A prior distribution for the underlying graph is introduced in the framework of Gaussian graphical models. Such a prior distribution induces a block structure in the graph's adjacency matrix, ...allowing learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for learning block structured graphs under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single edge of the graph but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional dependence structure. Since the elements of a B-Spline basis have compact support, the conditional dependence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among portions of the domain and improve the interpretability of the results.
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In today's world, bike sharing systems are becoming increasingly common in all main cities around the world. To understand the spatiotemporal patterns of how people move by bike through the city of ...Milan, we apply functional data analysis to study the flows of a bike sharing mobility network. We introduce a complete pipeline to properly analyse and model functional data through a concurrent functional‐on‐functional model taking into account the effects of weather conditions and calendar on the bike flows. In the end, we develop an interactive interface to explore the results of the analyses.
The problem of performing inference on the parameters of a functional mixed effect model for multivariate functional data is addressed, motivated by the analysis of 3D acceleration curves of trotting ...horses. Inference is performed in a local perspective, i.e., defining an adjusted p-value function on the same domain as the data. Such adjusted p-value functions can be thresholded at level α to select the regions of the domain and the coordinates of functional data presenting statistically significant effects. The probability of wrongly selecting as significant a region of the domain, and/or a coordinate of functional data where the null hypothesis is true, is always lower than the pre-specified level α due to the interval-wise control of the family-wise error rate. The procedure is based on nonparametric permutation tests, based on different permutation strategies. It is shown by simulations that all strategies proposed gain in power by taking random effects into account in permutations. Finally, the procedure is applied to the acceleration curves of trotting horses for testing differences between different levels of induced lameness. The method can clearly identify group differences.
The curse of outlier measurements in estimation problems is a well-known issue in a variety of fields. Therefore, outlier removal procedures, which enables the identification of spurious measurements ...within a set, have been developed for many different scenarios and applications. In this paper, we propose a statistically motivated outlier removal algorithm for time differences of arrival (TDOAs), or equivalently range differences (RD), acquired at sensor arrays. The method exploits the TDOA-space formalism and works by only knowing relative sensor positions. As the proposed method is completely independent from the application for which measurements are used, it can be reliably used to identify outliers within a set of TDOA/RD measurements in different fields (e.g., acoustic source localization, sensor synchronization, radar, remote sensing, etc.). The proposed outlier removal algorithm is validated by means of synthetic simulations and real experiments.
Motivated by the analysis of spectrometric data, a Gaussian graphical model for learning the dependence structure among frequency bands of the infrared absorbance spectrum is introduced. The spectra ...are modeled as continuous functional data through a B-spline basis expansion and a Gaussian graphical model is assumed as a prior specification for the smoothing coefficients to induce sparsity in their precision matrix. Bayesian inference is carried out to simultaneously smooth the curves and to estimate the conditional independence structure between portions of the functional domain. The proposed model is applied to the analysis of infrared absorbance spectra of strawberry purees.
We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we ...propose a (re)definition of Hotelling's T-2 that naturally expands to any separable Hilbert space that we further embed within a permutation inferential approach. In detail, we present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling's T-2 statistic, using a permutation-based testing procedure of which we prove finite-sample exactness and consistency; we showcase the explicit form of Hotelling's T-2 statistic in the case of some famous spaces used in functional data analysis (i.e., Sobolev and Bayes spaces); we demonstrate, by means of simulations, that Hotelling's T-2 exhibits the best performances in terms of statistical power for detecting mean differences between Gaussian populations, compared to other state-of-the-art statistics, in most simulated scenarios; we propose a case study that demonstrate the importance of the space into which one decides to embed the data; we provide an implementation of the proposed tools in the R package fdahotelling available at https://github.com/astamm/fdahotelling.
Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate ...data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples, and compare their performance with other existing methods.
Hypothermic oxygenated machine perfusion (HOPE) has the potential to counterbalance the detrimental consequences of cold and warm ischemia time (WIT) in both donation after brain death (DBD) and ...donation after circulatory death (DCD). Herein we investigated the protective effects of HOPE in extended criteria donor (ECD) DBD and overextended WIT DCD grafts. The present retrospective case series included 50 livers subjected to end‐ischemic HOPE or dual DHOPE in 2 liver transplantation (LT) centers from January 2018 to December 2019. All DCD donors were subjected to normothermic regional perfusion before organ procurement. Results are expressed as median (interquartile range IQR). In the study period, 21 grafts were derived from overextended WIT DCD donors (total WIT 54 IQR, 40‐60 minutes and 75% classified as futile), whereas 29 were from ECD DBD. A total of 3 biliary complications and 1 case of ischemia‐type biliary lesion were diagnosed. The rate of early allograft dysfunction (EAD) was 20%, and those patients had higher Comprehensive Complication Index scores. Through a changing point analysis, cold preservation time >9 hours was associated with prolonged hospital stays (P = 0.02), higher rates of EAD (P = 0.009), and worst post‐LT complications (P = 0.02). Logistic regression analyses indicated a significant relationship between cold preservation time and EAD. No differences were shown in terms of the early post‐LT results between LTs performed with DCD and DBD. Overall, our data are fully comparable with benchmark criteria in LT. In conclusion, the application of DHOPE obtained satisfactory and promising results using ECD‐DBD and overextended DCD grafts. Our findings indicate the need to reduce cold preservation time also in the setting of DHOPE, particularly for grafts showing poor quality.
In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In detail, the present framework proceeds in four ...steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the R package nevada (NEtwork-VAlued Data Analysis).
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