TY - JOUR A1 - Molkenthin, Christian A1 - Donner, Christian A1 - Reich, Sebastian A1 - Zöller, Gert A1 - Hainzl, Sebastian A1 - Holschneider, Matthias A1 - Opper, Manfred T1 - GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model JF - Statistics and Computing N2 - 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. KW - Self-exciting point process KW - Hawkes process KW - Spatio-temporal ETAS model KW - Bayesian inference KW - Sampling KW - Earthquake modeling KW - Gaussian process KW - Data augmentation Y1 - 2022 U6 - https://doi.org/10.1007/s11222-022-10085-3 SN - 0960-3174 SN - 1573-1375 VL - 32 IS - 2 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Thapa, Samudrajit A1 - Park, Seongyu A1 - Kim, Yeongjin A1 - Jeon, Jae-Hyung A1 - Metzler, Ralf A1 - Lomholt, Michael A. T1 - Bayesian inference of scaled versus fractional Brownian motion JF - Journal of physics : A, mathematical and theoretical N2 - 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. KW - Bayesian inference KW - scaled Brownian motion KW - single particle tracking Y1 - 2022 U6 - https://doi.org/10.1088/1751-8121/ac60e7 SN - 1751-8113 SN - 1751-8121 VL - 55 IS - 19 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Malem-Shinitski, Noa A1 - Ojeda, Cesar A1 - Opper, Manfred T1 - Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects JF - Entropy N2 - 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. KW - Bayesian inference KW - point process KW - Gaussian process Y1 - 2022 U6 - https://doi.org/10.3390/e24030356 SN - 1099-4300 VL - 24 IS - 3 PB - MDPI CY - Basel ER - TY - THES A1 - Malem-Shinitski, Noa T1 - Bayesian inference and modeling for point processes with applications from neuronal activity to scene viewing T1 - Bayessche Inferenz und Modellierung für Punktprozesse mit Anwendungen von neuronaler Aktivität bis Szenenbetrachtung N2 - 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. N2 - Punktprozesse sind eine gängige Methode zur Modellierung von Ereignismengen. Von Erdbeben bis zu Social-Media-Posts, von den neuronalen Spikes bis zum Zeitpunkt von Verbrechen, von Aktienkursen bis zur Ausbreitung von Krankheiten - diese Phänomene lassen sich auf das Auftreten von Ereignissen reduzieren, die in Punkten konzentriert sind. Häufig treten diese Ereignisse nacheinander auf und bilden eine Zeitreihe. Modelle von Punktprozessen können verwendet werden, um unser Verständnis solcher Ereignisse für Klassifizierung und Vorhersage zu vertiefen. Solche Modelle umfassen einen zugrunde liegenden Zufallsprozess, der die Ereignisse erzeugt. In dieser Arbeit wird die Bayes'sche Methodik verwendet, um den zugrunde liegenden generativen Prozess aus den beobachteten Daten abzuleiten. Wir leisten einen doppelten Beitrag: Wir entwickeln neue Modelle und neue Inferenzmethoden für diese Prozesse. Wir schlagen ein Modell vor, das die Familie der Punktprozesse erweitert, bei denen das Auftreten eines Ereignisses von den vorherigen Ereignissen abhängt. Diese Familie ist als Hawkes-Prozesse bekannt. Während in den meisten bestehenden Modellen solcher Prozesse davon ausgegangen wird, dass vergangene Ereignisse nur eine exzitatorische Wirkung auf zukünftige Ereignisse haben, konzentrieren wir uns auf den neu entwickelten nichtlinearen Hawkes-Prozess, bei dem vergangene Ereignisse exzitatorische und hemmende Wirkungen haben können. Nach der Definition des Modells stellen wir seine Inferenzmethode vor und wenden sie auf Daten aus verschiedenen Bereichen an, unter anderem auf die neuronale Aktivität. Das zweite Modell, das in dieser Arbeit beschrieben wird, betrifft einen speziellen Fall von Punktprozessen - den Entscheidungsprozess, der der menschlichen Blicksteuerung zugrunde liegt. Dieser Prozess führt zu einer Reihe von fixierten Positionen in einem Bild. Wir haben ein neues Modell entwickelt, um diesen Prozess zu beschreiben, motiviert durch das bekannte Exploration-Exploitation-Dilemma. Neben dem Modell stellen wir einen Bayes'schen Inferenzalgorithmus vor, um die Modellparameter abzuleiten. Wir bleiben auf dem Gebiet der menschlichen Szenenbetrachtung und stellen fest, dass es in diesem Bereich keine bewährten Verfahren für die Bayes'sche Inferenz gibt. Wir geben einen Überblick über vier gängige Algorithmen und vergleichen ihre Leistungen bei der Ableitung von Parametern für zwei Scanpfadmodelle. Die in dieser Dissertation vorgestellten neuen Modelle und Inferenzalgorithmen bereichern das Verständnis von Punktprozessdaten und ermöglichen es uns, sinnvolle Erkenntnisse zu gewinnen. KW - Bayesian inference KW - point process KW - statistical machine learning KW - sampling KW - modeling KW - Bayessche Inferenz KW - Modellierung KW - Punktprozess KW - Stichprobenentnahme aus einem statistischen Modell KW - statistisches maschinelles Lernen Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-614952 ER - TY - JOUR A1 - Schad, Daniel A1 - Vasishth, Shravan T1 - The posterior probability of a null hypothesis given a statistically significant result JF - The quantitative methods for psychology N2 - 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. KW - Null hypothesis significance testing KW - Bayesian inference KW - statistical KW - power Y1 - 2022 U6 - https://doi.org/10.20982/tqmp.18.2.p011 SN - 1913-4126 SN - 2292-1354 VL - 18 IS - 2 SP - 130 EP - 141 PB - University of Montreal, Department of Psychology CY - Montreal ER - TY - THES A1 - Malchow, Anne-Kathleen T1 - Developing an integrated platform for predicting niche and range dynamics BT - inverse calibration of spatially-explicit eco-evolutionary models N2 - Species are adapted to the environment they live in. Today, most environments are subjected to rapid global changes induced by human activity, most prominently land cover and climate changes. Such transformations can cause adjustments or disruptions in various eco-evolutionary processes. The repercussions of this can appear at the population level as shifted ranges and altered abundance patterns. This is where global change effects on species are usually detected first. To understand how eco-evolutionary processes act and interact to generate patterns of range and abundance and how these processes themselves are influenced by environmental conditions, spatially-explicit models provide effective tools. They estimate a species’ niche as the set of environmental conditions in which it can persist. However, the currently most commonly used models rely on static correlative associations that are established between a set of spatial predictors and observed species distributions. For this, they assume stationary conditions and are therefore unsuitable in contexts of global change. Better equipped are process-based models that explicitly implement algorithmic representations of eco-evolutionary mechanisms and evaluate their joint dynamics. These models have long been regarded as difficult to parameterise, but an increased data availability and improved methods for data integration lessen this challenge. Hence, the goal of this thesis is to further develop process-based models, integrate them into a complete modelling workflow, and provide the tools and guidance for their successful application. With my thesis, I presented an integrated platform for spatially-explicit eco-evolutionary modelling and provided a workflow for their inverse calibration to observational data. In the first chapter, I introduced RangeShiftR, a software tool that implements an individual-based modelling platform for the statistical programming language R. Its open-source licensing, extensive help pages and available tutorials make it accessible to a wide audience. In the second chapter, I demonstrated a comprehensive workflow for the specification, calibration and validation of RangeShiftR by the example of the red kite in Switzerland. The integration of heterogeneous data sources, such as literature and monitoring data, allowed to successfully calibrate the model. It was then used to make validated, spatio-temporal predictions of future red kite abundance. The presented workflow can be adopted to any study species if data is available. In the third chapter, I extended RangeShiftR to directly link demographic processes to climatic predictors. This allowed me to explore the climate-change responses of eight Swiss breeding birds in more detail. Specifically, the model could identify the most influential climatic predictors, delineate areas of projected demographic suitability, and attribute current population trends to contemporary climate change. My work shows that the application of complex, process-based models in conservation-relevant contexts is feasible, utilising available tools and data. Such models can be successfully calibrated and outperform other currently used modelling approaches in terms of predictive accuracy. Their projections can be used to predict future abundances or to assess alternative conservation scenarios. They further improve our mechanistic understanding of niche and range dynamics under climate change. However, only fully mechanistic models, that include all relevant processes, allow to precisely disentangle the effects of single processes on observed abundances. In this respect, the RangeShiftR model still has potential for further extensions that implement missing influential processes, such as species interactions. Dynamic, process-based models are needed to adequately model a dynamic reality. My work contributes towards the advancement, integration and dissemination of such models. This will facilitate numeric, model-based approaches for species assessments, generate ecological insights and strengthen the reliability of predictions on large spatial scales under changing conditions. N2 - Arten sind an ihren jeweiligen Lebensraum angepasst, doch viele Lebensräume sind heute einem globalen Wandel unterworfen. Dieser äußert sich vor allem in Veränderungen von Landnutzung und Klima, welche durch menschliche Aktivitäten verursacht werden und ganze Ökosysteme in ihrem Gefüge stören können. Störungen der grundlegenden öko-evolutionären Prozesse können auf der Populationsebene in Form von veränderten Verbreitungsgebieten und Häufigkeitsmustern sichtbar werden. Hier werden die Auswirkungen des globalen Wandels auf eine Art oftmals zuerst beobachtet. Um zu untersuchen, wie die Wirkung und Wechselwirkung der verschiedenen öko-evolutionären Prozesse die beobachteten Verbreitungs- und Häufigkeitsmuster erzeugen, und wie diese Prozesse wiederum von Umweltbedingungen beeinflusst werden, stellen räumlich explizite Modelle wirksame Instrumente dar. Sie beschreiben die ökologische Nische einer Art, also die Gesamtheit aller Umweltbedingungen, unter denen die Art fortbestehen kann. Die derzeit am häufigsten verwendeten Modelle stützen sich auf statische, korrelative Zusammenhänge, die zwischen bestimmten räumlichen Prädiktoren und den beobachteten Artverteilungen hergestellt werden. Allerdings werden dabei stationäre Bedingungen angenommen, was sie im Kontext des globalen Wandels ungeeignet macht. Deutlich besser geeignet sind prozessbasierte Modelle, welche explizite, algorithmische Repräsentationen von ökologischen Prozessen beinhalten und deren gemeinsame Dynamik berechnen. Solche Modelle galten lange Zeit als schwierig zu parametrisieren, doch die zunehmende Verfügbarkeit von Beobachtungsdaten sowie die verbesserten Methoden zur Datenintegration machen ihre Verwendung zunehmend praktikabel. Das Ziel der vorliegenden Arbeit ist es, diese prozessbasierten Modelle weiterzuentwickeln, sie in umfassende Modellierungsabläufe einzubinden, sowie Software und Anleitungen für ihre erfolgreiche Anwendung verfügbar zu machen. In meiner Dissertation präsentiere ich eine integrierte Plattform für räumlich-explizite, öko-evolutionäre Modellierung und entwickle einen Arbeitsablauf für dessen inverse Kalibrierung an Beobachtungsdaten. Im ersten Kapitel stelle ich RangeShiftR vor: eine Software, die eine individuenbasierte Modellierungsplattform für die statistische Programmiersprache R implementiert. Durch die Open-Source-Lizenzierung, umfangreichen Hilfeseiten und online verfügbaren Tutorials ist RangeShiftR einem breiten Publikum zugänglich. Im zweiten Kapitel demonstriere ich einen vollständigen Modellierungsablauf am Beispiel des Rotmilans in der Schweiz, der die Spezifikation, Kalibrierung und Validierung von RangeShiftR umfasst.Durch die Integration heterogener Datenquellen, wie Literatur- und Monitoringdaten, konnte das Modell erfolgreich kalibriert werden. Damit konnten anschließend validierte, raum-zeitliche Vorhersagen über das Vorkommen des Rotmilans erstellt und die dafür relevanten Prozesse identifiziert werden. Der vorgestellte Arbeitsablauf kann auf andere Arten übertragen werden, sofern geeignete Daten verfügbar sind. Im dritten Kapitel habe ich RangeShiftR erweitert, sodass demografische Prozessraten direkt mit Klimavariablen verknüpft werden können. Dies ermöglichte es, die Reaktionen von acht Schweizer Brutvogelarten auf den Klimawandel genauer zu untersuchen. Insbesondere konnte das Modell die einflussreichsten klimatischen Faktoren identifizieren, demografisch geeignete Gebiete abgrenzen und aktuelle Populationstrends auf den bisherigen Klimawandel zurückführen. Meine Arbeit zeigt, dass die Anwendung komplexer, prozessbasierter Modelle in naturschutzrelevanten Kontexten mit verfügbaren Daten möglich ist. Solche Modelle können erfolgreich kalibriert werden und andere, derzeit verwendete Modellierungsansätze in Bezug auf ihre Vorhersagegenauigkeit übertreffen. Ihre Projektionen können zur Vorhersage zukünftiger Artvorkommen und zur Einschätzung alternativer Naturschutzmaßnahmen verwendet werden. Sie verbessern außerdem unser mechanistisches Verständnis von Nischen- und Verbreitungsdynamiken unter dem Einfluss des Klimawandels. Jedoch ermöglichen nur vollständig prozessbasierte Modelle, die alle relevanten Prozesse vereinen, eine korrekte Aufschlüsselung der Auswirkungen einzelner Prozesse auf die beobachteten Abundanzen. In dieser Hinsicht hat das RangeShiftR-Modell noch Potenzial für Weiterentwicklungen, um fehlende, einflussreiche Prozesse hinzuzufügen, wie zum Beispiel die Interaktionen zwischen Arten. Um eine dynamische Realität adäquat abbilden zu können, werden dynamische, prozessbasierte Modelle benötigt. Meine Arbeit leistet einen Beitrag zur Weiterentwicklung, Integration und Verbreitung solcher Modelle und stärkt somit die Anwendung numerischer, modellbasierter Methoden für die Bewertung des Zustands von Arten, die Untersuchung ökologischer Zusammenhänge und die Steigerung der Zuverlässigkeit von Vorhersagen auf großen räumlichen Skalen unter Umweltveränderungen. T2 - Entwicklung einer integrierten Modellierungs-Plattform zur Vorhersage von Nischen- und Verbreitungs-dynamiken: Inverse Kalibrierung räumlich-expliziter öko-evolutionärer Modelle KW - species distribution modelling KW - Bayesian inference KW - individual-based modelling KW - range shifts KW - ecological modelling KW - population dynamics KW - Bayes'sche Inferenz KW - ökologische Modellierung KW - individuen-basierte Modellierung KW - Populationsdynamik KW - Arealverschiebungen KW - Artverbreitungsmodelle Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-602737 ER - TY - JOUR A1 - Berner, Nadine A1 - Trauth, Martin H. A1 - Holschneider, Matthias T1 - Bayesian inference about Plio-Pleistocene climate transitions in Africa JF - Quaternary science reviews : the international multidisciplinary research and review journal N2 - 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. . KW - Plio-Pleistocene KW - Hadley-Walker Circulation KW - climate transition KW - Bayesian inference KW - time series analysis KW - ODP 659 KW - ODP 721/722 KW - ODP 967 Y1 - 2022 U6 - https://doi.org/10.1016/j.quascirev.2021.107287 SN - 0277-3791 SN - 1873-457X VL - 277 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Seelig, Stefan A. A1 - Rabe, Maximilian Michael A1 - Malem-Shinitski, Noa A1 - Risse, Sarah A1 - Reich, Sebastian A1 - Engbert, Ralf T1 - Bayesian parameter estimation for the SWIFT model of eye-movement control during reading JF - Journal of mathematical psychology N2 - 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. KW - dynamical models KW - reading KW - eye movements KW - saccades KW - likelihood function KW - Bayesian inference KW - MCMC KW - interindividual differences Y1 - 2020 U6 - https://doi.org/10.1016/j.jmp.2019.102313 SN - 0022-2496 SN - 1096-0880 VL - 95 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Acevedo, Walter A1 - De Wiljes, Jana A1 - Reich, Sebastian T1 - Second-order accurate ensemble transform particle filters JF - SIAM journal on scientific computing N2 - 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. KW - Bayesian inference KW - data assimilation KW - particle filter KW - ensemble Kalman filter KW - Sinkhorn approximation Y1 - 2017 U6 - https://doi.org/10.1137/16M1095184 SN - 1064-8275 SN - 1095-7197 SN - 2168-3417 VL - 39 IS - 5 SP - A1834 EP - A1850 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Garbuno-Inigo, Alfredo A1 - Nüsken, Nikolas A1 - Reich, Sebastian T1 - Affine invariant interacting Langevin dynamics for Bayesian inference JF - SIAM journal on applied dynamical systems N2 - 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. KW - Langevin dynamics KW - interacting particle systems KW - Bayesian inference KW - gradient flow KW - multiplicative noise KW - affine invariance KW - gradient-free Y1 - 2020 U6 - https://doi.org/10.1137/19M1304891 SN - 1536-0040 VL - 19 IS - 3 SP - 1633 EP - 1658 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER -