Bayesian Inference in the Multinomial Logit Model

The multinomial logit model (MNL) possesses a latent variable representation in terms of random variables following a multivariate logistic distribution. Based on multivariate finite mixture approximations of the multivariate logistic distribution, various data-augmented Metropolis-Hastings algorithms are developed for a Bayesian inference of the MNL model

Vertex finding by sparse model-based clustering

The application of sparse model-based clustering to the problem of primary vertex finding is discussed. The observed z-positions of the charged primary tracks in a bunch crossing are modeled by a Gaussian mixture. The mixture parameters are estimated via Markov Chain Monte Carlo (MCMC). Sparsity is achieved by an appropriate prior on the mixture weights. The results are shown and compared to clustering by the expectation-maximization (EM) algorithm

Statistical analysis of event classification in experimental data

The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test optimization. Aspects of the base data sample if being created by Poisson processes are discussed, and a method for estimating the unknown numbers of signal and background events is presented. Data quality of the selected events sample is assessed by the expected purity and background contamination. Part II contains a rigorous statistical analysis of the methods discussed in Part I. Both Bayesian and frequentist estimators of the unknown signal/background content are investigated. The estimates and their stochastic uncertainties are calculated for various conjugate priors in the Bayesian case, and for three choices of the virtual parent population in the frequentist case.Comment: 26 pages, 6 figure

Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors

The book describes methods of track and vertex resonstruction in particle detectors. The main topics are pattern recognition and statistical estimation of geometrical and physical properties of charged particles and of interaction and decay vertices

Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors

This open access book is a comprehensive review of the methods and algorithms that are used in the reconstruction of events recorded by past, running and planned experiments at particle accelerators such as the LHC, SuperKEKB and FAIR. The main topics are pattern recognition for track and vertex finding, solving the equations of motion by analytical or numerical methods, treatment of material effects such as multiple Coulomb scattering and energy loss, and the estimation of track and vertex parameters by statistical algorithms. The material covers both established methods and recent developments in these fields and illustrates them by outlining exemplary solutions developed by selected experiments. The clear presentation enables readers to easily implement the material in a high-level programming language. It also highlights software solutions that are in the public domain whenever possible. It is a valuable resource for PhD students and researchers working on online or offline reconstruction for their experiments

Labor Market Entry and Earnings Dynamics: Bayesian Inference Using Mixtures-of-Experts Markov Chain Clustering

This paper analyzes patterns in the earnings development of young labor market entrants over their life cycle. We identify four distinctly different types of transition patterns between discrete earnings states in a large administrative data set. Further, we investigate the effects of labor market conditions at the time of entry on the probability of belonging to each transition type. To estimate our statistical model we use a model-based clustering approach. The statistical challenge in our application comes from the di±culty in extending distance-based clustering approaches to the problem of identify groups of similar time series in a panel of discrete-valued time series. We use Markov chain clustering, proposed by Pamminger and Frühwirth-Schnatter (2010), which is an approach for clustering discrete-valued time series obtained by observing a categorical variable with several states. This method is based on finite mixtures of first-order time-homogeneous Markov chain models. In order to analyze group membership we present an extension to this approach by formulating a probabilistic model for the latent group indicators within the Bayesian classification rule using a multinomial logit model.Labor Market Entry Conditions, Transition Data, Markov Chain Monte Carlo, Multinomial Logit, Panel Data, Auxiliary Mixture Sampler, Bayesian Statistics

Labor Market Entry and Earnings Dynamics: Bayesian Inference Using Mixtures-of-Experts Markov Chain Clustering

This paper analyzes patterns in the earnings development of young labor market en- trants over their life cycle. We identify four distinctly di®erent types of transition patterns between discrete earnings states in a large administrative data set. Further, we investigate the e®ects of labor market conditions at the time of entry on the probability of belonging to each transition type. To estimate our statistical model we use a model-based clustering approach. The statistical challenge in our application comes from the di±culty in extending distance-based clustering approaches to the problem of identify groups of similar time series in a panel of discrete-valued time series. We use Markov chain clustering, proposed by Pam- minger and FrÄuhwirth-Schnatter (2010), which is an approach for clustering discrete-valued time series obtained by observing a categorical variable with several states. This method is based on ¯nite mixtures of ¯rst-order time-homogeneous Markov chain models. In order to analyze group membership we present an extension to this approach by formulating a prob- abilistic model for the latent group indicators within the Bayesian classi¯cation rule using a multinomial logit model.Labor Market Entry Conditions, Transition Data, Markov Chain Monte Carlo, Multinomial Logit, Panel Data, Auxiliary Mixture Sampler, Bayesian Statistics