| 16-mar-2012 (fri) |
Sander Greenland
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Integrating Bayesian and frequentist statistics, or: Seeing both sides of the same biased coin.
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
Outlines of a bayes-non-Bayes compromise or fusion have been emerging for decades. Nonetheless, basic teaching remains mired in conventional frequentist methods that are misunderstood and misrepresented by most users (including many statisticians) and that are highly misleading outside of ideal experimental conditions. Thus it is essential to revolutionize how we introduce elementary statistical inference in health and social science, by providing Bayesian concepts and methods in tandem with frequentist concepts and methods. Contrary to prevalent beliefs, basic Bayesian methods require no new computational formulas or software beyond familiar frequentist ones; they do not even require Bayes theorem. Those methods can help reveal untenably strong assumptions hidden in conventional methods, and allow relaxation of those assumptions into a more reasonable form.
Background cite: Greenland, S. (2009). Relaxation penalties and priors for plausible modeling of non identified bias sources. Statistical Science, 24, 195-210 |
| Speakers: |
Sander Greenland
(University of California, Los Angeles)
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| 20-mar-2012 (tue) |
Bin Yu
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Spectral clustering and high-dim stochastic block model for undirected and directed graphs
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
In recent years network analysis have become the focus of much research in many fields including biology, communication studies, economics, information science, organizational studies, and social psychology. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities.
The Stochastic Block Model is a social network model with well defined communities. This talk will give conditions for spectral clustering to correctly estimate the community membership of nearly all nodes. These asymptotic results are the first clustering results that allow the number of clusters in the model to grow with the number of nodes, hence the name high-dimensional. Moreover, I will present on-going work on directed spectral clustering for networks whose edges are directed, including the enron data as an example. |
| Speakers: |
Bin Yu
(University of California, Berkeley)
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| 23-mar-2012 (fri) |
Marc Hallin
|
One-Sided Representations of Generalized Dynamic Factor Models
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000). In that paper, however, estimation relies on Brillinger's concept of dynamic principal components, which produces filters that are in general two-sided and therefore yield poor performances at the end of the observation period and hardly can be used for prediction purposes. In this talk, we show how to remedy this problem, and how, based on recent results on singular stationary processes with rational spectra, one-sided estimators can be constructed for the parameters and the common shocks in the GDFM. Consistency is obtained, along with rates. An empirical example, based on US macroeconomic time series, compares estimates based on our model with those based on the usual static-representation restriction, and provides convincing evidence that the assumptions underlying the latter are not supported by the data. |
| Speakers: |
Marc Hallin
(Universität Brüssel)
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| 30-mar-2012 (fri) |
Claudia Czado
Alexander Bauer
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Model selection for pair-copula constructions of regular vine and non-Gaussian DAG models
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
Pair-copula constructions (PCCs) allow to build very flexible multivariate statistical models based on a graphical representation called a regular vine (Kurowicka and Cooke, 2006) as well as models represented by directed acyclic graphs (DAGs). PCCs are very useful for modeling multivariate data in economics and finance, since they can capture non-symmetric and different tail dependences for different pairs of variables separately. Vine models are characterized by a sequence of linked trees called a vine-tree structure, bivariate copula families and families of marginal distributions. Two often studied subclasses are C- and D-vines. The multivariate normal and t distribution families are special cases. Moreover, PCCs can be used to construct non-Gaussian DAG models. First, research was focused on the development of efficient estimation methods. For regular vine models see for example Aas et. al. (2009) for likelihood based and Min and Czado (2010) for Bayesian estimation methods. For non-Gaussian DAGs model formulation and estimation methods are considered in Bauer et. al. (2012). Since the class of regular vine models is very large, model selection is vital. Dissmann et. al. (2011) provide a fast selection method in which trees are sampled sequentially using algorithms for weighted graphs. Bayesian alternatives are available. For non-Gaussian DAGs the model selection involves also a data-based selection of the DAG. We provide an alternative approach to the PC algorithm (Spirtes et. al., 2001) based on regular vines to allow for the detection of non-Gaussian dependency structures and compare its performance to the benchmark PC algorithm based on an independence test for zero partial correlation. We will discuss these PCC models and the associated selection methods as well illustrate them in an application to daily stock returns. |
| Speakers: |
Claudia Czado
(TU München)
Alexander Bauer
(TU München)
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|
| 23-apr-2012 (mon) |
Michael Gutmann
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On the Estimation of Unnormalized Statistical Models
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11:15-12:30 |
HG G 19.2 |
| Abstract: |
The talk is on the basic problem of estimating, from observed data, a probabilistic model which is parameterized by a finite number of parameters.
Focus of the talk is on the particular situation where the model probability density function is unnormalized. That is, the model will not integrate to one for all values of the parameters.
Maximum likelihood estimation can then not be used without resorting to numerical approximations which are often computationally expensive.
In the talk, I will first give some background on unnormalized models. Then, I will introduce you to a novel method to estimate them, explain some of its properties, and show how it is used in the modeling of images.
The talk is based on the following publication:
Michael U. Gutmann and Aapo Hyvärinen,
Noise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics, Journal of Machine Learning Research, 13(Feb):307−361, 2012.
http://jmlr.csail.mit.edu/papers/v13/gutmann12a.html
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| Speakers: |
Michael Gutmann
(Dept of Computer Science and Mathematics & Statistics, University of Helsinki)
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|
| 1-jun-2012 (fri) |
Bodhisattva Sen
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Inference and estimation using nonprametric shape restricted functions
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
The talk will introduce nonparametric function estimation under known shape constraints. In the fi rst part of the talk, I focus on construction of confidence intervals (CIs) for an unknown non-increasing density function on the positive real line based on the Grenander estimator, the nonparametric maximum likelihood estimator. This estimator, a prototypical example of a class of shape constrained estimators in one dimension, converges at rate cube-root n to a non-normal limit distribution. I investigate the consistency and performance of di fferent bootstrap schemes for constructing point-wise CIs in this setup.
In the second part of the talk I consider the nonparametric least squares estimation of a convex regression function when the dimension of the covariate can be greater than one. I characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. I prove that under mild regularity conditions the estimator and its subdiff- erentials are consistent in both fixed and stochastic design regression settings. |
| Speakers: |
Bodhisattva Sen
(Columbia University New York, Cambridge University, UK)
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|
| 5-jun-2012 (tue) |
Caroline Uhler
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Geometry of the Faithfulness assumption in causal inference
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
Algorithms for inferring causality are heavily based on the Faithfulness assumption. The unfaithful distributions have measure zero and can be seen as a collection of hypersurfaces in a hypercube. The Faithfulness condition alone is not sufficient to guarantee uniform consistency and Strong-Faithfulness has been proposed to overcome this problem. In contrast to the original Faithfulness assumption, the set of distributions satisfying Strong-Faithfulness does not have measure one. We study the (Strong) Faithfulness condition from the point of view of real algebraic geometry and give upper and lower bounds on the proportion of unfaithful distributions
for various classes of graphs.
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| Speakers: |
Caroline Uhler
(ETH Zürich, SfS)
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| 22-jun-2012 (fri) |
Richard Nickl
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Donsker's central limit theorem for Estimating Lévy Measures
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15:15-16:30 |
HG G 19.1 |
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| 29-jun-2012 (fri) |
Joseph Salmon
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"Poisson noise reduction with non-local PCA"
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15:15-16:30 |
HG G 19.1 |
| Abstract: |
Photon-limited imaging, which arises in applications such as spectral imaging, night vision, nuclear medicine and astronomy, occurs when the number of photons collected by a sensor is small relative to the desired image resolution. Typically a Poisson distribution is used to model these observations, and the iherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse epresentations for image patches. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise.
A comprehensive empirical evaluation of the performance of the proposed method helps characterize the performance of this approach in very low light regimes relative to other state-of-the-art denoising methods. The results reveal that, despite its implicity, PCA-flavored denoising appears to be highly competitive in the presence of significant Poisson noise. |
| Speakers: |
Joseph Salmon
(Duke University, Durham, NC, USA)
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