases on the surface of a high fidelity finite element grid and show their efficiency for compression. We further utilize the approach to predict the van Mises stress in areas of interest using low and high fidelity simulations. Due to the high dimension of the data we have to take extra care to keep the problem numerically feasible. This is also a major concern of this work.

math.NA↗

arXiv2023

Nonparametric Two-Sample Test for Networks Using Joint Graphon Estimation

This paper focuses on the comparison of networks on the basis of statistical inference. For that purpose, we rely on smooth graphon models as a nonparametric modeling strategy that is able to capture complex structural patterns. The graphon itself can be viewed more broadly as density or intensity function on networks, making the model a natural choice for comparison purposes. Extending graphon estimation towards modeling multiple networks simultaneously consequently provides substantial information about the (dis-)similarity between networks. Fitting such a joint model - which can be accomplished by applying an EM-type algorithm - provides a joint graphon estimate plus a corresponding prediction of the node positions for each network. In particular, it entails a generalized network alignment, where nearby nodes play similar structural roles in their respective domains. Given that, we construct a chi-squared test on equivalence of network structures. Simulation studies and real-world examples support the applicability of our network comparison strategy.

stat.ME↗

arXiv2022

Going Beyond One-Hot Encoding in Classification: Can Human Uncertainty Improve Model Performance?

Technological and computational advances continuously drive forward the broad field of deep learning. In recent years, the derivation of quantities describing theuncertainty in the prediction - which naturally accompanies the modeling process - has sparked general interest in the deep learning community. Often neglected in the machine learning setting is the human uncertainty that influences numerous labeling processes. As the core of this work, label uncertainty is explicitly embedded into the training process via distributional labels. We demonstrate the effectiveness of our approach on image classification with a remote sensing data set that contains multiple label votes by domain experts for each image: The incorporation of label uncertainty helps the model to generalize better to unseen data and increases model performance. Similar to existing calibration methods, the distributional labels lead to better-calibrated probabilities, which in turn yield more certain and trustworthy predictions.

cs.LG↗

arXiv2022

All that Glitters is not Gold: Relational Events Models with Spurious Events

As relational event models are an increasingly popular model for studying relational structures, the reliability of large-scale event data collection becomes more and more important. Automated or human-coded events often suffer from non-negligible false-discovery rates in event identification. And most sensor data is primarily based on actors' spatial proximity for predefined time windows; hence, the observed events could relate either to a social relationship or random co-location. Both examples imply spurious events that may bias estimates and inference. We propose the Relational Event Model for Spurious Events (REMSE), an extension to existing approaches for interaction data. The model provides a flexible solution for modeling data while controlling for spurious events. Estimation of our model is carried out in an empirical Bayesian approach via data augmentation. Based on a simulation study, we investigate the properties of the estimation procedure. To demonstrate its usefulness in two distinct applications, we employ this model to combat events from the Syrian civil war and student co-location data. Results from the simulation and the applications identify the REMSE as a suitable approach to modeling relational event data in the presence of spurious events.

stat.ME↗

arXiv2022

Stochastic Block Smooth Graphon Model

The paper proposes the combination of stochastic blockmodels with smooth graphon models. The first allow for partitioning the set of individuals in a network into blocks which represent groups of nodes that presumably connect stochastically equivalently, therefore often also called communities. Smooth graphon models instead assume that the network's nodes can be arranged on a one-dimensional scale such that closeness implies a similar connectivity behavior. Both models belong to the model class of node-specific latent variables, entailing a natural relationship. While these model strands have developed more or less completely independently, this paper proposes their generalization towards stochastic block smooth graphon models. This approach enables to exploit the advantages of both worlds. We pursue a general EM-type algorithm for estimation and demonstrate the usability by applying the model to both simulated and real-world examples.

stat.ME↗

arXiv2022

Modelling the large and dynamically growing bipartite network of German patents and inventors

We analyse the bipartite dynamic network of inventors and patents registered within the main area of electrical engineering in Germany to explore the driving forces behind innovation. The data at hand leads to a bipartite network, where an edge between an inventor and a patent is present if the inventor is a co-owner of the respective patent. Since more than a hundred thousand patents were filed by similarly as many inventors during the observational period, this amounts to a massive bipartite network, too large to be analysed as a whole. Therefore, we decompose the bipartite network by utilising an essential characteristic of the network: most inventors tend to stay active only for a relatively short period, while new ones become active at each point in time. Consequently, the adjacency matrix carries several structural zeros. To accommodate for these, we propose a bipartite variant of the Temporal Exponential Random Graph Model (TERGM) in which we let the actor set vary over time, differentiate between inventors that already submitted patents and those that did not, and account for pairwise statistics of inventors. Our results corroborate the hypotheses that inventor characteristics and knowledge flows play a crucial role in the dynamics of invention.

physics.soc-ph↗

arXiv2022

Statistical modelling of COVID-19 data: Putting Generalised Additive Models to work

Over the course of the COVID-19 pandemic, Generalised Additive Models (GAMs) have been successfully employed on numerous occasions to obtain vital data-driven insights. In this paper we further substantiate the success story of GAMs, demonstrating their flexibility by focusing on three relevant pandemic-related issues. First, we examine the interdepency among infections in different age groups, concentrating on school children. In this context, we derive the setting under which parameter estimates are independent of the (unknown) case-detection ratio, which plays an important role in COVID-19 surveillance data. Second, we model the incidence of hospitalisations, for which data is only available with a temporal delay. We illustrate how correcting for this reporting delay through a nowcasting procedure can be naturally incorporated into the GAM framework as an offset term. Third, we propose a multinomial model for the weekly occupancy of intensive care units (ICU), where we distinguish between the number of COVID-19 patients, other patients and vacant beds. With these three examples, we aim to showcase the practical and "off-the-shelf" applicability of GAMs to gain new insights from real-world data.

stat.AP↗

arXiv2021

Iterative Estimation of Mixed Exponential Random Graph Models with Nodal Random Effects

The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node specific random effects that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by combining approximate penalized pseudolikelihood estimation for the random effects with maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the AIC to check for node specific heterogeneity.

stat.CO↗

arXiv2021

EM-Based Smooth Graphon Estimation Using Bayesian and Spline-Based Approaches

This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the EM algorithm. The approach considers both variability with respect to ordering the nodes of a network and smooth estimation of the graphon by nonparametric regression. To do so, (linear) B-splines are used, which allow for smooth estimation of the graphon, conditional on the node ordering. This provides the M-step. The true ordering of the nodes arising from the graphon model remains unobserved and Bayesian ideas are employed to obtain posterior samples given the network data. This yields the E-step. Combining both steps gives an EM-based approach for smooth graphon estimation. Unlike common other methods, this procedure does not require the restriction of a monotonic marginal function. The proposed graphon estimate allows to explore node-ordering strategies and therefore to compare the common degree-based node ranking with the ordering conditional on the network. Variability and uncertainty are taken into account using MCMC techniques. Examples and simulation studies support the applicability of the approach.

stat.ME↗

arXiv2021

On the Interplay of Regional Mobility, Social Connectedness, and the Spread of COVID-19 in Germany

Since the primary mode of respiratory virus transmission is person-to-person interaction, we are required to reconsider physical interaction patterns to mitigate the number of people infected with COVID-19. While research has shown that non-pharmaceutical interventions (NPI) had an evident impact on national mobility patterns, we investigate the relative regional mobility behaviour to assess the effect of human movement on the spread of COVID-19. In particular, we explore the impact of human mobility and social connectivity derived from Facebook activities on the weekly rate of new infections in Germany between March 3rd and June 22nd, 2020. Our results confirm that reduced social activity lowers the infection rate, accounting for regional and temporal patterns. The extent of social distancing, quantified by the percentage of people staying put within a federal administrative district, has an overall negative effect on the incidence of infections. Additionally, our results show spatial infection patterns based on geographic as well as social distances.

stat.AP↗

arXiv2021

On assessing excess mortality in Germany during the COVID-19 pandemic

Coronavirus disease 2019 (COVID-19) is associated with a very high number of casualties in the general population. Assessing the exact magnitude of this number is a non-trivial problem, as relying only on officially reported COVID-19 associated fatalities runs the risk of incurring in several kinds of biases. One of the ways to approach the issue is to compare overall mortality during the pandemic with expected mortality computed using the observed mortality figures of previous years. In this paper, we build on existing methodology and propose two ways to compute expected as well as excess mortality, namely at the weekly and at the yearly level. Particular focus is put on the role of age, which plays a central part in both COVID-19-associated and overall mortality. We illustrate our methods by making use of age-stratified mortality data from the years 2016 to 2020 in Germany to compute age group-specific excess mortality during the COVID-19 pandemic in 2020.

stat.AP↗

arXiv2021

Statistical modeling of on-street parking lot occupancy in smart cities

Many studies suggest that searching for parking is associated with significant direct and indirect costs. Therefore, it is appealing to reduce the time which car drivers spend on finding an available parking lot, especially in urban areas where the space for all road users is limited. The prediction of on-street parking lot occupancy can provide drivers a guidance where clear parking lots are likely to be found. This field of research has gained more and more attention in the last decade through the increasing availability of real-time parking lot occupancy data. In this paper, we pursue a statistical approach for the prediction of parking lot occupancy, where we make use of time to event models and semi-Markov process theory. The latter involves the employment of Laplace transformations as well as their inversion which is an ambitious numerical task. We apply our methodology to data from the City of Melbourne in Australia. Our main result is that the semi-Markov model outperforms a Markov model in terms of both true negative rate and true positive rate while this is essentially achieved by respecting the current duration which a parking lot already sojourns in its initial state.

stat.AP↗

arXiv2021

Separable and Semiparametric Network-based Counting Processes applied to the International Combat Aircraft Trades

We propose a novel tie-oriented model for longitudinal event network data. The generating mechanism is assumed to be a multivariate Poisson process that governs the onset and repetition of yearly observed events with two separate intensity functions. We apply the model to a network obtained from the number of international deliveries of combat aircraft trades between 1950 and 2017. Based on a modified trade gravity approach we identify economic and political factors impeding or lightening the number of transfers. Extensive dynamics as well as country heterogeneity require the specification of semiparametric time-varying effects as well as random effects.

stat.AP↗

arXiv2021

Regional now- and forecasting for data reported with delay: Towards surveillance of COVID-19 infections

Governments around the world continue to act to contain and mitigate the spread of COVID-19. The rapidly evolving situation compels officials and executives to continuously adapt policies and social distancing measures depending on the current state of the spread of the disease. In this context, it is crucial for policymakers to have a firm grasp on what the current state of the pandemic is as well as to have an idea of how the infective situation is going to unfold in the next days. However, as in many other situations of compulsorily-notifiable diseases and beyond, cases are reported with delay to a central register, with this delay deferring an up-to-date view of the state of things. We provide a stable tool for monitoring current infection levels as well as predicting infection numbers in the immediate future at the regional level. We accomplish this through nowcasting of cases that have not yet been reported as well as through predictions of future infections. We apply our model to German data, for which our focus lies in predicting and explain infectious behavior by district.

stat.AP↗

arXiv2021

Matrix-free Penalized Spline Smoothing with Multiple Covariates

The paper motivates high dimensional smoothing with penalized splines and its numerical calculation in an efficient way. If smoothing is carried out over three or more covariates the classical tensor product spline bases explode in their dimension bringing the estimation to its numerical limits. A recent approach by Siebenborn and Wagner(2019) circumvents storage expensive implementations by proposing matrix-free calculations which allows to smooth over several covariates. We extend their approach here by linking penalized smoothing and its Bayesian formulation as mixed model which provides a matrix-free calculation of the smoothing parameter to avoid the use of high-computational cross validation. Further, we show how to extend the ideas towards generalized regression models. The extended approach is applied to remote sensing satellite data in combination with spatial smoothing.

stat.ME↗

arXiv2020

The Role of Governmental Weapons Procurements in Forecasting Monthly Fatalities in Intrastate Conflicts: A Semiparametric Hierarchical Hurdle Model

Accurate and interpretable forecasting models predicting spatially and temporally fine-grained changes in the numbers of intrastate conflict casualties are of crucial importance for policymakers and international non-governmental organisations (NGOs). Using a count data approach, we propose a hierarchical hurdle regression model to address the corresponding prediction challenge at the monthly PRIO-grid level. More precisely, we model the intensity of local armed conflict at a specific point in time as a three-stage process. Stages one and two of our approach estimate whether we will observe any casualties at the country- and grid-cell-level, respectively, while stage three applies a regression model for truncated data to predict the number of such fatalities conditional upon the previous two stages. Within this modelling framework, we focus on the role of governmental arms imports as a processual factor allowing governments to intensify or deter from fighting. We further argue that a grid cell's geographic remoteness is bound to moderate the effects of these military buildups. Out-of-sample predictions corroborate the effectiveness of our parsimonious and theory-driven model, which enables full transparency combined with accuracy in the forecasting process.

stat.AP↗

arXiv2020

Nowcasting fatal COVID-19 infections on a regional level in Germany

We analyse the temporal and regional structure in mortality rates related to COVID-19 infections. We relate the fatality date of each deceased patient to the corresponding day of registration of the infection, leading to a nowcasting model which allows us to estimate the number of present-day infections that will, at a later date, prove to be fatal. The numbers are broken down to the district level in Germany. Given that death counts generally provide more reliable information on the spread of the disease compared to infection counts, which inevitably depend on testing strategy and capacity, the proposed model and the presented results allow to obtain reliable insight into the current state of the pandemic in Germany.

stat.AP↗