Abstract: Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects which are modelled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used intrinsic conditional autoregressive model which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on sparse Cholesky factors. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated random effects, can also be applied directly to model other dependent multivariate data like images and networks. Theoretical and empirical results demonstrate the interpretability of parameters in our model. Our precision matrix is sparse and the model is highly scalable for large datasets. We also derive a novel order-free version which remedies the dependence of directed acyclic graphs on the ordering of the regions by averaging over all possible orderings. The resulting precision matrix is still sparse and available in closed form. We demonstrate the superior performance of our models over competing models using simulation experiments and a public health application.

Abstract: This paper analyses the statistical properties of the threshold model, under the assumption that the participation rate is a increasing function of the willingness to participate. In such a case, it can be modelled as a Pólya schema, and the sequence of participation rates converge almost surely to a random variable Z that has beta distribution. Also, under the feedback leadership condition, the process is exchangeable for some t > te, which guarantees that the process does not depend on the individual behaviour, despite the social interaction between actions. We apply these results to characterize the process of adoption of the hybrid corn in Iowa.

Abstract: Earth Quake causes massive damages to both property and life. The prediction of earthquake may help in preventive measures. Earth quake prediction is a challenging task. When viewed as a time series data it forms a complex pattern consisting mixture of statistical features. ARIMA and Spectral analysis techniques are applied in this work to improve the prediction accuracy.

In this work there are three goals, [1] To build ARIMA model for forecasting the occurrence of earthquakes. Techniques like Auto regressive, moving average, non-seasonal and seasonal ARIMA models are applied. [2] Spectral analysis and filtering technique are used to predict the period of occurrence of the earthquakes. In this, spectrum and cross spectrum of different earth quake time series which uses the past data to forecast the future. [3] To predict the arrival of the P wave from the Earth’s seismic waves using techniques such as short time Fourier transform, continuous wavelet transform and discrete wavelet transform which acts as a warning system and that can be used to find the magnitude of the earthquakes.

This work highlights the application of statistical techniques in finding solutions to real world problems.

Abstract: In this paper, we have developed the maximum likelihood and Bayesian estimation procedures for estimating the unknown parameters of Exponentiated Exponential distribution based on a generalized progressively hybrid censored sample. We have derived the expression for the Shannon entropy, expected total time on test and expected number of failures for the same. The Bayes estimators of parameters and entropy of Exponentiated Exponential distribution based on symmetric and asymmetric loss function is computed using MCMC method. We have used the simulation method to check the performance of our proposed estimators. Further, we have considered a real dataset for illustration purpose.

Abstract: We will present the definition and important properties of the fractional Poisson process (FPP) and its connection with fractional calculus, stochastic subordination and renewal process. The approaches generalization of the FPP viz, the fractional negative binomial process, the time-changed Poisson process and the non-homogeneous Poisson process will be exhibited. We will present long-range dependence results for the FPP and other related processes.

Abstract: Latent class analysis(LCA) identifies unobserved subgroups in the population based on the behavior on several manifest variables or indicators. Traditional latent class models assumes the samples to be taken from the population through SRS sampling scheme. There may be existing subgroups in the data representing different populations and latent class parameters may vary across these observed subgroups. The interaction of this observed and latent subgroups can be modelled using multiple group latent class analysis. A multiple group LCA model is fitted to the data set on several risk factors of cardiac disease and the observed grouping is made on the basis of age group. It is assumed that the latent class prevalence varies across age groups, but the item-response probabilities do not. Parameters of the model are estimated by maximizing the probabilistic formulation of the latent class model, i.e without using any link function unlike the traditional model which is based on loglinear parameterization. The comparison of the maximum likelihood estimates with that of traditional LCA is performed along with the empirical and analytical standard errors for both types of models. The corresponding single sample model counterpart is also examined and the different model selection criteria for testing goodness-of-fit of the models are compared.

Abstract: Recently Asimit et al. used EM algorithm to estimate singular Marshall-Olkin bivariate Pareto distribution. We describe absolutely continuous version of this distribution. We study estimation of the parameters by EM algorithm both in presence and without presence of location and scale parameters. Some innovative solutions are provided for different problems arised during implementation of EM algorithm. A real-life data analysis is also shown for illustrative purpose. [https://arxiv.org/abs/1608.02199]

Abstract: In Bayesian estimation of finite mixture models with unknown number of components, it is often common practice to use an infinite mixture model with Dirichlet process prior for the mixing components. However, with this prior, the convergence rate of the posterior distribution for mixing distribution is not optimal. Another alternative approach is to instead use symmetric Dirichlet weights for the mixing component weights, and put a prior on the number of components. In this paper we show that this approach is amenable to the optimal convergence behavior, and we obtain an optimal \(\sqrt{n}\) convergence rate for the estimation of mixing measures relative to the Wasserstein metric. Convergence in Wasserstein metrics for discrete measures implies convergence of individual atoms that provide support for the measures. We also study the case the true data generating distribution may not be included in the support of the prior, sometimes due to misspecification of kernel or misspecification of the parameter space. We establish the convergence behavior of finite mixtures under such misspecified settings relative to the Wasserstein metric.

Abstract: We address a control problem for a queueing system, known as the “N-system”, under the Halfin-Whitt heavy traffic regime. It has two customer classes and two server pools: servers from one pool can serve both customer classes, while servers from the other pool can only serve one class. The service time is assumed to follows a special case of hyper-exponential distributions, called the \(H_{2}^{*}\) distribution, and customers are impatient. We consider an expected infinite-horizon discounted cost function, with linear holding and abandonment cost-components. A static priority policy is proposed and is shown to be asymptotically optimal, using weak convergence techniques.

Abstract: In this paper we report findings of an experimental study that examines the usefulness of some of the well known statistical procedures in the high velocity streaming data context. Working with some publicly available large datasets from the transportation domain we examine the performance of some of the standard statistical procedures. The performances of widely used statistical procedures such as Linear regression, Multivariate multiple linear regression and K-Nearest neighbour regression are compared with those of popular machine learning algorithms such as Artificial neural networks and Support vector regression using metrics such as predictive accuracy and computation time, that are important for use in the streaming data set-up. We find that some of the statistical algorithms perform quite well in this set-up and with simple modifications compete very favourably with the newer machine learning algorithms.

(This is joint work with Sayan Putatunda)

Abstract: The WHO initiated the Expanded Program on Immunization (EPI) in 1974. It has been widely used in different studies. Along with this other survey methodologies have been compared to study immunization coverage at different regions. To consider different survey methodologies one of the most important factor is the cost incurred in survey methodologies. A survey method is considered to be more efficient than the other survey method if the cost incurred in a particular method is less than the other one. In this study cost incurred in two stage (30×30) cluster sampling and systematic random sampling methods have been compared using a cost function for Hepatitis B vaccine coverage. The results show that there are no significant differences between the point estimates of Hepatitis B vaccine coverage under the considered survey methodologies. But the cost incurred in systematic random sampling is more than that of two stage cluster sampling. It can be concluded that two stage cluster sampling is more efficient than that of systematic random sampling for this study population.

Abstract: In an observational study, regression analysis is commonly used to estimate the causal effect of a treatment; in order to provide an unbiased estimate, the regression analysis depends, among other things, on there being no unmeasured confounding. To address the concern of unmeasured confounding, instrumental variable (IV) analysis is often used when a plausible IV can be found. When unmeasured confounding is not expected to be severe, regression analysis is often used as the primary analysis and IV as the secondary analysis. However, these two analyses are correlated and it is not clear how much independent evidence is provided by the IV analysis.

We develop a statistically sound method of analysis to resolve this redundancy by introducing a new estimator, the EX estimator, which extracts the part of the regression estimator uncorrelated to the IV based 2SLS estimator. The EX and 2SLS estimators form evidence factors. We propose to conduct two secondary analyses using the 2SLS and EX estimators when a primary regression analysis gives a positive signal; we control the familywise error rate by using results from ordered testing theory.

We apply our approach to analyze the effect of exposure to violent conflict on preferences for altruistic behavior, time and risk.

Abstract: We consider the problem of multiple testing when additional covariate information is available on each of the hypothesis tests. We propose a model for such data and develop likelihood based methods for estimating the unknown parameters. The theoretical properties of the proposed estimators are studied. We illustrate the practical efficacy of our methodology in applications in neuroscience, astronomy and genomics. This is joint work with Sujayam Saha and Adityanand Guntuboyina.

Abstract: Financial & Economic performance is one of the foremost goals of any company. This involves important decisions to augment the allocation of resources. The objectives of the organization can be measured as effectiveness (the extent to which objectives have been met) or as efficiency (the extent to which objectives have been achieved in the available resources). In this regard, it is particularly important to identify factors that influence getting the desired income and the degree of their influence on the economic performance of the organization. This paper aims is to realize an analysis of these factors and their degree of correlation on economic performance using aspects of Correlation and Multiple regression with Business point of view. Relevant Data has been collected from a particular organization over a period of time and applying the multiple regression techniques various results are obtained. Based on those results various conclusions are drawn and it also opens gates for future research as well.

Abstract: In this work we derive some general recurrence relations between single and product moments of dual Generalized Order Statistics from a General Class of Distributions, thus generalizing and unifying the earlier results in this direction due to several authors.

Abstract: The modeling of lifetime data has received prime attention of researchers from the last one decade. Many continuous probability models such as exponential, gamma, Weibull have been frequently used in statistical literature to analyze the lifetime data, but these probability models cannot be used efficiently to model the lifetime data that is bathtub shaped and have unimodel failure rates. To overcome this problem, researchers have focused their attention on compounding mechanism which is an innovative way to construct suitable, flexible and alternative models to fit the lifetime data of different types.

In this paper, we shall introduce a new lifetime distributions which is obtained by compounding generalized Pareto distribution with power series distribution. This new class of continuous lifetime distributions so obtained will be called Generalized pareto power series (GPPS) distribution. The proposed class of compound distribution contains several lifetime distributions as its special cases that are very flexible to accommodate different types of data sets. The properties such as moments, moment generating function, order statistics and estimation of parameters via maximum likelihood have also been discussed. The potentiality of proposed model has been tested statistically by using it to model some real life data set.

Abstract: There are many continuous distributions in statistics that can be used to model lifetime data, among them the most popular are gamma, log normal and Weibull distribution. Weibull distribution has been used extensively by researchers to model lifetime data because of its closed form for survival function. However all these lifetime model suffer from a major drawback i.e., none of the them exhibit bathtub shapes for their hazard rate functions and hence cannot be used efficiently to model real life data that has bathtub shape for hazard rate function.

Nadhraj, Bakouch and Tahmasbi (2011) proposed a new lifetime distribution called generalized Lindley distribution that removes all these mentioned drawbacks. The authors showed that generalized Lindley distribution has an attractive feature of allowing for monotonically decreasing, monotonically increasing and bath tub shaped hazard rate functions while not allowing for constant hazard rate functions.

In the present paper we construct a complementary version of generalized Lindley power series distribution that is obtained by compounding generalized Lindley distribution with that of power series distribution, the new distribution so obtained arises on a latent complementary scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. The mathematical properties of the new family, such as moment generating function, moments, hazard function, survival function, order statistics and estimation of parameters via maximum likelihood estimation have also been studied. The beauty of this model lies in the fact that it does not only generate several new lifetime distributions but they are also very flexible in terms of density and hazard rate functions. Finally the potentiality of proposed family is justified by using it to model the real life data set.

Abstract: This paper considers the factor type estimator as an estimation tool to deal with the problem of estimation of population variance in presence of random non-response under two-phase sampling. A distribution is assumed for the number of sampling units on which information could not be obtained due to random non-response .The proposed estimator has been suggested in two different situations of random non-response: i) When non-response is present in study as well as auxiliary variable, and ii) When non response exits only in study variable. Expressions of optimization for the proposed estimator are derived and an empirical study has also been carried out to demonstrate the theoretical results.

Abstract: In this article, we consider a single index model where the link is a monotonic function of the index and the dimension of the covariates is comparable with the sample size. We model the univariate response as a monotone function of a linear combination of the covariates.Existing approaches to this problem suffer from the lack of computational efficiency and scalability to even moderately high-dimensional \(x\). We propose a frequentist pproach to solve the problem. In the frequentist framework, we propose a simple two-step profiling based approach to estimate the monotone function and the linear combination. In the first stage, we use a Bernstein polynomial basis to estimate the monotone function. In the second stage, we estimate the coefficients corresponding to the linear combination using multiple linear regression leveraging on the first order Taylor series approximation of the link function with respect to estimate of previous iteration \(\alpha_0\). In high dimensional setup, we select variables by placing an appropriate penalty on \(\alpha\) in the simplified equation and solve LASSO type optimization problem. We illustrate the methods through simulated and real data examples.

Abstract: Testing of equality of location parameters against umbrella alternatives has many real life applications. If the effects due to increasing level of treatments are firstly increasing up to a point followed by decrease then the treatments effects are said to follow an umbrella pattern. The first and well-known test for testing umbrella alternative is proposed by Mack and Wolfe (1981) [Mack G.A. and Wolfe D.A. (1981) K-Sample Rank Tests for Umbrella Alternatives. Journal of the American Statistical Association, 76, 175-181]. In this paper, we propose a general class of non-parametric tests for testing the umbrella alternatives. The distribution of the test is established. In order to have maximum efficiency, an optimal choice of weights is determined. We also compare the proposed class of tests with other competing tests for some underlying distributions. A numerical example is provided for illustrative purpose. Power of the proposed test is assessed using Monte Carlo simulation.

Abstract: Forbes Magazine offers an annual list of the 2000 largest publicly traded companies, shedding light on four different measurements: Sales, profits, market value and assets held. Soriano-Hernandez, del Castillo-Mussot, Campiran-Chavez and Montemayor-Aldrete [Physica A, 471, 733-749, 2017] modeled these wealth metrics using composite distributions made up of two parts. In this paper, we introduce different composite distributions to more accurately describe the spread of these wealth metrics.

Abstract: A recent study on multi-phase calibration has adopted a particular distance function for calibrating survey design weights that enables to present a multi-phase calibrated estimator in the form of a one-phase multivariate calibrated estimator and therefor to produce a closed form expressions for its variance. As this new theory holds for any number of phases of calibration, in our present study we use it in order to analyze the raking calibration process (sometimes called iterative proportional fitting) as a multi-phase calibration process.

In a purely sampling context, many alternative forms of calibration weighting were proved to be asymptotically identical. This led to a breakthrough in our understanding of some commonly used calibration estimators that do not have closed-form solutions such as raking. As a result, the generalized regression (GREG) estimator is often considered a good approximation of some general calibration estimators, but usually with no specific notion of what the rate of conversion really is.

We show that the raking estimator differs from the GREG approximation only by a magnitude of Op(n^(-1)), and consequently provide a strict approximation to its variance. Particularly, we also provide an approximation to the variance of the raking estimator after exactly p iterations.

Reference: Cohen, N., Ben-Hur, D. and Burck, L. (2017). Variance estimation in multi-phase calibration. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 43, No. 1.

Abstract: Statistical process control (SPC) charts are widely used to monitor the stability of certain sequential processes in various industries including health care systems. Most SPC charts are designed to monitor mean and/or variance of the “in-control” process distribution. However, in real-world problems, shifts in higher moments can occur without much change in mean and variance. If we fail to detect those and fix the underlying cause, it can eventually become worse and a shift in mean or variance can creep in. In this talk, a Phase II SPC chart will be proposed for detecting arbitrary change in univariate process distribution when the “in-control” distribution is assumed to be continuous and the observations are independent. Unlike many other charts, it does not require “in-control” Phase I data, which is unavailable in many real-life problems. The proposed SPC chart is based on change-point detection and the charting statistics is based on p-values for better interpretability. The proposed chart also involves p-value based pruning of data from distant past and a computationally efficient method to detect possible change-point. Wider applications such approaches will also be discussed. Simulation results and a real-data analysis will be shown in comparison with some state-of-the-art charts.

Abstract: The classical measures of inequality viz. Lorenz curve and related Gini, are based upon comparing the incomes of less fortunate with the mean income of the entire population, which may not be adequate to take into account the increase in disparities between less and more fortunate individuals. In this context, a new curve of inequality known as Zenga curve is introduced which accounts for the relative nature of ‘poor’ and ‘rich’ and is based on the ratio of the lower and upper group means . The Zenga curve represents an alternative to the well-known Lorenz curve, as a measure of economic inequality. The Zenga curve assumes different shapes for different distributions and can serve as a very useful tool to graphically discriminate between them. The Bayesian estimation of this new but important curve of inequality still awaits the attention of researchers though some results in this direction are available in the Classical estimation setup. In this paper, Bayesian estimator for Zenga curve is obtained for Pareto distribution under Assymmetric Loss Functions viz; LINEX loss, General Entropy Loss Function (GELF) and Precautionary Loss for different priors. Using simulation techniques, the relative efficiency of the proposed estimators is obtained in terms of expected loss for different configurations of sample sizes and shape parameter for different loss functions.

Abstract: In this article, we consider the problem of Bayes estimation of the stress strength reliability R=P(Y < X), when X and Y are two generalized inverted exponential random variables with different and unknown shape and scale parameters. The Bayesian estimation for stress strength reliability R=P(Y < X) are derived using upper record values for different loss functions using different priors in case of generalized inverted exponential distribution. A Monte Carlo simulation study is carried out for comparing the proposed methods of estimation. Finally, the methods developed are illustrated with a couple of real data examples.

Abstract: This paper develops a new identification result for the causal ordering of observation units in a recursive network or directed acyclic graph. Inferences are developed for an unknown spatial weights matrix in a spatial lag model under the assumption of recursive ordering. The performance of the methods infinite sample settings is very good. Application to data on portfolio returns produces interesting new evidences on the contemporaneous lead-lag relationships between the portfolios, and generates superior predictions.

Abstract: Clinical trials are acceptable gold standard for determining whether an intervention works for particular disease. However it requires substantial resources to be successful in making that determination. These resources can be quantified not only as a monetary cost, but also from an ethical view point as it requires exposing subjects to an unverified treatment regime from which benefits are yet to be determined. Hence reducing sample size if possible without undermining the integrity of the trial is always desirable. Historical trials often provide substantial information for legacy disease areas in many cases. Noninferiority trials are unique because they are dependent upon historical information in order to make meaningful interpretation of their results. Bayesian paradigm provides a natural framework in incorporating this historical information as a prior, which could reduce sample size burden substantially. In this talk we will review some of these Bayesian approaches from Noninferiority point of view with some application in depression trial.

Abstract: Vector autoregressive (VAR) models aim to capture linear temporal interdependencies among multiple time series. They have been widely used in macro and financial econometrics and more recently have found novel applications in functional genomics and neuroscience. These applications have also accentuated the need to investigate the behavior of the VAR model in a high-dimensional regime, which will provide novel insights into the role of temporal dependence for regularized estimates of the model's parameters. However, hardly anything is known regarding properties of the posterior distribution for Bayesian VAR models in such regimes. In this work, we consider a VAR model with two prior choices for the autoregressive coefficient matrix: a non-hierarchical matrix-normal prior and a hierarchical prior which corresponds to an arbitrary scale mixture of normals. We establish posterior consistency for both these priors under standard regularity assumptions, when the dimension \(p\) of the VAR model grows with the sample size \(n\) (but still remains smaller than \(n\)). In particular, this establishes posterior consistency under a variety of shrinkage priors, which introduces (group) sparsity in the columns of the model coefficient matrices. The performance of the model estimates are illustrated on synthetic and real macroeconomic data sets.

Abstract: In trivariate meta analysis of diagnostic studies, accounting for prevalence and non-evaluable subjects, only the logit transformation on sensitivity, specificity, positive and negative likelihood ratios (LR+ and LR-), disease prevalence, test prevalence, positive predictive value (PPV) and negative predictive value (NPV) have been considered in the literatue. Non-evaluable test outcomes is an important issue while comparing an index test with reference test in meta analysis studies. Many times this leads to overestimation and biasedness of sensitivity, specificity and other indicators even under the assumption of missing at random (MAR). Most of these studies have been carried out by using logit as link function. We used the extended trivariate generalized linear mixed model (TGLMM) approach to handle non-evaluable index test results for other link functions like probit and complementary log-log and compared their results with existing logit link based on Akaike Information Criterion (AIC). These link functions result into better goodness of fit.

Abstract: We present clustering methods for multivariate data exploiting the underlying topology of the graphical structure of variables. We first account for the uncertainty of the associated graphical structures through probabilistic modeling of the variables, and subsequently develop a Bayesian nonparametric graph clustering model. The clustering model is built on a lower dimensional projection of the associated graph Laplacians using spectral embedding. As an alternative graph clustering tool, we discuss the concept of graphical wavelets, incorporating the uncertainty in graph structure learning. We provide theoretical validations for using the eigenspace of the associated graph Laplacians, so as to achieve consistency in graph clustering, both for the Bayesian approach and the graph wavelets approach. We illustrate the performance of our methods using extensive simulations and also using several real-life datasets, including proteomics data and financial data.

Abstract: The conformational properties of a DNA molecule when mapped onto a Heisenberg spin system denaturation transition can be formulated in terms of quantum phase transition induced by a quench where the temperature effect is incorporated in the quench time. Here torsion takes the role of the external field. The denaturation transition occurs when entanglement entropy of the spin system vanishes. As the critical region corresponds to a two-limit behaviour the entanglement entropy gradually decreases with the gradual increase in the fraction of open base pairs and when the entropy vanishes the two strands are separated. The sequence heterogeneity interplays with the entropy effects and we have the onset of denaturation bubbles.. It is here argued that when we transcribe this result in the rod –like-chain (RLC) model of DNA, these defects correspond to bends. These bend lead to cyclization of short DNA molecules. We also study transcription, genetic coding also genetic information from this viewpoint of denaturation .

Abstract: Application of information technology in health care helps gain valuable knowledge from data to guide decision making in practice of medicine. Meta-analysis can help medical researchers and physicians to synthesize results and data in studies to identify effective treatments. Different steps in planning, conducting and reporting will be presented. Meta-analysis for different types of data, statistical methods and tools to analyze them in different settings and assessing the strength of evidence will be presented. How research synthesis helps in clinical decision making will be demonstrated

Abstract: In this paper, we consider a variant of a discrete time Galton Watson Branching Process in which an individual is allowed to survive for more than one (but finite) number of generations and may also give birth to off-springs more than once. We derive conditions on the mean matrix that determines the long-run behavior of the process. Next, we analyze the distribution of the number of forefathers in a given generation. Here, number of forefathers of an individual is defined as all the individuals since zeroth generation who have contributed to the birth of the individual under consideration. We derive an exact expression for expected number of individuals in a given generation having a specified number of forefathers. A simulation based analysis is also performed assuming that the offspring distribution is (a) binomial, (b) Poisson and (c) negative binomial. Some interesting insights and possible applications are also discussed.

Abstract: This article delineates the implementation of Product of spacings under Progressive Hybrid Type-I censoring with binomial removals. Both point and interval estimates of the parameters of generalized inverse Lindley distribution have been obtained under classical as well as Bayesian paradigm using product of spacings. The proposed estimators can be used in lieu of Maximum likelihood estimator and usual Bayes estimator based on likelihood function which is corroborated by a comparative simulation study. The implicit integrals involved in the process are evaluated using Metropolis-Hastings algorithm within Gibbs sampler. The applicability of the proposed methodology is demonstrated by analysing a real data set of active repair times for an airborne communication transceiver.