Department of Statistics & Operations Research
Statistics Seminars
2006/2007
Note: the program is not final and is subject to possible changes
Summer term
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19,
July* |
Katherine S. Pollard, UC |
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Second term
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6, March |
Tom Trigano, |
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Statistical signal processing and
spectrometry: some processing methods for higher counting rates |
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27, March |
Dean Foster, |
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1, May |
Nitzan Rosenfeld, Rosetta Genomics |
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8, May |
Svetlana Bunimovich, Tel Aviv University |
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Immunotherapy
treatment of Bladder Cancer: A mathematical model |
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29, May |
Mariana Pensky, |
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Bayesian Approach to Estimation and Testing in
Time Course Microarray Experiments |
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19, June |
Ruth Heller, |
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First Term
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31,
October |
Meir Smorodinsky, |
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7,
November |
Felix Abramovich, |
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28,
November |
Isaac Meilijson and Alon Kaufman, Tel Aviv University |
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Does the neuron's gene expression carry information on its
synaptic connectivity? |
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26,
December |
Adi Ben-Israel |
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2, January* |
David M. Steinberg, Tel Aviv University |
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9,
January |
Sigal Levy, |
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16,
January |
Tal Pupko, Tel Aviv University |
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* Notice: special time / date / venue
Seminars are held on
Tuesdays, 10.30 am, Schreiber
Building, 309 (see the
TAU map ). 
is served before.
The seminar organizer is Daniel Yekutieli.
To join the seminar mailing list or any other inquiries - please call (03)-6409612 or email yekutiel@post.tau.ac.il
Details of previous seminars:
ABSTRACTS
מידול הסתברותי של הסיכונים בפרוצדורות רפואיות
מקובל
להעריך פרוצדורות רפואיות באמצעות שקלול, על פני אוכלוסיית החולים, של מחירן
והסיכון הכרוך בביצוען לעומת התועלת שיכולה לצמוח מהם. את החולה, לעומת זאת,
מעניינים סיכויי ההחלמה שלו עצמו. לצורך כך, אציג מודלים הסתברותיים לרעש רציף
בזמן עבור אומדני הסיכון האינדיבידואליים של הפעולות האפשריות בהינתן התיק הרפואי
של החולה.
·
Felix
Abramovich, Tel Aviv University
Prelude
and Fugue in Bayesian Testimation
In the Prelude (a joint composition with Claudia Angelini, CNR Napoli) we
present a Bayesian multiple testing procedure. A hierarchical prior model
is based on imposing a prior distribution on the number of hypotheses arising
from alternatives (false nulls). We then apply the maximum a posteriori (MAP)
rule to find the most likely configuration of nulls and alternatives. We
discuss the relations between the proposed MAP procedure and its several existing
frequentist counterparts.
In the Fugue (a joint composition with Vadim Grinshtein, the Open University
and Marianna Pensky, University
of Central Florida
testimator leads to a general thresholding rule which accomodates many of the
known thresholding and model selection procedures as its particular
cases. We discuss the optimality of the MAP testimator and specify the class of
priors for which it is adaptively minimax for a wide range of sparse
sequences.
·
Isaac Meilijson and Alon Kaufman, Tel Aviv University
Does
the neuron's gene expression carry information on its synaptic connectivity?
The speakers will discuss a large-scale investigation on
the nematode Caenorhabditis Elegans – joint work with Gideon Dror and Eytan
Ruppin.
·
Adi Ben-Israel, Rutgers University
Probabilistic Distance
Clustering
Clustering
is a process of partitioning a data set into clusters, i.e. subsets of data
points that are similar in some sense. Probabilistic clustering is when cluster
membership is expressed by probabilities p(x|C) that a point x belongs to a
cluster C. Distance clustering is when similar means close w.r.t. a given
distance function (Euclidean, Mahalanobis, etc.)
I present new approach and method for probabilistic clustering of data. Given
clusters, their sizes (except if these are unknown and have to be estimated),
centers, and the distances of data points from these centers, the probability
of cluster membership at any point is assumed to be inversely proportional to
its distance from the center of that cluster, and directly proportional to the
cluster size. The method is based on the above assumption, and on the joint
distance function, a weighted harmonic mean of distance from all cluster
centers, that evolves during the iterations, and captures the data in its low
contours. The method is simple, and works well and fast.
In addition to clustering, I present application to location of several
capacitated facilities, and to demixing of mixtures of distributions, where the
proposed method is a viable alternative to the EM method for estimating the
relevant parameters.
Joint work with Cem Iyigun, Rutgers
University
· David M. Steinberg, Tel Aviv University
Orthogonal
Latin Hypercube Designs
Latin
Hypercube (LHC) designs are one of the most popular choices for experiments run
on computer simulators. As first
proposed by McKay, Beckman and Conover in 1979, LHC designs guarantee that
input factor settings are uniformly spread for each single factor, but rely on
“random mating” to achieve good spread in high dimensions. In experiments with many factors, some pairs
of factors typically have moderately high correlations and a number of schemes
have been proposed to reduce the correlations.
In this talk we show how to generate completely orthogonal LHC designs
by rotating two-level factorial designs into LHC designs. For example, with 256 runs, our method
produces a LHC design with 248 orthogonal factors. The best known result previous to our work
achieved only 14 orthogonal factors. As
a side problem, we show how to arrange the columns of a saturated two-level
fractional factorial with 2m runs so that every consecutive set of m columns is
a full two-level factorial. We will also
present some results on orthogonal designs that are “nearly” LHC designs.
This is
joint work with Dennis Lin.
·
Sigal Levy, Tel Aviv University
The analysis of time dependent computer experiments
Computer
experiments are a convenient substitute to real life experiments, when such an
experiment is too complex, expensive or time consuming. This work is concerned with experiments in
which the output from each computer run is a dense time trace that is a
function of some low dimensional set of explanatory variables. We suggest
two-stage methods for modelling and predicting such data, separating the model
for time from the model for the explanatory variables. The time dependence is
modelled by fitting known basis functions such as splines, as well as data
derived, shape-based basis functions. Such basis functions are generated by
clustering the data into similarly shaped functions and taking the mean
function of each cluster as a basis function. Several methods were tested for
modelling the relation to the explanatory variables. Bayesian and other models
that used additional information about the data set were considered as a means
of improving the fit obtained by the two-stage methods.
Two data sets were analysed using these methods: a
simulation of response to chemotherapy, which yields the amount of cancer cells
in a patient’s body in response to different chemotherapy treatment protocols,
and a circadian rhythm simulation, showing the mRNA production and degradation
throughout a sleep-wake cycle. Results show that the shape-based estimation
methods proved to be efficient in both cases, and that usually Kriging
predicted relation to the explanatory variables with the most accuracy.
·
Tal Pupko, Tel Aviv University
Probabilistic
evolutionary models and their applications.
In my talk
I will first give all needed biological background and will provide the
motivation for using evolutionary models. For example I will
discuss the evolutionary relationships between humans and Neanderthals. I will
then explain what are probabilistic evolution models and why they
are needed in the context of phylogenetic tree reconstruction. I will then give
the statistical/mathematical background of these continuous
time Markov models. I will discuss the maximum likelihood approach for learning
with these models. I will also explain the computational
challenges and will give a few applications.
·
Tom
Trigano,
Statistical signal processing
and spectrometry: some processing
methods for higher counting rates...
The main objective of spectrometry is to characterize the radioactive
elements of an unknown source by studying the energy of the emitted photons. When a photon interacts with a
detector, its photonic energy is converted into an electrical pulse, whose
integral energy is measured.
Since the detector has a finite
resolution, close arrival times of photons which can be modeled as an
homogeneous Poisson process cause pile-ups of individual pulses. This
phenomenon distorts energy spectra by introducing amongst other perturbations
multiple fake spikes.
Since the shape of photonic
impulses depends on many physical parameters, we consider this problem in a
nonparametric framework. By introducing an adapted model based on two marked
point processes, we establish a nonlinear relation between the probability
measure associated to the observations and the probability density function we
wish to estimate. It provides a framework to this problem, which can be
consider as a problem of nonlinear density deconvolution and nonparametric
density estimation from indirect measurements.
Using these considerations, we
propose an estimator obtained by direct inversion. We show that this estimator
is consistent and almost achieves the usual rate of convergence obtained in
classical nonparametric density estimation in the L2 sense. We show in both
simulated and real examples that the distortions caused by the pile-up
phenomenon are well corrected by the algorithms derived from our estimators.
·
Dean Foster,
On the Intrinsic Dimensionality
of Multi-View Regression
In the multi-view regression problem, we have
a regression problem where the input variable can be partitioned into two
different views, where it is assumed that either view of the example would be
sufficient for learning --- this is essentially the co-training assumption for
the regression problem. For example, the task might be to identify a person,
and the two views might be a video stream of the person and an audio stream of
the person.
We show how Canonical Correlation Analysis,CCA, (related to PCA for two random
variables) implies a ridge regression algorithm, where we can characterize the
intrinsic dimensionality of this regression problem by the correlation of the
two views. An interesting aspect of our analysis is that the norm used by the
ridge regression algorithm is derived from the CCA --- no norm or Hilbert space
is assumed apriori (unlike in kernel methods).
(with Sham Kakade)
·
Nitzan Rosenfeld, Rosetta Genomics
MicroRNA discovery and application for diagnostics
I will describe the computational methodology we used for
identification of microRNAs in the human genome. I will introduce some of the
challenges and pitfalls of cancer diagnostics, and open the topic for
discussion. I will conclude by presenting our algorithmic approach to tissue
classification.
·
Svetlana
Bunimovich, Tel Aviv University
Immunotherapy
treatment of Bladder Cancer: A mathematical model
I present a modeling study of bladder cancer growth and its treatment via immunotherapy with Bacillus Calmette-Gue´rin (BCG) - an attenuated strain of Mycobacterium bovis (M. bovis). BCG immunotherapy is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite extensive biological research. The mathematical model presented here attempts to gain insights into the different dynamical outcomes arising from tumor-immune interactions in the bladder. I studied two types of the treatment: continuous and pulsed BCG therapy. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. A mathematical analysis of the differential equations identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has the potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. In the case of continuous therapy, the model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient. The model predicts i) regimes in which immunotherapy cannot help; ii) the optimal BCG dosage. Intense therapy can incur damage and side effects via the immune system; iii) quantitative relationships between BCG dosage, the cancer’s initial condition and tumour growth rate that can be calculated prior to treatment.
Impulsive differential equations are used for studying periodic BCG instillations (pulsed BCG therapy). The mathematical analysis defines the critical threshold values of the BCG instillation dose and rate of pulsing for tumor elimination. The final goal in this work is to determine the applicable treatment regime that prevents the immune system side effects (caused by BCG) and enhances tumor destruction.