Theoretical Statistics and Mathematics Unit Seminars

Model Diagnosis Of Mixed Linear Models
Abstract: In a linear mixed model the output variable is the result of a systematic effect, a random effect and a random error. The aim of a statistical analysis then is to provide some information on the single sources. In this talk we discuss some new methodology how to estimate relevant quantities and test hypotheses. In particular, we investigate the role of the design and the number of replications in each group.

Some results on transition probabilities
Abstract: PDF

Degradation Models in Reliability Analysis
Abstract: The life testing experiments with reliable units often result in no or fewer failures. The units, however, undergo degradation before failing and the measurements on degradation characteristic over time can be used to infer about the product reliability. Various stochastic models are used to represent degradation over time. The talk will mainly review the recent literature on degradation models. We consider certain functions to relate time-to-failure and degradation process and present reliability estimation based on failure times and degradation data.

Holiday

Sequential Calibration of Computer Models
Abstract: Computer experiments are becoming popular for their ability to simulate complex physical systems at relatively cheap cost. Many computer experiments run large time consuming codes making it difficult to obtain large number of observations. Statistical models are used to approximate the response surface from such codes. If observations from physical experiments are available then finding the best setting of the calibration parameters (parameters that are fixed for the physical experiment but can be varied in the computer experiment like the reaction rate of a chemical reaction) so that the outputs from the physical experiment and computer experiment are in agreement, is known as the calibration problem. Calibration problem is regularly encountered in car crash simulation, climate modeling, prosthesis design etc. In this talk, I will discuss a new sequential approach to solve the calibration problem arising from a time consuming computer experiment. This is joint work with Dr. William Notz from Ohio State University.

Extremal Discriminant Analysis
Abstract: Classical discriminant analysis focuses on Gaussian and nonparametric models where in the second case the unknown densities are replaced by kernel densities based on the training sample. We assume that it suffices to base the classification on exceedances above higher thresholds, which can be interpreted as observations in a conditional framework. Therefore, the statistical modeling of truncated distributions is merely required. In this context, a nonparametric modeling is not adequate because the kernel method is inaccurate in the upper tail region. Yet one may deal with truncated parametric distributions like the Gaussian ones. Primary aim is to replace truncated Gaussian distributions by appropriate generalized Pareto distributions and to explore properties and the relationship of discriminant functions in both models.

Holiday

Bayes Estimation of Pareto life time model under Asymmetric loss function
Abstract: Asymmetrical loss function used in a situation where overestimation and under estimation are not equally serious. In the present talk we mainly focus on Bayesian estimation of life time parameters such as reliability and hazard function of Pareto model under asymmetric loss (LINEX loss and general entropy loss) function. The estimators are derived by using the conjugate prior of the shape parameter. The properties of Bayes estimator in respect of risk have been studied and it is found that the asymmetric loss estimator is preferable to the symmetric (squared error) loss estimator in some circumstances.

Holiday

Key Management & Key Pre-distribution
Abstract: In modern Cryptography, the security of a cryptosystem lies on secrecy of the key, not on secrecy of the encryption algorithm. Hence key management is a very important issue. There are several methods for key management, but most of these are based on Public Key Cryptography, which are typically based on Number Theory. Key Pre-Distribution is an alternative method based on Combinatorics. This method may be used for a scenario where security requirement is not so stringent.

On Linear Wavelet Density Estimation: Some Recent Developments
Abstract: The theory of wavelets has found wide applications in nonparametric es- timation, especially for density and related functionals. It has been adapted to many other situations in addition to density estimation for iid data. Such procedures may potentially be useful for nonparametric density estimation in agricultural setting such as in modeling yield of crops and crop insurance claims distribution. This article presents some recent developments in this area in a comprehensive way dealing with different data types in addition to the iid setup.

Strong Solutions of SDE-s with coefficients in S'
Abstract: In this talk, we describe existence and uniqueness results for a class of infinite dimensional stochastic differential equations in S', the space of tempered distributions. Mathematically, these results maybe viewed as extensions (to more general coefficients and initial conditions) of Ito's SDE-s with Lipschitz coefficients. The solutions have a particularly simple form: that of a (non-linear) translation of the initial condition by a finite dimensional diffusion. Physically, these solutions maybe viewed as describing the evolution (via drift and diffusion) of an arbitrary initial configuration of particles, represented by a tempered distribution, in the presence of a given Brownian motion.

Cancelled

Critical Probabilities of bond percolation in Delaunay triangulation and Voronoi tessellation
Abstract: We consider bond percolation with parameter p on the Delaunay Triangulation (DT) generated by a Poisson point process of unit intensity in R^2. Let p_c and p*_c , respectively, denote the critical probabilities for the bond percolation in DT and its dual, the Voronoi Tessellation (VT). In many regular lattices, we know that p_c + p*_c = 1 (1). In random lattices, very few exact critical probabilities have been established. For the Voronoi site percolation, Bollobas and Riordan (2006) have recently shown that the critical probability is 1/2. Using a crucial RSW result of Bollobas and Riordan (2006), we prove that bond percolation in DT and VT satisfy (1).

Comparison of the $\mu$-invariant under isogeny
Abstract: We consider an isogeny between two elliptic curves and compare their $\mu$-invariants. We do the same for abelian varieties.

Lateral and Longitudinal Collision Risk Assessment over the Bay of Bengal Airspace
Abstract: In this talk we will report about an on going investigation of the collision risk between two aircrafts flying over the Bay of Bengal. This safety assessment data analysis is undertaken jointly by the Airports Authority of India (AAI) and the Indian Statistical Institute, Delhi Centre under the MoA signed between the two organizations on January 13, 2011. The goal of this study is to confirm that the target level of safety (TLS) which is $5 \times 10^-9$ accidents per flight hour, is currently met. This project will eventually help the AAI to establish En-route Monitoring Agency (EMA) which is necessary for further lateral and longitudinal separation reductions. [This is a joint work with Deepayan Sarkar and BOBASMA team members from AAI.]

Modeling opportunistic maintenance and repair as competing risks
Abstract: Consider a system in continuous operation. It gives signals each time its deteri- oration state worsens. The signals provide insight into the condition of the system, which the operator/maintenance staff uses in order to plan preventive maintenance. Assume that maintenance occurs at the first opportunity after a critical degradation signal is observed. We propose a Signal Model for studying the life of the system time by taking into account the signals, the rate of opportunities for maintenance, and the competition between maintenance and failure.