Past Seminars

In reliability or survival analysis, researchers are often interested in the effects of different stress levels such as temperature, voltage, dose etc. on the lifetimes of experimental units. Accelerated testing allows the experimenter to increase these stress levels to obtain information on the parameters of the life distributions more quickly than would be possible under normal operating conditions. A special class of accelerated tests is the class of step-stress tests which allow the experimenter to increase the stress level at fixed times during the experiment. In this talk, we consider step-stress models assuming different parametric forms for the hazard function and allowing for the presence of an immune population. The immune population represents resistant items that are not affected by the stress. We adapt the cumulative exposure model discussed by Nelson and obtain the MLE’s of the parameters. The model is fit to some data on altitude decompression sickness.

Eugene Fama (1960s) in his PhD thesis developed the concept of “Efficient Market Hypothesis (EMH). According to EMH, financial market is “information-efficient”. This results the price of stock to behave like random-walk. In consequence of this, one cannot consistently achieve return in excess of average market return on riskadjusted basis. However, by late 1990 and early 2000s many empirical studies shown that EMH is not necessarily true. If EMH is true then all the assets in market are always fairly priced; otherwise assets are either under or overpriced. This turns out to be a testing of hypothesis problem, where null hypothesis is EMH is true or assets are fairly priced versus alternative hypothesis as EMH is false or assets are either over/under-priced. As there are thousands of assets, this problem turns out to be a multiple testing problem. In this talk we will walk through the concepts of EMH, Capital Asset Pricing Model (CAPM) and multiple testing problems. Then I will present Bayesian multiple testing with diffused prior for CAPM for 500 stocks that are considered in S&P 500 index. We present the back-testing (aka out-of-sample performance) of the method for the period from 2008 to 2013.

Noted environmental statistician Professor Anil Gore, University of Pune, dealt with the problem of estimation of nonidentifiable bird species in BNHS Survey. This study was conducted around mid 1970's. In recent time, Dr. Tommy Wright of US Census Bureau posed a similar problem. The speaker had the opportunity to be involved in both the studies in a limited way. He will discuss salient features of the problem and the proposed solutions.

In this talk we will address the problems of unbiased estimation of parameters in linear and quadratic mixture models. We will discuss some standard mixture designs for this purpose. The information matrices of the parameters involved in the linear and quadratic mixture models will be displayed for these standard designs. Some generalizations of the axial designs have be presented and a comparative study of these designs, in respect of their information matrices, will be considered. Other types of mixture models viz. Becker’s homogeneous model and Draper - St. John’s models will also be briefly presented and the estimation problems will be addressed by using some axial type designs.

Firstly, we will introduce Carry Value Transformation(CVT) and will try to understand the famous Goldbach Conjecture in the light of CVT. Next we will discuss the generalized form of CVT, called IVT (Integral Value Transformation) and try to understand another famous conjecture, Collatz Conjecture, in the light of IVT. Actually we had solved the characterization of Collatz-like IVTs. Finally, if time permits, we will discuss the classification strategies of n-variable Boolean functions to apply in classification of Proteins, our ongoing studies in Genomics.

An introduction to the Kolmogoroff model for probability theory will be given. It will be illustrated with finite sample spaces, countable case, real line, Euclidean spaces, sequence spaces, function spaces.

Clinical end-point traits are often defined in terms of quantitative precursors (e.g., systolic blood pressure for hypertension, fasting glucose levels for Type 2 Diabetes, etc.) It has been argued that analyzing the quantitative precursors instead of the binary clinical end-points may be a statistically a more powerful strategy to identify novel genomic regions harboring genes that modulate the underlying complex trait. It is now well established that population stratification can result in spurious association findings in genetic case-control studies. Thus, it is of interest to evaluate the adverse effects of population stratification on the analyses of quantitative traits. The two popular statistical tests of association for quantitative traits using population level data are ANOVA and Kruskal-Wallis. We have theoretically shown that neither genetic heterogeneity nor phenotypic heterogeneity alone can affect the false positive rate of either of the tests. However, if the data comprise subpopulations with different allele frequencies at the marker locus of interest as well as different phenotypic means or distributions, the rate of false positives will be elevated. We have also carried out extensive simulations under different genetic models and probability distributions of quantitative traits to assess the extent of increase in the rate of false positives in the presence of population stratification. The classical Transmission Disequilibrium Test (TDT) for binary traits circumvents the problem of population stratification as it tests for allelic association in the presence of linkage. We propose a simple logistic regression based test for transmission disequilibrium in the context of quantitative traits that can be analytically shown to be statistically equivalent to the TDT for binary traits. We perform Monte-Carlo simulations under a wide spectrum of genetic models and probability distributions of the quantitative trait values to evaluate the power of the proposed procedure and compare with the FBAT approach with identical data. We find that our method yields more power than FBAT if we suitably incorporate trios with both parents heterozygous in our likelihood. The method can be easily extended to incorporate multivariate phenotypes. We apply our method to analyze externalizing symptoms, an alcoholism related endophenotype from the Collaborative Study on the Genetics Of Alcoholism (COGA) project.

The concepts and the practical implementation of the Continuous-Time Quantum Monte Carlo (CT-QMC) impurity solver using the hybridisation expansion, for the Dynamical Mean Field Theory of strongly correlated electron systems will be presented. This method is applied for the one-band Hubbard model on a Bethe lattice in the presence of an external magnetic field. The results of the CT-QMC solver are benchmarked against the numerical exact NRG - DMFT solver. Using the same model parameters, a rather good agreement between the two methods is obtained, except difficulties in reproducing features of the spectral functions. These difficulties are connected with the analytical continuation performed using the maximum entropy method the technique inherently used in stochastic analysis.

The recent outburst of context-dependent knowledge on the (Semantic) Web has led to the realization of the importance of the quads in the web community. Quads, which extend a standard RDF triple, by adding a new parameter of the ‘context’ of an RDF triple, thus informs a reasoner to distinguish between the knowledge in various contexts. Although this distinction separates the triples in an RDF graph into various contexts, and allows the reasoning to be decoupled across various contexts, bridge rules need to be provided for inter-operating the knowledge across these contexts. We call a set of quads together with the bridge rules, a quad-system. In this Seminar, I will try to describe the problem of query answering over quad-systems with expressive forall-existential bridge rules. It turns out the query answering over quad-systems is undecidable, in general. We derive a decidable class of quad-systems, namely context-acyclic quadsystems, for which query answering can be done using forward chaining. Tight bounds for data and combined complexity of query entailment has been established for the derived class. The topics/results are part of Joint work between Dr. Luciano Serafini (FBK-IRST) and Prof. Gabriel Kuper (DISI, University of Trento)

Statisticians or any quantitative analysts are interested in terms such as “information,” “knowledge,” and “data”. These terms are critical in understanding the concept of “Big Data” that’s currently sweeping the scientific community. By definition, data refers to structured information in some schematic form such as a table or a list, and knowledge is derived from studying and synthesizing the information hidden in the data. Data is often but not always quantitative, and it is often derived by processing unstructured information. When we visualize data, we are interested in portraying abstract relationships among variables that contain the unstructured information. Visualization has been used for centuries to map our world (cartography) and describe the animal and plant kingdoms (scientific illustration). Data visualization, which is more abstract, emerged more recently. An early innovator was William Playfair, whose extensive charting of economic data in the 1800s (Wainer & Spence 2005a, Wainer & Spence 2005b) contributed to its emergence. The early history of visualization has been richly — and beautifully— documented (Friendly & Denis 2006, Tufte 1983, Tufte 1990, Ford 1992, Wainer 2000) (Ref: Dianne Cook and Deborah Swayne, 2007).
Grammar of Graphics, a term originally coined by Leland Wilkinson (2005), is a concise tool that enables us to describe the components of a graph that is the backbone of any data visualization. A recent R package, ggplot2, implements Wilkinson’s Grammar of Graphics. Written by Hadley Wickham, it was set out a set of general unifying principles for the data visualization. For this reason, ggplot2 offers a more elegant and arguably more natural approach than does the base R graphics package.
In this presentation, we will first introduce the grammar of graphics, followed by several basic and advanced examples, which will describe the features of ggplot2. We will also contrast the features in ggplot2 with other R tools such as ‘plot’ and ‘lattice’. Our primary goal in this presentation is to make the audience comfortable in using the freeware R and expose them to what it offers to the World of Graphics that is easy to use with abundant flexibility.

It is well known that sampling plays a vital role in all discipline including Physical and Chemical sciences; Biological and Environmental sciences; Economic and Social sciences; Engineering and Medical sciences whenever one has to undertake a study to understand the behavior of some entities in their respective fields. The problem in our hand is to estimate the population mean and variance on the basis of a random sample selected from the population with some desirable properties like Unbiasedness / Minimum Bias and Minimum Variance / Mean squared error. When there is no auxiliary information available, the simplest estimator of population mean and variance is the sample mean and variance obtained by using simple random sampling without replacement. Sometimes in sample surveys, along with the study variable Y , information on auxiliary variable X, which is positively correlated with Y , is also available. This information on auxiliary variable X, may be utilized to obtain a more efficient estimator of the population mean and variance. Ratio method of estimation is an attempt in this direction. In recent times a lot of attempts are made on improving or modifying the usual ratio estimator by introducing a large number of modified ratio estimators with known Coefficient of Variation, Kurtosis, Skewness, Population Correlation Coefficient, Median, Quartiles, Deciles and their linear combinations. In this talk we will discuss briefly about the developments taken place on the ratio estimator for estimating finite population mean and variance. Further the relative performances of the ratio estimator and modified ratio estimators are assessed for certain natural populations.

An m-order n-dimensional square real tensor A is a multidimensional array of nm elements of the form A=(Ai1 im ), Ai1 im R, 1 i1 im n (A square matrix of order n is a 2-order n-dimensional square tensor.) An m-order n-dimensional square real tensor is said to be a nonnegative (positive) tensor if all its entries are nonnegative (positive). We shall discuss the Perron-Frobenius theory for nonnegative tensors and strict monotonicity of the spectral radius of some classes of nonnegative tensors. Using these results we establish some properties of M-tensors. This is a joint work with Abraham Berman and Naomi Shaked-Monderer.

Curves that measure inequality in incomes have been a topic of immense interest for more than a century ever since the work of Lorenz in 1905. A measure of income inequality is designed to provide an index that can abridge the variations prevailing in income among the individuals in a group. Different forms of curves and summary indices of inequality measurement were discussed along with their justifications through applications to real data. A probability distribution can be specified in two ways namely (i) in terms of the distribution function and (ii) in terms of the quantile function. There are many properties for quantile functions that are not shared by distribution functions even though both of them convey the same information about the distribution. In many cases, quantile function provides a straight forward analysis and in many situations it permits the use of distributions which have no closed form. More aspects on the Zenga measure as well as other income inequality measures using quantile function approach are included. We also look into the application and interpretation of the inequality measure in the reliability context. Usually in reliability based works, the ageing properties are studied using the monotonic behaviour of certain reliability concepts. Here we look at the problem from another point of view by utilizing the truncated L moments which have their own economic interpretations.