## Mathematics Colloquium: Bikas K Sinha : Indian Statistical Institute, Kolkata

Description
```Title :
Group Testing Designs :
A Combinatorial Marvel
Speaker: Bikas K Sinha

Retired Professor of Statistics

Indian Statistical Institute, Kolkata

Abstract :

Group Testing is a technique to test a collection of units in several
groups, rather than in isolation (i.e., one-at-a-time), in order to
ascertain the 'status' of each individual unit in the collection in
respect of a well-deﬁned 'feature'. The problem is to plan the testing
procedure so as to be able to do so without any ambiguity and with a
minimum number of such tests [called Group Tests (GTs)]. The response to
be extracted from each unit is on the same 'feature' and it is 'binary'
in nature.  It is tacitly assumed that 'possession' of the feature by at
least one unit within a group [so formed] would render the group
'identiﬁable' as 'possessed'. When this happens, we need to 'open up'
the group and go for further exploration of the status of individual
units of the group, possibly by sub-group(s) testing or by other means.
Other possibility is that the group would be declared as 'passed', and
consequently, it would mean that all constituent units within the group
would be declared as 'passed' and 'at one go'!

This interpretation is accepted for Group Testing schemes to work. When
this latter phenomenon happens, the merit of Group Testing prevails over
testing individual units in terms of reduction in the required number of
tests. For a given collection of units, we may adopt one-at-a-time
testing or Group Testing with formation of suitable groups, or even a
combination of the two strategies. As is mentioned above, the sole
purpose is to minimize the number of GTs in such situations for a given
collection of test items.

The above formulation looks deceptively simple! Hidden are probabilistic
and combinatorial challenges. In this talk, we will discuss some issues
related to combinatorial challenges only.

Key Words.... Group tests; Hypergeometric group tests, Sequential group
tests, t-completeness, Detecting power of order t, Group Divisible
Designs, Petersen graphs.```
Description
Ramanujan Hall, Department of Mathematics
Date
Wed, November 9, 2022
Start Time
4:00pm IST
Priority
5-Medium
Access
Public
Created by