Maria Eduarda Silva

Abstract
Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit. Ignoring censoring produces biased estimates and unreliable statistical inference. The aim of this work is to contribute to the modelling of time series of counts under censoring using convolution closed infinitely divisible (CCID) models. The emphasis is on estimation and inference problems, using Bayesian approaches with Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms.

Abstract
<p align="justify">Greenland ice core records display abrupt transitions, designated as Dansgaard-Oeschger (DO) events, characterised by episodes of rapid warming (typically decades) followed by a slower cooling. The identification of abrupt transitions is hindered by the typical low resolution and small size of paleoclimate records, and their significant temporal variability. Furthermore, the amplitude and duration of the DO events varies substantially along the last glacial period, which further hinders the objective identification of abrupt transitions from ice core records Automatic, purely data-driven methods, have the potential to foster the identification of abrupt transitions in palaeoclimate time series in an objective way, complementing the traditional identification of transitions by visual inspection of the time series.</p> <p align="justify">In this study we apply an algorithmic time series method, the Matrix Profile approach, to the analysis of the NGRIP Greenland ice core record, focusing on:</p> <p align="justify">- the ability of the method to retrieve in an automatic way abrupt transitions, by comparing the anomalies identified by the matrix profile method with the expert-based identification of DO events;</p> <p align="justify">- the characterisation of DO events, by classifying DO events in terms of shape and identifying events with similar warming/cooling temporal pattern</p> <p align="justify">The results for the NGRIP time series show that the matrix profile approach struggles to retrieve all the abrupt transitions that are identified by experts as DO events, the main limitation arising from the diversity in length of DO events and the method’s dependence on fixed-size sub-sequences within the time series. However, the matrix profile method is able to characterise the similarity of shape patterns between DO events in an objective and consistent way.</p>

Abstract

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Abstract Objective: In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations. Approach: We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress. Main Results: We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors. Significance: The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.

Abstract