9h30-10h20 - Cristiano Bocci (Siena) - Algebraic geometry for algebraic statistics<br>

<br>This is an introductory talk about the basic relationships 
among  algebra, geometry and statistics.<br>
After a preparatory part, where the main concepts of Algebraic Geometry 
and Statistics are stated and explained, we turn to define the 
connection between them: the so-called "invariant" of a statical model (leading successively to the concept of "invariants ideal", as its natural generalization). Many examples will be shown to make everything 
clearer.<br>

<br>10h40-11h30 - Jan Draisma (Bern) - Graphical models, mixtures, and their equations<br>

<br> In graphical models, random variables are represented by vertices of a 
graph and (non)edges encode (in)dependencies in a manner that I'll make 
precise in the talk. I will then concentrate on discrete graphical 
models and their mixtures, and discuss some recent results that imply 
that, as the model grows in a certain specified manner, its equations 
stabilise. <br>


<br>11h50-12h40 - Marta Casanellas (UPC Barcelona) - Algebraic statistics in phylogenetics<br>

<br>Many of the usual statistical evolutionary models used in phylogenetics can be viewed as algebraic varieties. In this talk we will show the relationship between evolutionary models and algebraic geometry. Moreover, we will see how an in-depth geometric study leads to improvements on phylogenetic reconstruction methods. We illustrate these improvements by showing results on simulated and real data and by comparing them to widely used methods in phylogenetics. <br>


<br>14h30-15h20 - Piotr Zwiernik - Maximum likelihood estimation of the Latent Class Model through model boundary decomposition <br>

<br>This talk is about the latent class model in statistics, which corresponds to the secant variety of the Segre variety.<br>

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. <br>

<br> 15h40-16h30 - Fabio Rapallo  - Algebraic Statistics for contingency tables <br>
<br> In this talk, I will present a review of "classical" Algebraic Statistics for the analyis of contingency tables together with some pointers to current research. The following topics will be covered: (a) The Diaconis-Sturmfels algorithm for exact goodness-of-fit tests; (b) The notion of Markov basis and the computation of Markov bases for several log-linear models, in both the two-way and the multi-way setting; (c) Analysis of tables with structural zeros; (d) Applications: goodness-of-fit tests for rater agreement models, analysis of social mobility tables, detection of outliers. <br>


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