Conceição Nunes Rocha

Abstract

Abstract

Abstract
The problem of joint estimation of parameters and state of continuous time systems using discrete time observations is addressed. The plant parameters are assumed to be modeled by a Wiener process. The a priori probability density function (pdf) of an extended state that comprises the plant state variables and the parameters is propagated in time using an approximate solution of the Fokker-Planck equation that relies on Trotter's formula for semigroup decomposition. The a posteriori (i. e., given the observations) pdf is then computed at the observation instants using Bayes law.

Abstract
In this work we study a way to explore and extract more information from data sets with a hierarchical tree structure. We propose that any statistical study on this type of data should be made by group, after clustering. In this sense, the most adequate approach is to use the Mahalanobis-Wasserstein distance as a measure of similarity between the cases, to carry out clustering or unsupervised classification. This methodology allows for the clustering of cases, as well as the identification of their profiles, based on the distribution of all the variables that characterises each subject associated with each case. An application to a set of teenagers' interviews regarding their habits of communication is described. The interviewees answered several questions about the kind of contacts they had on their phone, Facebook, email or messenger as well as the frequency of communication between them. The results indicate that the methodology is adequate to cluster this kind of data sets, since it allows us to identify and characterise different profiles from the data. We compare the results obtained with this methodology with the ones obtained using the entire database, and we conclude that they may lead to different findings.

Abstract