Department of Statistics & Operations Research
Statistics Seminars
2008/2009
To subscribe to the list, please follow this link or send email to 12345saharon@post.tau.ac.il54321 (remove numbers unless you are a spammer…)
Second Semester
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3
March |
Yoav Benjamini, Tel Aviv University |
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Simultaneous and selective inference: current successes and
future challenges |
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10
March |
Purim |
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17
March |
Daniel Yekutieli, Tel Aviv University |
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24
March |
No seminar (MCP09) |
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31
March |
Armin Schwartzman, Harvard University |
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The Effect of Correlation in False Discovery Rate Estimation |
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April |
No seminars scheduled (Pesach,
Yom Hashoah, Yom Hazikaron) |
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5 May |
Amir Globerson, Hebrew University |
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12 May |
Eran Halperin, Tel Aviv University |
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19 May |
Allan Sampson, |
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Modeling Issues For Multiple
Outcomes In Post-Mortem Tissue Studies |
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26 May |
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9 June |
Inbal
Yahav, |
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Combining Residuals and Monitor Charts to Detect Outbreaks in Syndromic Surveillance Data |
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16 June |
Ofer
Harel, |
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Multiple imputation for correcting verification bias in
estimating sensitivity and specificity |
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23 June |
Alex Goldenshluger, Haifa University |
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First Semester
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28
October |
Yulia Gavrilov, Tel Aviv University |
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The Multiple Stage FDR Controlling Procedure and Its Use in
Model Selection |
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4
November |
Isaac Meilijson,
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11
November |
Shahar Mendelson, Australian National University
and Technion |
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18
November |
Yuval Nov, Haifa University |
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Minimum-Norm Estimation for Binormal
Receiver Operating Characteristic (ROC) Curves |
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25 November |
Andrea De Gaetano, Università Cattolica
del Sacro Cuore, Rome |
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Physiological models: design issues and parameter estimation |
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2 December |
No seminar |
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9 December |
Elad
Ziv, |
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Effect of Genetic Architecture on Prediction of Complex Diseases |
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16 December |
Lilach Hadany, Tel Aviv University |
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Second order models of genetic variation: sex, stress, and
adaptation |
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23 December |
Eitan
Greenshtein, Central Bureau of Statistics |
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Application of Non Parametric Empirical Bayes
Estimation to High Dimensional Classification |
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30 December |
Haim Bar, Cornell University |
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Random effects and shrinkage estimation in comparative
microarray experiments |
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6 January |
Elad
Yom Tov, IBM Research |
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13 January |
No seminar |
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20 January |
Meir Smorodinsky,
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Laplace – the father of probability theory and its
applications to statistics and other fields: some historical remarks |
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27 January |
No seminar (originally scheduled Alex Goldenshluger, postponed to next semester) |
Seminars are held on Tuesdays, 10.30 am, Schreiber Building, 309 (see the TAU map ). The seminar organizer is Saharon Rosset.
To join the seminar mailing list or any other inquiries - please call (03)-6408820 or email 12345saharon@post.tau.ac.il54321 (remove numbers unless you are a spammer…)
Seminars from previous years, organized by Daniel Yekutieli:
Organized by Felix Abramovich:
ABSTRACTS
The Multiple Stage
FDR Controlling Procedure and Its Use in Model Selection
Abstract:
Our work is going to deal with the problem of variable selection from a point
of view offered by multiple hypotheses testing. The connection between these
two statistical fields is obvious as dropping the variable from the prediction
equation is equivalent to setting its value to zero. Whether the coefficient
value is indeed not zero is a question that can be answered by testing. In this
work we offer a new adaptive multiple testing procedure with proven FDR control
asymptotically as well as in the finite case. We compare the power of the
proposed procedure to the power of other adaptive procedures with proven FDR
control, and discuss the FDR property of the proposed multiple stage step-down
testing procedure for positively dependent test statistics. We introduce this
testing procedure as a penalized method for model selection and show in the
example its good performance. We also demonstrate how easily it can be
implemented using standard statistical software. We then compare the performances
of competing model selection procedures on different data sets, with the
reference performance being that of a newly defined “random oracle” – the
oracle model selection performance on data dependent nested family of potential
models. By a simulation study we show that the proposed penalized procedure has
empirical minimax performance in this setting. We
finish by the example that shows good performance of the multiple stage
penalized procedure for the logistic model as well.
Joint work with Yoav Benjamini. This talk is part of Ph. D. thesis defense.
The Garman-Klass volatility estimator revisited
Abstract:
The Garman-Klass unbiased estimator of the variance
per unit time of a zero-drift Brownian Motion B, based on the usual financial
data that reports for time windows of equal length the open, minimum, maximum
and close values, is quadratic in the statistic S1=(CLOSE-OPEN, OPEN-MIN,
MAX-OPEN). This estimator, with efficiency 7.4 with respect to the classical estimator
(CLOSE-OPEN)^2, is widely believed to be of minimal
variance. The current report disproves this belief by exhibiting an unbiased
estimator with slightly but strictly higher efficiency 7.7322. The essence of
the improvement lies in the observation that the data should be compressed to
the statistic S2 defined on W(t)= B(0)+[B(t)-B(0)] sign[(B(1)-B(0)] as S1 was
defined on the Brownian path B(t). The best S2-based quadratic unbiased
estimator is presented explicitly. The Cramer-Rao
upper bound for the efficiency of unbiased estimators, corresponding to the
efficiency of large-sample Maximum Likelihood estimators, is 8.471. This bound
cannot be attained because the distribution is not of exponential type.
Aggregation and empirical minimization
Abstract: Given a
finite set of estimators, the problem of aggregation is to construct a new
estimator whose risk is as close as possible to the risk of the best estimator in
the set. It was conjectured that empirical minimization performed in the convex
hull of the given set is an optimal aggregation method. In this talk I will
show that this conjecture is false. I will also show that despite that,
empirical minimization in the convex hull of a well chosen, empirically
determined subset of the original set is an optimal aggregation method.
Minimum-Norm Estimation for Binormal
Receiver Operating Characteristic (ROC) Curves
Abstract: The
Receiver Operating Characteristic (ROC) curve is often used to assess the
usefulness of a diagnostic test. We
present a novel method to estimate the parameters of a popular semi-parametric
ROC model, called the binormal model. Our method is based on minimization of the
functional distance between two estimators of an unknown transformation
postulated by the model, and has a simple, closed-form solution. We study the asymptotics
of our estimators, show via simulation that they compare favorably with
existing estimators, and illustrate how covariates may be incorporated into the
norm minimization framework.
Joint work with Ori Davidov.
Physiological models: design issues and parameter
estimation
Abstract: In this
talk the physiological control system glucose/insulin will be described,
together with its connection with the increasing prevalence of diabetes. The
criteria whereby a mathematical model can be judged to be appropriate will be
discussed. Counter-examples from the literature will be used to show pitfalls
in parameter estimation techniques. Finally, the application of GLS and MCMC to
the estimation of model parameters will be described.
Effect of Genetic Architecture on Prediction of
Complex Diseases
Abstract: Complex diseases are considered diseases that are partially
influenced by some genetic factors, but that have no clear Mendelian
pattern of inheritance. The vast
majority of medical traits are considered complex diseases. One of the goals of modern genetics is to
discover the genetic variants that underlie these traits. It is assumed that discovery of these genetic
variants will lead to genetic tests that can be used to improve disease prediction
in individuals. A common model of
complex diseases, the "common disease common variant" model, suggests
that by identifying common variants that have modest effects on disease,
geneticists will be able to combine these to introduce accurate disease
prediction tools. In contrast, rare
variants that substantially increase risk have traditionally been considered
minimally useful from a public health perspective. We relate the allele frequency, population attributable risk and the C-statistic, a standard tool for
quantifying disease prediction, equivalent to the area under the curve of the
ROC curve. Using these relationships we
demonstrate that rare variants with a strong effect on disease are actually
more useful in a public health setting than common variants with modest
effects. Furthermore, we demonstrate that under many plausible circumstances,
most of the disease prediction potential in the genome is actually in the rare
allele frequency. Finally, we consider
the practical sample size limitations on discovery for both rare and common
variants related to disease and, at what point, disease prediction potential in
the genome has been optimally reached.
Our results have several important consequences for study design and for
clinical practice: (1) Study designs may have currently reached or are close to
reaching the limit of common variants useful for disease prediction. In contrast, the majority rare variants with
disease prediction potential remain undiscovered. (2) Designing clinical prediction
tools to optimally take advantage of the disease prediction potential of the
genome will require sequencing individuals patients at
some genetic loci.
Second order models of genetic variation: sex,
stress, and adaptation
Abstract: Genetic variation provides the raw material for evolutionary change.
In most population genetics models, variation is assumed to be generated at a
uniform rate, depending on the genes coding for variation but not on the state
of the individual. In this talk I discuss the implications of a new assumption
- that the generation of genetic variation is itself plastic, so that genetic
variation is generated at higher rates under stress. We found that
stress-induced genetic variation can evolve under a wide parameter range, and
might help explain the evolution of sex and the mechanisms of complex
adaptation. Theoretical models and experimental evidence will be discussed.
Application of Non Parametric Empirical Bayes Estimation to High Dimensional Classification
Abstract: We consider the problem of classification using high dimensional
features' space. In a paper by Bickel and Levina
(2004), it is recommended to use naive-Bayes
classifiers, i.e., to treat the features as if they are statistically
independent. Consider now a sparse setup, where only a few of the features are
informative for classification. Fan and Fan (2007), suggested a variable
selection and classification method, called FAIR. The FAIR method improves the
design of naive-Bayes classifiers in sparse setups.
The improvement is due to reducing the noise in estimating the features' means.
This reduction is since that only the means of a few selected variables should
be estimated.
We also consider the design of naive Bayes
classifiers. We show that a good alternative to variable selection is
estimation of the means through a certain non parametric empirical Bayes procedure. In sparse setups the empirical Bayes implicitly performs an efficient variable selection.
It also adapts very well to non sparse setups, and has the advantage of making
use of the information from many \weakly informative" variables, which
variable selection type of classification procedures give up on using. We
compare our method with FAIR and other classification methods in simulation for
sparse and non sparse setups, and in real data examples involving
classification of normal versus malignant tissues based on microarray data.
Joint work with Junyong Park
Random effects and shrinkage estimation in
comparative microarray experiments
Abstract: mixture of mixed-effects model for the comparison of (normalized) microarray
data from two treatment groups is proposed. Approximate maximum likelihood
fitting is accomplished via a fast EM-type algorithm. Posterior odds of reatment/gene interactions, derived from the model, involve
shrinkage estimates of both the interactions and of the gene specific error
variances. Genes are classified as being associated with treatment based on the
posterior odds or local FDR with a fixed cutoff. The approach is shown to
perform very well, and is more numerically stable, when compared with some well
known competitors. In principle the model can be generalized to more complex
designs and to multiplatform microarray data..
Towards automatic debugging of concurrent
programs
Abstract: Concurrent
computer programs are fast becoming prevalent in many critical applications.
Unfortunately, these programs are especially difficult to test and debug.
Recently, it has been suggested that injecting random timing noise into
multiple concurrency-related points within a program can assist in eliciting
bugs within the program. Upon eliciting the bug, it is necessary to identify a
minimal set of program locations that indicate the source of the bug to the
programmer.
I will show how this problem can be formulated as a sampling and feature
selection problem, and propose batch and active sampling methods as a solution
to the problem. I will focus on the active sampling algorithm, analyze its
convergence properties, and show how our approach can pinpoint specific lines
in the code which are related to bugs in the program, even in very large
programs.
Simultaneous and selective inference: current
successes and future challenges
Abstract: Building upon a short review of historical trends in MCP research, I
shall explain why the current decade can be viewed as a second golden era for
our field. I argue that much of the success stems from our being able to
address real current needs. At the same time, this success generated a plethora
of concepts for error-rate and power, as well as multiplicity of methods for
addressing them. This may seem all too confusing for the users of our
methodology and pose a threat.
To avoid the threat, it is our responsibility to match our theoretical goals to
the goals of our clients: scientists, educators, public policy setters,
engineers or business people. Only then should we match the methods to the
theoretical goals. I shall discuss some of the considerations that are related
to the needs of clients: addressing simultaneous inference or selective
inference, testing or estimation, decision-making or scientific reporting.
I shall then further argue that the vitality of our field in the future - as a
research area - depends upon our ability to continue and address the real needs
of statistical analyses in specific current problems. I shall demonstrate these
needs in two application areas that offer new challenges and have received less
attention in our community to date.
Adjusted Bayesian inference for selected
parameters
Abstract: We address the problem of providing inference for parameters selected
after viewing the data. A frequentist solution to
this problem is False Discovery Rate adjusted inference. We explain the role of
selection in controlling the occurrence of false discoveries in Bayesian
analysis, and argue that Bayesian inference may also affected by selection – in
particular Bayesian inference based on subjective priors. We introduce
selection-adjusted Bayesian methodology based on the conditional posterior
distribution of the parameters given selection; show how it can be used to
specify selection criteria; explain how it relates to the Bayesian FDR
approach; and apply it to microarray data.
The Effect of Correlation in False Discovery Rate
Estimation
Abstract: Current FDR methods mostly ignore the correlation structure in the
data. The objective of this work is to quantify the effect of correlation in
FDR analysis. Specifically, we derive practical approximations for the
expectation, variance, and quantiles of the FDR
estimator for arbitrarily correlated data. This is achieved using a negative
binomial model for the number of false discoveries, where the parameters are
found empirically from the data. We show that correlation may increase the bias
and variance dramatically with respect to the independent case, and that in
some extreme cases, such as an exchangeable correlation structure, the FDR
estimator fails to be consistent as the number of tests gets large.
This is joint work with Xihong Lin.
Exact probabilistic inference via iterative
refinement
Abstract: Graphical models are a powerful tool for representing distributions
over complex multivariate objects such as images or documents. Although
graphical models have been used with considerable success in many domains, such
as machine vision and signal processing, it is theoretically NP hard to infer
even simple model properties, such as the most likely assignment (MAP). This
difficulty has been addressed in practice by designing approximate inference
algorithms (such as belief propagation) that often work well in practice,
although with relatively weak theoretical guarantees.
A related approach to approximating the MAP problem is via Linear Programming
relaxations. However, these still do not yield an exact solution in the general
case. I will present an approach that uses sequences of LP relaxations that
yield tighter and tighter approximations, in a manner that is tailored to a
specific inference problem. These
approximations can be solved using simple message passing algorithms, which are
derived from the convex dual of the LP relaxation.
I will show how this approach can be applied to difficult inference problems
such as protein design and stereo vision, and in fact often yields provably
exact solutions to these problems.
Based on joint work with:
David Sontag, Talya Meltzer, Tommi Jaakkola and Yair Weiss
Estimating Local Ancestry in Recently Admixed
Populations
Abstract: Large-scale genotyping of genetic variants (Single Nucleotide
Polymorphism - SNPs) has shown a great promise in
identifying markers that could be linked to diseases, based on an evidence for
correlation between the disease and the marker. One of the major obstacles
involved in performing these studies is that the underlying population
sub-structure could produce spurious associations. Population sub-structure can
be caused by the presence of two distinct sub-populations or a single pool of
admixed individuals, such as African Americans or Latinos; such population are formed by the encounter and then mixing of
two or more populations some 10-20 generations ago. In such populations, different
bases in the genome may have originated from different populations.
In this talk, I will describe methods for the inference of the local ancestry
in such individuals. I will describe two methods that we have recently
developed to detect admixture, or the locus-specific ancestry in an admixed
population. We have run extensive experiments to haracterize
the important parameters that have to be optimized when considering this
problem - I will describe the results of these experiments in context with existing
tools such as SABER and STRUCTURE.
In-Season Prediction of Batting Averages: A
Field-test of Basic Empirical Bayes and Bayes Methodologies
Abstract: Batting average is one of the principle performance measures for an
individual baseball player. It has a simple numerical structure as the
percentage of successful attempts, “Hits”, as a proportion of the total number
of qualifying attempts, “At-Bats”. This situation, with Hits as a number of
successes within a qualifying number of attempts, makes it natural to
statistically model each player’s batting average as a binomial variable
outcome. This is a common data structure in many statistical applications; and
so the methodological study here has implications for such a range of
applications. [No prior knowledge about baseball is required for this talk, and
if you have none then don’t expect to have much more when you
leave.]
We will look at batting records for
every Major League player over the course of a single season (2005). The
primary focus is on using only the batting record from an earlier part of the
season (e.g., the first 3 months) in order to predict the batter’s latent
ability, and consequently to predict his batting-average performance for the remainder
of the season. Since we are using a season that has already concluded, we can validate our predictive performance by comparing
the predicted values to the actual values for the remainder of the season.
The methodological purpose of this
study is to gain experience with a variety of predictive methods applicable to
a much wider range of situations. Several of the methods to be investigated
derive from empirical Bayes and hierarchical Bayes interpretations. Although the general ideas behind
these techniques have been understood for many decades*, some of these methods
have only been refined relatively recently in a manner that promises to more
accurately fit data such as that at hand.
One feature of all of the statistical
methodologies here is the preliminary use of a particular form of variance
stabilizing transformation in order to transform the binomial data problem into
a somewhat more familiar structure involving (approximately) Normal
random variables with known variances. This transformation technique is also
useful in validating the binomial model assumption that is the conceptual basis
for all our analyses. If time permits we will also describe how it can be used
to test for the presence of “streaky hitters” whose latent ability appears to
significantly change over time.
* A particularly relevant background
reference is Efron, B. and Morris, C. (1977) Stein’s paradox in statistics” Scientific American 236 119-127, and the earlier, more technical version (1975),
“Data analysis using Stein’s estimator and its generalizations” Jour. Amer. Stat. Assoc. 70 311-319.
Combining Residuals and Monitor Charts to Detect
Outbreaks in Syndromic Surveillance Data
Abstract: The main goal of biosurveillance is the
early detection of disease outbreaks. Advances in technology have allowed the
collection, transfer, and storage of pre-diagnostic information in addition to
traditional diagnostic data. Such data carry the potential of an earlier
outbreak signature.
Analyzing data in the goal of detecting outbreaks composed of two main stages:
pre- processing the data to remove explainable patterns and monitoring the
`clean' data, using monitor charts, to determine outbreaks. The literature
suggests a variety of preprocessing functions and monitor charts to control syndromic surveillance data. However, it is well known that
each of these function is tuned for specific
outbreaks. For example, Shewhart is optimal for
detecting spikes in data; EWMA is a better detector for exponential outbreak.
When considering syndromic surveillance data streams,
the shape of an outbreak in still unknown. This leaves the question of which
function is optimal for such data and whether there is one function that
outperforms all the others. Motivated by such questions, we propose methods to
use a combination of functions to analyze and monitor a syndromic
surveillance data streams. We consider methods combination in different stages
of the monitoring process, i.e. combining residuals Vs.
combining monitor charts. For the combination of monitor charts we present a
static method where the weight of each chart is predefined. For residuals
combination we propose an adaptive method based on recent history.
Joint work with Galit
Shmueli.
Multiple imputation for
correcting verification bias in estimating sensitivity and specificity
Abstract: Sensitivity and specificity are widely used to describe a diagnostic
test. When all subjects have test results and true status, the estimation of
the sensitivity and specificity is built on two binomial distributions. This
estimation is not a trivial task. In the case in which all subjects are
screened using a common test, and a subset of these subjects are tested using a
golden standard test, there is a risk for bias, called verification bias. When
not all subjects have been verified, special methods of estimation need to be
used. There are several methods to estimate the sensitivity, specificity and
their standard errors in this kind of situation. The standard methods were
developed under some special cases of the verification choices. Approaching
this problem from a missing data prospective, allows us to use Multiple
Imputation (MI) technique in order to impute the data. We adopt MI framework,
and develop different MI procedures using the most common ”complete-data”
methods. We compare the procedures between themselves and to the standard
(incomplete) methods. We illustrate our procedure using a biomedical data
example.
This is joint work with Andrew Zhou.
- Alex Goldenshluger, Haifa University