@phdthesis{Thapa2020,
  author    = {Thapa, Samudrajit},
  title     = {Deciphering anomalous diffusion in complex systems using Bayesian inference and large deviation theory},
  pages     = {xx, 186},
  year      = {2020},
  abstract  = {The development of methods such as super-resolution microscopy (Nobel prize in Chemistry, 2014) and multi-scale computer modelling (Nobel prize in Chemistry, 2013) have provided scientists with powerful tools to study microscopic systems. Sub-micron particles or even fluorescently labelled single molecules can now be tracked for long times in a variety of systems such as living cells, biological membranes, colloidal solutions etc. at spatial and temporal resolutions previously inaccessible. Parallel to such single-particle tracking experiments, super-computing techniques enable simulations of large atomistic or coarse-grained systems such as biologically relevant membranes or proteins from picoseconds to seconds, generating large volume of data. These have led to an unprecedented rise in the number of reported cases of anomalous diffusion wherein the characteristic features of Brownian motion—namely linear growth of the mean squared displacement with time and the Gaussian form of the probability density function (PDF) to find a particle at a given position at some fixed time—are routinely violated. This presents a big challenge in identifying the underlying stochastic process and also estimating the corresponding parameters of the process to completely describe the observed behaviour. Finding the correct physical mechanism which leads to the observed dynamics is of paramount importance, for example, to understand the first-arrival time of transcription factors which govern gene regulation, or the survival probability of a pathogen in a biological cell post drug administration. Statistical Physics provides useful methods that can be applied to extract such vital information. This cumulative dissertation, based on five publications, focuses on the development, implementation and application of such tools with special emphasis on Bayesian inference and large deviation theory. Together with the implementation of Bayesian model comparison and parameter estimation methods for models of diffusion, complementary tools are developed based on different observables and large deviation theory to classify stochastic processes and gather pivotal information. Bayesian analysis of the data of micron-sized particles traced in mucin hydrogels at different pH conditions unveiled several interesting features and we gained insights into, for example, how in going from basic to acidic pH, the hydrogel becomes more heterogeneous and phase separation can set in, leading to observed non-ergodicity (non-equivalence of time and ensemble averages) and non-Gaussian PDF. With large deviation theory based analysis we could detect, for instance, non-Gaussianity in seeming Brownian diffusion of beads in aqueous solution, anisotropic motion of the beads in mucin at neutral pH conditions, and short-time correlations in climate data. Thus through the application of the developed methods to biological and meteorological datasets crucial information is garnered about the underlying stochastic processes and significant insights are obtained in understanding the physical nature of these systems.},
  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}
}
@phdthesis{Malchow2023,
  author    = {Malchow, Anne-Kathleen},
  title     = {Developing an integrated platform for predicting niche and range dynamics},
  doi       = {10.25932/publishup-60273},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-602737},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xiv, 169},
  year      = {2023},
  abstract  = {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.},
  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}
}