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[3:30pm] Raj Kamal Maurya, IIT Patna
 Description:
 Statistics Seminar.
Speaker: Raj Kamal Maurya.
Affiliation: IIT Patna.
Date and Time: Thursday, 16 May, 3:30 pm  4:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Some Problems of Estimation and Prediction under Progressive
Censoring.
Abstract: We have considered the problem of making statistical inferences for different lifetime
models on the basis of progressive typeII censored samples. In particular, we have
derived various estimates of parameters using both classical and Bayes methods. The
associated MLEs are computed using the EM algorithm. We also compute the ob
served Fisher information matrices and based on these computations, the asymptotic
confidence intervals of parameters are constructed. Bootstrap intervals are also dis
cussed. We also derive Bayesian estimates of parameters against different loss func
tions. Most of these estimates appear in analytically intractable forms and so we
have used different approximation methods like importance sampling, Lindley, Tier
ney and Kadane procedures to compute the Bayes estimates. In sequel, we have also
constructed highest posterior density intervals of parameters. We have also derived
predictive inference for censored observations under frequentist and Bayesian frame
works. In particular, we obtain best unbiased predictor, conditional median predictor
from frequentist perspective. Among prediction intervals, we construct pivotal in
terval, highest conditional density interval, equal tail interval and HPD interval for
future observations. Determination of optimal plans is one of the primary objective
in many life test studies. We have obtained such plans again using both frequentist
and Bayesian approaches under progressive censoring. We also consider estimation
of multicomponent stressstrength reliability under progressive censoring. We have
numerically compared the proposed methods using simulations for each problem. We
have also discussed real life examples in support of studied methods. We have provided
relevant information in each chapter of the thesis.
[3:30pm] Satya Mandal, University of Kansas
 Description:
 Algebra Seminar.
Speaker: Satya Mandal.
Affiliation: University of Kansas.
Date and Time: Thursday 16 May, 3:30 pm  4:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Homotopy obstructions for Projective Modules.
Abstract: The Theory for vector bundles in topology shaped the research in
projective modules in algebra, consistently. This includes Obstruction
Theory. The
algebra has always been trying to catch up. To an extent, this fact
remained under
appreciated.
For an affine scheme $X=\spec{A}$, and a projective $A$module $P$, our
objective
would be to define an obstruction class $\varepsilon(P)$ in a suitable
obstruction
house (preferably a group), so the triviality of $\varepsilon(P)$ would
imply $P
\equiv Q \oplus A$. One would further hope the obstruction house is an
invariant of
$X$; not of $P$. We would report on what is doable. We detect splitting $P
\equiv Q
\oplus A$ by homotopy.


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