62-XX STATISTICS
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Institute
Recurrences in past climates
(2023)
Our ability to predict the state of a system relies on its tendency to recur to states it has visited before. Recurrence also pervades common intuitions about the systems we are most familiar with: daily routines, social rituals and the return of the seasons are just a few relatable examples. To this end, recurrence plots (RP) provide a systematic framework to quantify the recurrence of states. Despite their conceptual simplicity, they are a versatile tool in the study of observational data. The global climate is a complex system for which an understanding based on observational data is not only of academical relevance, but vital for the predurance of human societies within the planetary boundaries. Contextualizing current global climate change, however, requires observational data far beyond the instrumental period. The palaeoclimate record offers a valuable archive of proxy data but demands methodological approaches that adequately address its complexities. In this regard, the following dissertation aims at devising novel and further developing existing methods in the framework of recurrence analysis (RA). The proposed research questions focus on using RA to capture scale-dependent properties in nonlinear time series and tailoring recurrence quantification analysis (RQA) to characterize seasonal variability in palaeoclimate records (‘Palaeoseasonality’).
In the first part of this thesis, we focus on the methodological development of novel approaches in RA. The predictability of nonlinear (palaeo)climate time series is limited by abrupt transitions between regimes that exhibit entirely different dynamical complexity (e.g. crossing of ‘tipping points’). These possibly depend on characteristic time scales. RPs are well-established for detecting transitions and capture scale-dependencies, yet few approaches have combined both aspects. We apply existing concepts from the study of self-similar textures to RPs to detect abrupt transitions, considering the most relevant time scales. This combination of methods further results in the definition of a novel recurrence based nonlinear dependence measure. Quantifying lagged interactions between multiple variables is a common problem, especially in the characterization of high-dimensional complex systems. The proposed ‘recurrence flow’ measure of nonlinear dependence offers an elegant way to characterize such couplings. For spatially extended complex systems, the coupled dynamics of local variables result in the emergence of spatial patterns. These patterns tend to recur in time. Based on this observation, we propose a novel method that entails dynamically distinct regimes of atmospheric circulation based on their recurrent spatial patterns. Bridging the two parts of this dissertation, we next turn to methodological advances of RA for the study of Palaeoseasonality. Observational series of palaeoclimate ‘proxy’ records involve inherent limitations, such as irregular temporal sampling. We reveal biases in the RQA of time series with a non-stationary sampling rate and propose a correction scheme.
In the second part of this thesis, we proceed with applications in Palaeoseasonality. A review of common and promising time series analysis methods shows that numerous valuable tools exist, but their sound application requires adaptions to archive-specific limitations and consolidating transdisciplinary knowledge. Next, we study stalagmite proxy records from the Central Pacific as sensitive recorders of mid-Holocene El Niño-Southern Oscillation (ENSO) dynamics. The records’ remarkably high temporal resolution allows to draw links between ENSO and seasonal dynamics, quantified by RA. The final study presented here examines how seasonal predictability could play a role for the stability of agricultural societies. The Classic Maya underwent a period of sociopolitical disintegration that has been linked to drought events. Based on seasonally resolved stable isotope records from Yok Balum cave in Belize, we propose a measure of seasonal predictability. It unveils the potential role declining seasonal predictability could have played in destabilizing agricultural and sociopolitical systems of Classic Maya populations.
The methodological approaches and applications presented in this work reveal multiple exciting future research avenues, both for RA and the study of Palaeoseasonality.
Gene expression data is analyzed to identify biomarkers, e.g. relevant genes, which serve for diagnostic, predictive, or prognostic use. Traditional approaches for biomarker detection select distinctive features from the data based exclusively on the signals therein, facing multiple shortcomings in regards to overfitting, biomarker robustness, and actual biological relevance. Prior knowledge approaches are expected to address these issues by incorporating prior biological knowledge, e.g. on gene-disease associations, into the actual analysis. However, prior knowledge approaches are currently not widely applied in practice because they are often use-case specific and seldom applicable in a different scope. This leads to a lack of comparability of prior knowledge approaches, which in turn makes it currently impossible to assess their effectiveness in a broader context.
Our work addresses the aforementioned issues with three contributions. Our first contribution provides formal definitions for both prior knowledge and the flexible integration thereof into the feature selection process. Central to these concepts is the automatic retrieval of prior knowledge from online knowledge bases, which allows for streamlining the retrieval process and agreeing on a uniform definition for prior knowledge. We subsequently describe novel and generalized prior knowledge approaches that are flexible regarding the used prior knowledge and applicable to varying use case domains. Our second contribution is the benchmarking platform Comprior. Comprior applies the aforementioned concepts in practice and allows for flexibly setting up comprehensive benchmarking studies for examining the performance of existing and novel prior knowledge approaches. It streamlines the retrieval of prior knowledge and allows for combining it with prior knowledge approaches. Comprior demonstrates the practical applicability of our concepts and further fosters the overall development and comparability of prior knowledge approaches. Our third contribution is a comprehensive case study on the effectiveness of prior knowledge approaches. For that, we used Comprior and tested a broad range of both traditional and prior knowledge approaches in combination with multiple knowledge bases on data sets from multiple disease domains. Ultimately, our case study constitutes a thorough assessment of a) the suitability of selected knowledge bases for integration, b) the impact of prior knowledge being applied at different integration levels, and c) the improvements in terms of classification performance, biological relevance, and overall robustness.
In summary, our contributions demonstrate that generalized concepts for prior knowledge and a streamlined retrieval process improve the applicability of prior knowledge approaches. Results from our case study show that the integration of prior knowledge positively affects biomarker results, particularly regarding their robustness. Our findings provide the first in-depth insights on the effectiveness of prior knowledge approaches and build a valuable foundation for future research.