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6. Nachwuchsworkshop des ZeSt

7. Dezember 2018 findet an der Universität Bielefeld der 6. Nachwuchsworkshop des Zentrums für Statistik statt.

Im Rahmen des Nachwuchsworkshops stellen sich Doktorandinnen und Doktoranden der am Zentrum für Statistik beteiligen Bereiche gegenseitig ihre Forschungsfelder vor und diskutieren darüber.

Bei Interesse melden Sie sich bitte per E-Mail bei Dr. Nina Westerheide.

Programm des Nachwuchsworkshops

 

Vorträge der teilnehmenden Doktorandinnen und Doktoranden (in alphabetischer Reihenfolge)

Timo Adam
Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

Semi-parametric hidden Markov models for discrete-valued time series

Hidden Markov models are popular tools for modeling discrete-valued time series where, at each point in time, a hidden state process selects among a finite set of possible distributions for the observations. Choosing an adequate class of parametric distributions, however, can be quite a complex task, and an inadequate choice may have a severe negative impact on the resulting model fit. To circumvent this problem, we propose semi-parametric hidden Markov models for discrete-valued time series, where the distributions are estimated in a completely data-driven way without relying on parametric assumptions. The feasibility of the suggested approach is assessed in simulation experiments and illustrated in a real-data example.

 

Manuel Batram

Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

Different configurations of pairwise likelihoods and their impact on the statistical and computational performance of MACML

Composite marginal likelihood (CML) estimation is used to estimate parameters from models for correlated data whose likelihoods are computationally burdensome to evaluate. The basic idea is to construct a pseudo-likelihood based on compositions of marginal densities (e.g. the product of all one-dimensional margins, which is equivalent to a working independence assumption). Usually weights are used to scale the impact of the – typically low-dimensional – margins. Especially relevant are weighting schemes which drop certain margins from the pseudo-likelihood by assigning zero weights. MACML estimation is an approach which inter alia utilizes pairwise CMLs to estimate multinomial probit models. Driven by the example of sequences of trip chaining choices I investigate the effect different weighting schemes have on the statistical and computational performance of the MACML estimator.

 

Sebastian Büscher
Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

An analysis of two decades of German mobility data with an emphasis on temporal stability using Multinomial Logit Models

Understanding the mobility of persons is important for a number of reasons, with agent based simulation models of mobility being one of the prime applications.
In previous studies it has been found that a small number of motifs (directed graphs encoding compressed information of daily travel behavior of a person) suffices to explain large proportions of observed choices with very similar frequencies across very different data sets in different regions. In this talk it will be highlighted, that this stability of motif choices can not only be observed across different data sets, but also across time.
For this, not only the overall distribution of the motif choices is analyzed, but also whether the determinants of motif choice are persistent over time. In order to do so the assessment is based on two decades (1994-2013) of yearly, week-long travel diaries from the German Mobility Panel (MOP).

 

Rainer Buschmeier
Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

System Order Estimation as Part of the Subspace Algorithm---A Simulation Study with Seasonally Integrated VARMA Processes

The estimation of the system order, i.e., the minimal state dimension of a state space system, is a crucial step in the subspace algorithm because, e.g., subsequent testing of the cointegrating rank can only be successful if the system order is estimated large enough. In this simulation study, different estimation methods are described and their performance is compared for seasonally integrated VARMA processes.

 

Anke Erdmann
Universität Bielefeld, Fakultät für Soziologie

What Influences the Chronic Victimization of Persistent Offenders? A Dual Trajectory Analysis of the Victim-Offender Overlap under the Perspective of Routine Activity Theory and Peer Groups

Although the consistent association between offending and victimization is a long-noted phenomenon, current criminological research is still engaged to gather profound knowledge on the etiology of this victim-offender overlap. Beyond that, the examination of its development over the life course requires further attention to create a better understanding of why offending and victimization are strongly connected. In this talk, I will present an examination of the overlap between distinct trajectories of
offending and violent victimization over the phase of youth and adolescence applying a joint trajectory technique. The data are seven consecutive waves from the German longitudinal study "Crime in the Modern City". In particular, the victimization of persistent offenders is investigated taking a routine activity perspective focusing activities with peers.

 

Sina Mews
Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

Nonparametric estimation in hidden Markov models using the EM algorithm

Hidden Markov models (HMMs) constitute a flexible class of models for time series data, in which the observations are generated by conditional distributions as selected by an underlying Markov chain. While the state-dependent distributions are typically assumed to be a member of some parametric family, misspecifications in this regard can lead to biased parameter estimates, to a high misclassification rate when decoding the hidden states, and to invalid inference on the number of states, to name just a few undesirable consequences. To overcome this restrictive assumption, the state-dependent distributions can be modelled nonparametrically based on penalized splines (P-splines) in order to obtain density estimates sufficiently flexible to capture any distributional shape, with a wiggliness penalty to avoid overfitting. However, parameter estimation based on numerical maximisation of the likelihood requires a computationally intensive determination of the smoothing parameters via grid search. Here we suggest to instead use the EM algorithm, leading to the main advantage that one can iteratively update the smoothing parameters within each M step. A simulation study as well as a real data example are used to assess the performance of the EM-based nonparametric estimation approach. Its results are compared to the numerical ML equivalent as well as to a parametric model formulation, indicating that the EM-based estimation approach is a suitable alternative to the numerical ML one.

 

Marius Ötting
Universität Bielefeld, Fakultät für Wirtschaftswissenschaften & Fakultät für Psychologie und Sportwissenschaft, Abteilung Sportwissenschaft, Arbeitsbereich V - Sport

Modelling Momentum in Soccer

In soccer, a topic which is often discussed by fans and journalists is the 'momentum' of a team with corresponding 'momentum shifts'. An example for a momentum shift is
a team trailing 0 - 2 and suddenly seeming to change from being on the back foot to dominating the game, possibly driven by an event such as a shot hitting the woodwork.
However, little is known about whether there really exist such momentum changes during a soccer match and which factors -- if there are momentum shifts in a match -- drive these shifts. To tackle these questions, hidden Markov models (HMMs) are considered to model several count variables (such as shots on goal and touches
on the ball, obtained every minute) of Bundesliga matches which are assumed to be driven by a hidden state process. This hidden process can be linked to different styles of play, e.g. attacking or defensive styles. Furthermore, within these HMMs, Copulas are used to model the multivariate data, taking into account the complex data structure by selecting marginal distributions such as the the Conway-Maxwell-Poisson distribution and Poisson hurdle models.

 

Jennifer Pohle

Universität Bielefeld, Fakultät für Wirtschaftswissenschaften

Modeling interactions between animals using coupled hidden Markov models

Hidden Markov models (HMMs) are widely used in ecology to analyse animal movement data (e.g. GPS or accelerometer data). Usually, the underlying hidden state sequence of the HMM is interpreted as a proxy for the behavioral modes of the animal, for instance resting, foraging or traveling. These unobserved modes are assumed to drive the observed movement patterns. However, when several animals are observed at the same time and the same location, they might interact and influence each other. This cannot be captured by a basic HMM. Therefore, we propose to extend the HMM and use coupled hidden Markov models to account for interactions between different individuals.  The model is illustrated using a case study on the movement of a dolphin mother and calf.

 

Houda Yaqine

Parameter Estimation for Lotka-Volterra switching model with a state-dependent switching process

The stochastic Lotka-Volterra model is used to describe species interaction as diffusion processes, but this interaction can be subject to some environmental noise. This latter can be presented by a Continuous Time Markov Chain (CTMC), referred to as the switching component. In this work the switching component depends on the diffusion process, and the switching Lotka-Volterra model is written in a parametric form, where the different rates are the parameters to be estimated using the likelihood function. Along the estimation procedure, filtering equations have been used to approximate the conditional expectation of the CTMC given the observations in time of the Switching diffusion process.

 



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