A Method of Finding Predictor Genes for a Particular Disease Using a Clustering Algorithm

Clustering Algorithms are nowadays really important tools in microarray data analysis. The different clustering algorithm generally used in biological science does not take into consideration the underlying probability distribution of the data. In this sense, they are heuristic in nature. In this work we proposed a clustering algorithm based on EM Algorithm. It gives 28% less misclassification than the K-means algorithm (which is mostly use in Bio science). We have also shown on a real data set that this algorithm can be efficiently used for detecting the genes which are responsible for a particular disease.     

Rao and Wu's re-scaling bootstrap modified to achieve extended coverages

Horvitz and Thompson's (HT) [1952. A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47, 663–685] well-known unbiased estimator for a finite population total admits an unbiased estimator for its variance as given by [Yates and Grundy, 1953. Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. B 15, 253–261], provided the parent sampling design involves a constant number of distinct units in every sample to be chosen. If the design, in addition, ensures uniform non-negativity of this variance estimator, Rao and Wu [1988. Resampling inference with complex survey data. J. Amer. Statist. Assoc. 83, 231–241] have given their re-scaling bootstrap technique to construct confidence interval and to estimate mean square error for non-linear functions of finite population totals of several real variables. Horvitz and Thompson's estimators (HTE) are used to estimate the finite population totals. Since they need to equate the bootstrap variance of the bootstrap estimator to the Yates and Grundy's estimator (YGE) for the variance of the HTE in case of a single variable, i.e., in the linear case the YG variance estimator is required to be positive for the sample usually drawn.     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

DOMAIN ESTIMATION IN FINITE POPULATIONS1

This paper suggests unbiased estimators (UE's) for the size, mean and total of a domain, with specific features, in a given finite population on the basis of simple random sampling without replacement (SRSWOR) continued till a preassigned number of domain members is observed.     

Bhattacharyya distance based linear discriminant function for stationary time series

The problem of classifying a covariance stationary normal time series is considered. Under certain regularity conditions, a compact form of the linear discriminant function in the sense of maximizing the Bhattacharyya distance is obtained.     

A new unrelated question randomized response model

In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied.     

Hypogonadotrophic hypogonadism in type 2 diabetes

Recent work shows a high prevalence of low testosterone and inappropriately low luteinizing hormone (LH) and follicle stimulating hormone (FSH) concentrations in type 2 diabetes. This syndrome of hypogonadotrophic hypogonadism (HH) is associated with obesity in patients with type 2 diabetes. However, the duration of diabetes or HbA1c are not related to HH. Furthermore, recent data show that HH is not associated with type 1 diabetes. C-reactive protein concentrations have been shown to be elevated in patients with HH and are inversely related to plasma testosterone concentrations. This inverse relationship between plasma free testosterone and C- reactive protein concentrations in patients with type 2 diabetes suggests that inflammation may play an important role in the pathogenesis of this syndrome. This is of interest since inflammatory mechanisms may have a cardinal role in the pathogenesis of insulin resistance. It is also relevant that in the mouse, deletion of the insulin receptor in neurons leads to HH in addition to a state of systemic insulin resistance. It has also been shown that insulin facilitates the secretion of gonadotrophin releasing hormone (GnRH) from neuronal cell cultures. Thus, HH may be the result of insulin resistance at the level of the GnRH secreting neuron. Low testosterone concentrations are also related to an increase in total and regional adiposity. This review discusses these issues and attempts to make the syndrome relevant as a clinical entity. Clinical trials are required to determine whether testosterone replacement alleviates insulin resistance and inflammation. In addition, low testosterone levels are associated with an increase in cardiovascular events. Testosterone therapy may therefore, reduce cardiovascular risk. This important aspect requires further investigation.     

Some implications of an intensity measure of envy

This article proposes a cardinal or an intensity measure of interpersonal envy by directly measuring the distance between the envied person's consumption bundle and the envious person's equilibrium indifference curve. The individual's intensity of envy is aggregated to form a social envy index, which in turn is combined with the Pareto criterion to form a social choice rule. This social choice rule generates a non-empty choice set with the fair set (envy-free and Pareto efficient social states) as a proper subset of the choice set. The intensity measure of envy is then applied to the Rawlsian problem of the worst-off person. It turns out that the person with the greatest envy need not be the poorest person. Finally, it is shown that if individuals have homothetic and identical preferences the measure of envy collapses into a measure of income inequality. This measure of income inequality satisfies soem appealing axioms.I am grateful to William Vickrey and Duncan Foley for orginally encouraging the idea of intensity of envy. This version has benefited greatly from suggestions and criticisms made by F. William McElroy     

“I Will Be Out There Every Day Strong!” Protest Policing and Future Activism Among Ferguson and Baltimore Protesters

An established body of literature shows that people engage in protest events for a number of reasons, including grievances, collective identity, increased efficacy, and emotions. However, it is unclear what happens to individuals’ motivation toward protest participation as they experience the reality of repressive policing. This study contributes to the theoretical body of knowledge of protest policing and social movements by investigating the microlevel processes that affect protest participation. Specifically, we build from the insights of previous research by examining how 102 Ferguson and Baltimore protesters with varying levels of commitment—revolutionary, intermittent, tourist—experienced repressive policing and how such tactics affected their subsequent decision to engage in future activism. Our findings suggest that those with the strongest commitment toward protest goals experienced the most repressive tactics, and yet did not seem to be deterred in their motivation to be engaged in future protests. In contrast, while repressive tactics appeared to deter the less committed individuals from street protests, they remained motivated to engage in other forms of civic engagement.     

Small domain estimation by empirical bayes and kalman filtering procedures - a case study

An application of empirical Bayes and Kalman filtering tecniques is reported, using live data from Indian Statistical Institute (ISI), Calcutta . to illustrate how initial small domain estimators may be vastly improved upon. A stratified two stage sampling procedure is adopted, allowing selection of first stage units with unequal probabilities but of second stage units with equal probabilities. Standard design-based estimators for domain totals are initialized based on domain specific survey data alone. Strength is then borrowed across domains and from past surveys. The resulting gains in efficacy are numlerically demonstrated, through replicated sampling from official records.