@article{MolkenthinDonnerReichetal.2022, author = {Molkenthin, Christian and Donner, Christian and Reich, Sebastian and Z{\"o}ller, Gert and Hainzl, Sebastian and Holschneider, Matthias and Opper, Manfred}, title = {GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model}, series = {Statistics and Computing}, volume = {32}, journal = {Statistics and Computing}, number = {2}, publisher = {Springer}, address = {Dordrecht}, issn = {0960-3174}, doi = {10.1007/s11222-022-10085-3}, pages = {25}, year = {2022}, abstract = {The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.}, 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{MalemShinitskiOjedaOpper2022, author = {Malem-Shinitski, Noa and Ojeda, Cesar and Opper, Manfred}, title = {Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects}, series = {Entropy}, volume = {24}, journal = {Entropy}, number = {3}, publisher = {MDPI}, address = {Basel}, issn = {1099-4300}, doi = {10.3390/e24030356}, pages = {22}, year = {2022}, abstract = {Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.}, language = {en} } @article{SchadVasishth2022, author = {Schad, Daniel and Vasishth, Shravan}, title = {The posterior probability of a null hypothesis given a statistically significant result}, series = {The quantitative methods for psychology}, volume = {18}, journal = {The quantitative methods for psychology}, number = {2}, publisher = {University of Montreal, Department of Psychology}, address = {Montreal}, issn = {1913-4126}, doi = {10.20982/tqmp.18.2.p011}, pages = {130 -- 141}, year = {2022}, abstract = {When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless for various reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relax certain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show in a step-by-step guide that the intuitively appealing belief, that Prob(H0) is low when significant results have been obtained under repeated sampling, is in general incorrect and depends greatly on: (a) the prior probability of the null being true; (b) type-I error rate, (c) type-II error rate, and (d) replication of a result. Through step-by-step simulations using open-source code in the R System of Statistical Computing, we show that uncertainty about the null hypothesis being true often remains high despite a significant result. To help the reader develop intuitions about this common misconception, we provide a Shiny app (https://danielschad.shinyapps.io/probnull/). We expect that this tutorial will help researchers better understand and judge results from null hypothesis significance tests.}, 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} } @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} } @article{AcevedoDeWiljesReich2017, author = {Acevedo, Walter and De Wiljes, Jana and Reich, Sebastian}, title = {Second-order accurate ensemble transform particle filters}, series = {SIAM journal on scientific computing}, volume = {39}, journal = {SIAM journal on scientific computing}, number = {5}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia}, issn = {1064-8275}, doi = {10.1137/16M1095184}, pages = {A1834 -- A1850}, year = {2017}, abstract = {Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.}, 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{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{RosenbaumRaatzWeithoffetal.2019, author = {Rosenbaum, Benjamin and Raatz, Michael and Weithoff, Guntram and Fussmann, Gregor F. and Gaedke, Ursula}, title = {Estimating parameters from multiple time series of population dynamics using bayesian inference}, series = {Frontiers in ecology and evolution}, volume = {6}, journal = {Frontiers in ecology and evolution}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {2296-701X}, doi = {10.3389/fevo.2018.00234}, pages = {14}, year = {2019}, abstract = {Empirical time series of interacting entities, e.g., species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations. In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics. Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics. By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.}, language = {en} }