TY - JOUR A1 - Marion, Glenn A1 - McInerny, Greg J. A1 - Pagel, Jörn A1 - Catterall, Stephen A1 - Cook, Alex R. A1 - Hartig, Florian A1 - O&rsquo, A1 - Hara, Robert B. T1 - Parameter and uncertainty estimation for process-oriented population and distribution models: data, statistics and the niche JF - JOURNAL OF BIOGEOGRAPHY N2 - The spatial distribution of a species is determined by dynamic processes such as reproduction, mortality and dispersal. Conventional static species distribution models (SDMs) do not incorporate these processes explicitly. This limits their applicability, particularly for non-equilibrium situations such as invasions or climate change. In this paper we show how dynamic SDMs can be formulated and fitted to data within a Bayesian framework. Our focus is on discrete state-space Markov process models which provide a flexible framework to account for stochasticity in key demographic processes, including dispersal, growth and competition. We show how to construct likelihood functions for such models (both discrete and continuous time versions) and how these can be combined with suitable observation models to conduct Bayesian parameter inference using computational techniques such as Markov chain Monte Carlo. We illustrate the current state-of-the-art with three contrasting examples using both simulated and empirical data. The use of simulated data allows the robustness of the methods to be tested with respect to deficiencies in both data and model. These examples show how mechanistic understanding of the processes that determine distribution and abundance can be combined with different sources of information at a range of spatial and temporal scales. Application of such techniques will enable more reliable inference and projections, e.g. under future climate change scenarios than is possible with purely correlative approaches. Conversely, confronting such process-oriented niche models with abundance and distribution data will test current understanding and may ultimately feedback to improve underlying ecological theory. KW - Bayesian inference KW - demography KW - dispersal KW - dynamic models KW - dynamic range models KW - establishment KW - global change KW - niche models KW - species distribution models Y1 - 2012 U6 - https://doi.org/10.1111/j.1365-2699.2012.02772.x SN - 0305-0270 SN - 1365-2699 VL - 39 IS - 12 SP - 2225 EP - 2239 PB - WILEY-BLACKWELL CY - HOBOKEN ER - TY - THES A1 - Makarava, Natallia T1 - Bayesian estimation of self-similarity exponent T1 - Bayessche Schätzung des selbstählichen Exponenten N2 - 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. N2 - Die Abschätzung des Selbstähnlichkeitsexponenten hat in den letzten Jahr-zehnten an Aufmerksamkeit gewonnen und ist in vielen wissenschaftlichen Gebieten und Disziplinen zu einem intensiven Forschungsthema geworden. Reelle Daten, die selbsähnliches Verhalten zeigen und/oder durch den Selbstähnlichkeitsexponenten (insbesondere durch den Hurst-Exponenten) parametrisiert werden, wurden in verschiedenen Gebieten gesammelt, die von Finanzwissenschaften über Humanwissenschaften bis zu Netzwerken in der Hydrologie und dem Verkehr reichen. Diese reiche Anzahl an möglichen Anwendungen verlangt von Forschern, neue Methoden zu entwickeln, um den Selbstähnlichkeitsexponenten abzuschätzen, sowie großskalige Abhängigkeiten zu erkennen. In dieser Arbeit stelle ich die Bayessche Schätzung des Hurst-Exponenten vor. Im Unterschied zu früheren Methoden, erlaubt die Bayessche Herangehensweise die Berechnung von Punktschätzungen zusammen mit Konfidenzintervallen, was von bedeutendem Vorteil in der Datenanalyse ist, wie in der Arbeit diskutiert wird. Zudem ist diese Methode anwendbar auf kurze und unregelmäßig verteilte Datensätze, wodurch die Auswahl der möglichen Anwendung, wo der Hurst-Exponent geschätzt werden soll, stark erweitert wird. Unter Berücksichtigung der Tatsache, dass der Gauß'sche selbstähnliche Prozess von bedeutender Interesse in der Modellierung ist, werden in dieser Arbeit Realisierungen der Prozesse der fraktionalen Brown'schen Bewegung und des fraktionalen Gauß'schen Rauschens untersucht. Zusätzlich werden Anwendungen auf reelle Daten, wie Wasserstände des Nil und fixierte Augenbewegungen, diskutiert. KW - Hurst-Exponent KW - Bayessche Statistik KW - fraktionale Brown'schen Bewegung KW - fraktionales Gauß'sches Rauschen KW - fixierte Augenbewegungen KW - Hurst exponent KW - Bayesian inference KW - fractional Brownian motion KW - fractional Gaussian noise KW - fixational eye movements Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64099 ER -