@article{RabeChandraKruegeletal.2021, author = {Rabe, Maximilian Michael and Chandra, Johan and Kr{\"u}gel, Andr{\´e} and Seelig, Stefan A. and Vasishth, Shravan and Engbert, Ralf}, title = {A bayesian approach to dynamical modeling of eye-movement control in reading of normal, mirrored, and scrambled texts}, series = {Psychological Review}, volume = {128}, journal = {Psychological Review}, number = {5}, publisher = {American Psychological Association}, address = {Washington}, issn = {0033-295X}, doi = {10.1037/rev0000268}, pages = {803 -- 823}, year = {2021}, abstract = {In eye-movement control during reading, advanced process-oriented models have been developed to reproduce behavioral data. So far, model complexity and large numbers of model parameters prevented rigorous statistical inference and modeling of interindividual differences. Here we propose a Bayesian approach to both problems for one representative computational model of sentence reading (SWIFT; Engbert et al., Psychological Review, 112, 2005, pp. 777-813). We used experimental data from 36 subjects who read the text in a normal and one of four manipulated text layouts (e.g., mirrored and scrambled letters). The SWIFT model was fitted to subjects and experimental conditions individually to investigate between- subject variability. Based on posterior distributions of model parameters, fixation probabilities and durations are reliably recovered from simulated data and reproduced for withheld empirical data, at both the experimental condition and subject levels. A subsequent statistical analysis of model parameters across reading conditions generates model-driven explanations for observable effects between conditions.}, language = {en} } @article{Reich2013, author = {Reich, Sebastian}, title = {A nonparametric ensemble transform method for bayesian inference}, series = {SIAM journal on scientific computing}, volume = {35}, journal = {SIAM journal on scientific computing}, number = {4}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/130907367}, pages = {A2013 -- A2024}, year = {2013}, abstract = {Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.}, language = {en} } @article{GarbunoInigoNueskenReich2020, author = {Garbuno-Inigo, Alfredo and N{\"u}sken, Nikolas and Reich, Sebastian}, title = {Affine invariant interacting Langevin dynamics for Bayesian inference}, series = {SIAM journal on applied dynamical systems}, volume = {19}, journal = {SIAM journal on applied dynamical systems}, number = {3}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1536-0040}, doi = {10.1137/19M1304891}, pages = {1633 -- 1658}, year = {2020}, abstract = {We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of nondegeneracy and ergodicity. Furthermore, we study its connections to diffusion on Riemannian manifolds and Wasserstein gradient flows. Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free approximation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem.}, language = {en} } @article{MillerSchwarz2011, author = {Miller, Jeff and Schwarz, Wolfgang}, title = {Aggregate and individual replication probability within an explicit model of the research process}, series = {Psychological methods}, volume = {16}, journal = {Psychological methods}, number = {3}, publisher = {American Psychological Association}, address = {Washington}, issn = {1082-989X}, doi = {10.1037/a0023347}, pages = {337 -- 360}, year = {2011}, abstract = {We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by obtaining either a statistically significant result in the same direction or any effect in that direction. We analyze both the probability of successfully replicating a particular experimental effect (i.e., the individual replication probability) and the average probability of successful replication across different studies within some research context (i.e., the aggregate replication probability), and we identify the conditions under which the latter can be approximated using the formulas of Killeen (2005a, 2007). We show how both of these probabilities depend on parameters of the research context that would rarely be known in practice. In addition, we show that the statistical uncertainty associated with the size of an initial observed effect would often prevent accurate estimation of the desired individual replication probability even if these research context parameters were known exactly. We conclude that accurate estimates of replication probability are generally unattainable.}, language = {en} } @article{GianniotisSchnoerrMolkenthinetal.2016, author = {Gianniotis, Nikolaos and Schnoerr, Christoph and Molkenthin, Christian and Bora, Sanjay Singh}, title = {Approximate variational inference based on a finite sample of Gaussian latent variables}, series = {Pattern Analysis \& Applications}, volume = {19}, journal = {Pattern Analysis \& Applications}, publisher = {Springer}, address = {New York}, issn = {1433-7541}, doi = {10.1007/s10044-015-0496-9}, pages = {475 -- 485}, year = {2016}, abstract = {Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower bound on the desired integral to be approximated, e.g. marginal likelihood. The lower bound is then optimised with respect to its free parameters, the so-called variational parameters. However, this is not always possible as for certain integrals it is very challenging (or tedious) to come up with a suitable lower bound. Here, we propose a simple scheme that overcomes some of the awkward cases where the usual variational treatment becomes difficult. The scheme relies on a rewriting of the lower bound on the model log-likelihood. We demonstrate the proposed scheme on a number of synthetic and real examples, as well as on a real geophysical model for which the standard variational approaches are inapplicable.}, language = {en} } @phdthesis{Makarava2012, author = {Makarava, Natallia}, title = {Bayesian estimation of self-similarity exponent}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64099}, school = {Universit{\"a}t Potsdam}, year = {2012}, abstract = {Estimation of the self-similarity exponent has attracted growing interest in recent decades and became a research subject in various fields and disciplines. Real-world data exhibiting self-similar behavior and/or parametrized by self-similarity exponent (in particular Hurst exponent) have been collected in different fields ranging from finance and human sciencies to hydrologic and traffic networks. Such rich classes of possible applications obligates researchers to investigate qualitatively new methods for estimation of the self-similarity exponent as well as identification of long-range dependencies (or long memory). In this thesis I present the Bayesian estimation of the Hurst exponent. In contrast to previous methods, the Bayesian approach allows the possibility to calculate the point estimator and confidence intervals at the same time, bringing significant advantages in data-analysis as discussed in this thesis. Moreover, it is also applicable to short data and unevenly sampled data, thus broadening the range of systems where the estimation of the Hurst exponent is possible. Taking into account that one of the substantial classes of great interest in modeling is the class of Gaussian self-similar processes, this thesis considers the realizations of the processes of fractional Brownian motion and fractional Gaussian noise. Additionally, applications to real-world data, such as the data of water level of the Nile River and fixational eye movements are also discussed.}, language = {en} } @article{BernerTrauthHolschneider2022, author = {Berner, Nadine and Trauth, Martin H. and Holschneider, Matthias}, title = {Bayesian inference about Plio-Pleistocene climate transitions in Africa}, series = {Quaternary science reviews : the international multidisciplinary research and review journal}, volume = {277}, journal = {Quaternary science reviews : the international multidisciplinary research and review journal}, publisher = {Elsevier}, address = {Oxford}, issn = {0277-3791}, doi = {10.1016/j.quascirev.2021.107287}, pages = {12}, year = {2022}, abstract = {During the last 5 Ma the Earth's ocean-atmosphere system passed through several major transitions, many of which are discussed as possible triggers for human evolution. A classic in this context is the possible influence of the closure of the Panama Strait, the intensification of Northern Hemisphere Glaciation, a stepwise increase in aridity in Africa, and the first appearance of the genus Homo about 2.5 - 2.7 Ma ago. Apart from the fact that the correlation between these events does not necessarily imply causality, many attempts to establish a relationship between climate and evolution fail due to the challenge of precisely localizing an a priori unknown number of changes potentially underlying complex climate records. The kernel-based Bayesian inference approach applied here allows inferring the location, generic shape, and temporal scale of multiple transitions in established records of Plio-Pleistocene African climate. By defining a transparent probabilistic analysis strategy, we are able to identify conjoint changes occurring across the investigated terrigenous dust records from Ocean Drilling Programme (ODP) sites in the Atlantic Ocean (ODP 659), Arabian (ODP 721/722) and Mediterranean Sea (ODP 967). The study indicates a two-step transition in the African climate proxy records at (2.35-2.10) Ma and (1.70 - 1.50) Ma, that may be associated with the reorganization of the Hadley-Walker Circulation. .}, language = {en} } @phdthesis{MalemShinitski2023, author = {Malem-Shinitski, Noa}, title = {Bayesian inference and modeling for point processes with applications from neuronal activity to scene viewing}, doi = {10.25932/publishup-61495}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-614952}, school = {Universit{\"a}t Potsdam}, pages = {vii, 129}, year = {2023}, abstract = {Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series. Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes. We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity. The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters. Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models. The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights.}, language = {en} } @article{ThapaParkKimetal.2022, author = {Thapa, Samudrajit and Park, Seongyu and Kim, Yeongjin and Jeon, Jae-Hyung and Metzler, Ralf and Lomholt, Michael A.}, title = {Bayesian inference of scaled versus fractional Brownian motion}, series = {Journal of physics : A, mathematical and theoretical}, volume = {55}, journal = {Journal of physics : A, mathematical and theoretical}, number = {19}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ac60e7}, pages = {21}, year = {2022}, abstract = {We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the possibility of measurement noise in both models. We find that for trajectories of a few hundred time points the procedure is able to resolve well the true model and parameters. Using the prior of the synthetic data generation process also for the inference, the approach is optimal based on decision theory. We include a comparison with inference using a prior different from the data generating one.}, language = {en} } @article{SeeligRabeMalemShinitskietal.2020, author = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf}, title = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading}, series = {Journal of mathematical psychology}, volume = {95}, journal = {Journal of mathematical psychology}, publisher = {Elsevier}, address = {San Diego}, issn = {0022-2496}, doi = {10.1016/j.jmp.2019.102313}, pages = {32}, year = {2020}, abstract = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.}, language = {en} }