webcal

Thu, May 16, 2019
Public Access

Category: All

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3:00pm	[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 type-II 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 stress-strength 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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