[Events] biostatistics seminars at the University of Limerick

[David.Ramsey]

The BIO-SI project, based in Limerick and Galway, invites you to the following seminars to take place as follows (please note the change from the usual venue):

 

Friday, May 7th, 2-pm

ROOM CG054, MAIN BUILDING

UNIVERSITY OF LIMERICK

 

2pm Chris Cannings (University of Sheffield) The Coalescent

3pm Florian Frommlet (University of Vienna) Asymptotic optimality properties of multiple testing and model selection procedures under sparsity

 

The abstracts are given below

 

The Coalescent

Chris Cannings,

School of Mathematics and Statistics, 

University of Sheffield

 

The Wright-Fisher model of "genetic drift" considers a population of

 fixed size N, with non-overlapping generations. Each individual in the

  population at time t+1 is the offspring of any particular individual in the population

   at time t with probability 1/N, (mutually) independently of the parentage of other

   individuals. It is possible in this and in a wider class of

   models (Cannings,1974) to specify the eigenvalues and

   eigenvectors in a fairly full fashion and thus to study various

   aspects of the process.

 

 Kingman(1982) introduced a major insight

   for the study of such processes, the Coalescent. Instead of

   looking at whole generations with time running forward the

   coalescent runs time backward. Since the number of individuals in

   generation t who are actually, rather than potentially, parents of some set of k

   individuals in generation t+1, is ≤ k (with non-zero probability for

   <k), the ancestry of any set of individuals is a tree running

   backwards in time to a MRCA (most recent common ancestor of the

   set). This is the coalescent, and the study of the genetic drift process

   reduces to the study of this tree.

 

A brief survey of some of the features of this process will include

the probabilities of various tree topologies, and the time to the

MRCA. 

 

The coalescent approach will then be used to tackle two problems.

 

(1) Suppose that individuals have a type specified by an integer,

and that a parent of type x produces an offspring of type x-1,

x or x+1 with probabilities u/2, 1-u and u/2. We

wish to specify aspects of the distribution of the types in the

population at some time n. This model correspond to genetic

situations in which an individual has some number of copies of a

genetic unit, and that due to errors in the copying process required

for producing an offspring, that offspring may have a slightly

different number of copies. We derive certain results for the moments of

 this and a related normalised process.

 

(2) The branch from an individual backwards in time to the

coalescent tree is called an external edge. Some results regarding

the lengths of such edges will be derived.

 

 

  Malgorzata Bogdan, Arijit Chakrabarti, Florian Frommlet,  Jayanta K. Ghosh

Asymptotic optimality properties of multiple testing and model selection procedures under sparsity

 

Asymptotic optimality of a large class of multiple testing rules is investigated using

the framework of Bayesian Decision Theory. A normal scale mixture model is considered, leading to an asymptotic 

framework which can be naturally motivated under the assumption of sparsity, 

where the proportion of ``true'' alternatives  converges to zero. Within this setup optimality of a rule is proved by 

showing that the ratio of its Bayes risk and that of the

 Bayes oracle (a rule which minimizes the Bayes risk) converges to one. 

The class of fixed threshold multiple testing rules which are asymptotically optimal is fully characterized as well 

as the class of optimal rules controlling the Bayesian False Discovery Rate (BFDR). 

Furthermore, conditions are provided under which the popular Benjamini-Hochberg  procedure is asymptotically optimal. 

It is shown that for a wide class of sparsity levels, the threshold of the former can

be approximated very well by a non-random threshold. 

 

Apart from multiple testing the problem of model selection for multiple regression under sparsity is considered. 

Under the assumption of orthogonality and for known variances results from multiple testing immediately translate into the regression setting, 

where the scale mixture model is extended to a more general class of priors.

 We illustrate asymptotic optimality properties of modified versions of the Bayesian Information Criterion (mBIC), 

where we specifically discuss modifications allowing to control FDR. Finally optimality of mBIC in the case of unknown variances is proven.

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