#### An introduction to mixture models for environmental applications.

Nell'ambito del corso Spatial Statistics and statistical tools for the environment Il prof. Francesco Lagona dell'Università di ROMA TRE, il giorno 3/12/2018 alle ore 10:30 presso l'aula XII, terrà una lezione dal titolo: An introduction to mixture models for environmental applications   Nell'ambito del corso Spatial Statistics and statistical tools for the environment Il prof. Francesco Lagona dell'Università di ROMA TRE, il giorno 3/12/2018 alle ore 10:30 presso l'aula XII, terrà una lezione dal titolo: An introduction to mixture models for environmental applications. Abstract. The distribution of environmental data is often multimodal because these data are typically observed under heterogeneous latent conditions. Parametric mixture models naturally capture such heterogeneity by assuming that the data are sampled from a mixture of a finite number of parametric distributions, each associated with a specific class of conditions under which the data are observed. This lecture is divided in three sections. I the first section I introduce the class of the Gaussian mixture models and the Expectation-Maximization algorithm that is typically used to find the maximum likelihood estimates of the parameters. The second section extends mixture models to time series data. Traditional mixture models typically assume that the data are independent and are therefore not suitable for the analysis of time series. A class of mixture models that is specifically tailored for the analysis of heterogenous time series (i.e. time series data with a multimodal marginal distribution) is the class of the hidden Markov models (HMMs). HMMs are mixture models whose parameters are driven by a latent (hidden) Markov chain. As such, they require an appropriate extension of the standard EM algorithm. To show the flexibility of HMMs in environmental applications, the third section of the lecture is devoted to a case study of height and direction of sea waves. The analysis of these data is complicated by the unconventional support of the data (a cylinder), the difficulties in modelling the correlations between linear and circular data, the multimodality and the skewness of the marginal distributions of waves directions and heights and, finally, the temporal autocorrelation of the data. I present a HMM that parsimoniously describes the dynamic of sea waves, simultaneously accounting for the specific complexity of the data.
Relatore:
Prof. Francesco Lagona
Data:
03/12/2018 - 10:30
Luogo:
[Aula XII piano terra Palazzina Presidenza (ex Tuminelli) ]