15:30 - 16:00 |
Eleonora Arnone: A time-dependent PDE regularization to model functional data defined over spatio-temporal domains ↓ We propose a new method for the analysis of functional data defined over spatio-temporal domains. These data can be interpreted as time evolving surfaces or spatially dependent curves. The proposed method is based on regression with differential regularization. We are in particular interested to the case when prior knowledge on the phenomenon under study is available. The prior knowledge is described in terms of a time-dependent Partial Differential Equation (PDE) that jointly models the spatial and temporal variation of the phenomenon. We consider various samplings designs, including geo-statistical and areal data. We show that the corresponding estimation problem are well posed and can be discretized in space by means of the Finite Element method, and in time by means of the Finite Difference method. The model can handle data distributed over spatial domains having complex shapes, such as domains with strong concavities and holes. Moreover, various types of boundary conditions can be considered.
The proposed method is compared to existing techniques for the analysis of spatio-temporal models, including space-time kriging and methods based on thin plate splines and soap film smoothing.
As a motivating example, we study the blood flow velocity field in the common carotid artery, using data from Echo-Color Doppler. (Conference Room San Felipe) |
16:30 - 17:00 |
Simone Vantini: Non-parametric multi-aspect local null hypothesis testing for functional data ↓ In the talk, we will present and discuss a general framework for multi-aspect local non-parametric null-hypothesis testing for functional data defined on a common domain (Pini and Vantini, 2017). In detail: “multi-aspect” pertains to the fact the procedure allows the simultaneous investigation of many different data aspects like means, variances, quantiles of functional data and their associated differential and/or integral quantities; “local” pertains instead to the fact the procedure can impute the rejection to aspect-specific regions of the domain; finally, “non-parametric” refers to the fact that the specific implementation of the procedure is permutation-based and thus finite-sample exact and consistent independently on data Gaussianity. For ease of clarity, the focus will be on functional two-population tests and functional one-way ANOVA with an application on the statistical comparison of ultrasound tongue profiles pertaining to different allophones pronounced by the same speaker which can be modelled as functions varying on a spatio-temporal domain (Pini et al. 2017a). Finally, we will quickly show how to extend the approach to deal with more complex testing problems like functional two-way ANOVA and functional-on-scalar linear regression with applications to the analysis of spectral data (Pini et al. 2017b) and human movement data (Pini et al. 2015), respectively.
Hébert-Losier, K., Pini, A., Vantini, S., Strandberg, J., Abramowicz, K., Schelin, L., Häger, C. K. (2015): "One-leg hop kinematics 20 years following anterior cruciate ligament rupture: Data revisited using functional data analysis", Clinical Biomechanics, Vol. 30(10), pp. 1153-1161.
Pini, A., Vantini, S. (2017): “Interval-Wise Testing for Functional Data”, Journal of Nonparametric Statistics. 29 (2), pp. 407-424.
Pini, A., Spreafico, L., Vantini, S., Vietti, A. (2017): Multi-aspect local inference for functional data: analysis of ultrasound tongue profiles. Tech. Rep. MOX 28/2017, Dept. of Mathematics, Politecnico di Milano (https://mox.polimi.it).
Pini, A., Vantini, S., Colosimo, B. M., Grasso, M. (2017): “Domain-Selective Functional Analysis of Variance for Supervised Statistical Profile Monitoring of Signal Data”, Journal of the Royal Statistical Society – Series C (to appear). (Conference Room San Felipe) |