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<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>The BIO-SI project, based in Limerick and <st1:place w:st="on">Galway</st1:place>,
invites you to the following seminars to take place as follows<font color=navy><span
style='color:navy'> (please note the change from the usual venue)</span></font>:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Friday, May 7<sup>th</sup>, 2-pm<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>ROOM CG054, <st1:place w:st="on"><st1:PlaceName w:st="on">MAIN</st1:PlaceName>
<st1:PlaceType w:st="on">BUILDING</st1:PlaceType></st1:place><o:p></o:p></span></font></p>
<p class=MsoNormal><st1:place w:st="on"><st1:PlaceType w:st="on"><font size=3
face=Arial><span style='font-size:12.0pt;font-family:Arial'>UNIVERSITY</span></font></st1:PlaceType><font
face=Arial><span style='font-family:Arial'> OF <st1:PlaceName w:st="on">LIMERICK</st1:PlaceName></span></font></st1:place><font
face=Arial><span style='font-family:Arial'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>2pm Chris Cannings (<st1:place w:st="on"><st1:PlaceType
w:st="on">University</st1:PlaceType> of <st1:PlaceName w:st="on">Sheffield</st1:PlaceName></st1:place>)
The Coalescent<o:p></o:p></span></font></b></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>3pm Florian Frommlet (<st1:place w:st="on"><st1:PlaceType
w:st="on">University</st1:PlaceType> of <st1:PlaceName w:st="on">Vienna</st1:PlaceName></st1:place>)
Asymptotic optimality properties of multiple testing and model selection
procedures under sparsity<o:p></o:p></span></font></b></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'><o:p> </o:p></span></font></b></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>The abstracts are given below<o:p></o:p></span></font></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'><o:p> </o:p></span></font></b></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>The Coalescent<o:p></o:p></span></font></b></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Chris Cannings,<o:p></o:p></span></font></b></p>
<p class=MsoNormal><st1:place w:st="on"><st1:PlaceType w:st="on"><b><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial;font-weight:
bold'>School</span></font></b></st1:PlaceType><b><font face=Arial><span
style='font-family:Arial;font-weight:bold'> of <st1:PlaceName w:st="on">Mathematics</st1:PlaceName></span></font></b></st1:place><b><font
face=Arial><span style='font-family:Arial;font-weight:bold'> and Statistics, <o:p></o:p></span></font></b></p>
<p class=MsoNormal><st1:place w:st="on"><st1:PlaceType w:st="on"><b><font
size=3 face=Arial><span style='font-size:12.0pt;font-family:Arial;font-weight:
bold'>University</span></font></b></st1:PlaceType><b><font face=Arial><span
style='font-family:Arial;font-weight:bold'> of <st1:PlaceName w:st="on">Sheffield</st1:PlaceName></span></font></b></st1:place><b><font
face=Arial><span style='font-family:Arial;font-weight:bold'><o:p></o:p></span></font></b></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>The Wright-Fisher model of "genetic drift"
considers a population of<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> fixed size <i><span style='font-style:italic'>N</span></i>,
with non-overlapping generations. Each individual in the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> population at time <i><span style='font-style:italic'>t+1</span></i>
is the offspring of any particular individual in the population<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> at time<i><span style='font-style:italic'> t</span></i>
with probability <i><span style='font-style:italic'>1/N</span></i>, (mutually)
independently of the parentage of other<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> individuals. It is possible in this and in a
wider class of<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> models (Cannings,1974) to specify the
eigenvalues and<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> eigenvectors in a fairly full fashion and thus
to study various<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> aspects of the process.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Kingman(1982) introduced a major insight<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> for the study of such processes, the
Coalescent. Instead of<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> looking at whole generations with time running
forward the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> coalescent runs time backward. Since the number
of individuals in<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> generation <i><span style='font-style:italic'>t</span></i>
who are actually, rather than potentially, parents of some set of <i><span
style='font-style:italic'>k</span></i><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> individuals in generation <i><span
style='font-style:italic'>t+1</span></i>, is <i><span style='font-style:italic'>˜
k</span></i> (with non-zero probability for<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> <i><span style='font-style:italic'><k</span></i>),
the ancestry of any set of individuals is a tree running<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> backwards in time to a MRCA (most recent common
ancestor of the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> set). This is the coalescent, and the study of
the genetic drift process<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> reduces to the study of this tree.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>A brief survey of some of the features of this process will
include<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>the probabilities of various tree topologies, and the time
to the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>MRCA. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>The coalescent approach will then be used to tackle two
problems.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>(1) Suppose that individuals have a type specified by an
integer,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>and that a parent of type <i><span style='font-style:italic'>x</span></i>
produces an offspring of type <i><span style='font-style:italic'>x-1,<o:p></o:p></span></i></span></font></p>
<p class=MsoNormal><i><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial;font-style:italic'>x</span></font></i><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'> or <i><span
style='font-style:italic'>x+1</span></i> with probabilities <i><span
style='font-style:italic'>u/2, 1-u</span></i> and <i><span style='font-style:
italic'>u/2</span></i>. We<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>wish to specify aspects of the distribution of the types in
the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>population at some time <i><span style='font-style:italic'>n</span></i>.
This model correspond to genetic<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>situations in which an individual has some number of copies
of a<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>genetic unit, and that due to errors in the copying process
required<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>for producing an offspring, that offspring may have a
slightly<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>different number of copies. We derive certain results for
the moments of<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> this and a related normalised process.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>(2) The branch from an individual backwards in time to the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>coalescent tree is called an external edge. Some results
regarding<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>the lengths of such edges will be derived.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'> Malgorzata Bogdan, Arijit
Chakrabarti, Florian Frommlet, Jayanta K. Ghosh<o:p></o:p></span></font></b></p>
<p class=MsoNormal><b><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial;font-weight:bold'>Asymptotic optimality properties of
multiple testing and model selection procedures under sparsity<o:p></o:p></span></font></b></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Asymptotic optimality of a large class of multiple testing
rules is investigated using<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>the framework of Bayesian Decision Theory. A normal scale
mixture model is considered, leading to an asymptotic <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>framework which can be naturally motivated under the
assumption of sparsity, <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>where the proportion of ``true'' alternatives
converges to zero. Within this setup optimality of a rule is proved by <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>showing that the ratio of its Bayes risk and that of the<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> Bayes oracle (a rule which minimizes the Bayes risk)
converges to one. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>The class of fixed threshold multiple testing rules which
are asymptotically optimal is fully characterized as well <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>as the class of optimal rules controlling the Bayesian False
Discovery Rate (BFDR). <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Furthermore, conditions are provided under which the popular
Benjamini-Hochberg procedure is asymptotically optimal. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>It is shown that for a wide class of sparsity levels, the
threshold of the former can<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>be approximated very well by a non-random threshold. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Apart from multiple testing the problem of model selection
for multiple regression under sparsity is considered. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Under the assumption of orthogonality and for known
variances results from multiple testing immediately translate into the
regression setting, <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>where the scale mixture model is extended to a more general
class of priors.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'> We illustrate asymptotic optimality properties of
modified versions of the Bayesian Information Criterion (mBIC), <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>where we specifically discuss modifications allowing to
control FDR. Finally optimality of mBIC in the case of unknown variances is
proven.<o:p></o:p></span></font></p>
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