Research Seminar

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Spring Semester 2018

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Speaker

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4 May 2018
16:15-17:00

Guido Consonni
Università Cattolica del Sacro Cuore, Milano

Event Details

Research Seminar in Statistics

Title	Objective Bayes Model Selection of Gaussian Essential Graphs with Observational and Interventional Data
Speaker, Affiliation	Guido Consonni, Università Cattolica del Sacro Cuore, Milano
Date, Time	4 May 2018, 16:15-17:00
Location	HG G 19.1
Abstract	Graphical models based on Directed Acyclic Graphs (DAGs) represent a powerful tool for investigating dependencies among variables. It is well known that one cannot distinguish between DAGs encoding the same set of conditional independencies (Markov equivalent DAGs) using only observational data. However, the space of all DAGs can be partitioned into Markov equivalence classes, each being represented by a unique Essential Graph (EG), also called Completed Partially Directed Graph (CPDAG). In some fields, in particular genomics, one can have both observational and interventional data, the latter being produced after an exogenous perturbation of some variables in the system, or from randomized intervention experiments. Interventions destroy the original causal structure, and modify the Markov property of theunderlying DAG, leading to a finer partition of DAGs into equivalence classes, each one being represented by an Interventional Essential Graph (I-EG) (Hauser and Buehlmann). In this talk we consider Bayesian model selection of EGs under the assumption that the variables are jointly Gaussian. In particular, we adopt an objective Bayes approach, based on the notion of fractional Bayes factor, and obtain a closed form expression for the marginal likelihood of an EG. Next we construct a Markov chain to explore the EG space under a sparsity constraint, and propose an MCMC algorithm to approximate the posterior distribution over the space of EGs. Our methodology, which we name Objective Bayes Essential graph Search (OBES), allows to evaluate the inferential uncertainty associated to any features of interest, for instance the posterior probability of edge inclusion. An extension of OBES to deal simultaneously with observational and interventional data is also presented: this involves suitable modifications of the likelihood and prior, as well as of the MCMC algorithm. We conclude by presenting results for simulated and real experiments (protein-signaling data). This is joint work with Federico Castelletti, Stefano Peluso and Marco Della Vedova (Universita' Cattolica del Sacro Cuore).

Objective Bayes Model Selection of Gaussian Essential Graphs with Observational and Interventional Dataread_more

HG G 19.1

8 May 2018
11:15-12:00

Housen Li
Institut für Mathematische Stochastik, Göttingen

Event Details

Research Seminar in Statistics

Title	The Essential Histogram
Speaker, Affiliation	Housen Li, Institut für Mathematische Stochastik, Göttingen
Date, Time	8 May 2018, 11:15-12:00
Location	HG G 19.2
Abstract	The histogram is widely used as a simple, exploratory display of data, but it is usually not clear how to choose the number and size of bins for this purpose. We construct a confidence set of distribution functions that optimally address the two main tasks of the histogram: estimating probabilities and detecting features such as increases and (anti)modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. We provide a fast algorithm for computing a slightly relaxed version of the essential histogram, which still possesses most of its beneficial theoretical properties, and we illustrate our methodology with examples. This is a joint work with Axel Munk, Hannes Sieling, and Guenter Walther.

The Essential Histogram read_more

HG G 19.2

11 May 2018
15:15-16:00

Marcelo Cunha Medeiros
Pontifical Catholic University of Rio de Janeiro

Event Details

Research Seminar in Statistics

Title	Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage
Speaker, Affiliation	Marcelo Cunha Medeiros, Pontifical Catholic University of Rio de Janeiro
Date, Time	11 May 2018, 15:15-16:00
Location	HG G 19.1
Abstract	We propose a model to forecast very large realized covariance matrices of returns, applying it to the constituents of the S&P 500 on a daily basis. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive (VHAR) models estimated with the least absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of the minimum variance portfolios.

Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkageread_more

HG G 19.1

14 June 2018
16:45-17:30

Event Details

Research Seminar in Statistics

Title	Title T.B.A.
Speaker, Affiliation
Date, Time	14 June 2018, 16:45-17:30
Location	HG G 19.1
Abstract	tba

Title T.B.A.read_more

HG G 19.1

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