Statistics

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

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Journal of Statistical Research

Analysis of ordinal longitudinal data using semi-parametric mixed models

Proper classification of different astronomical objects are of great importance in order to study the nature of origin of those objects. Although clustering and classification techniques are exploratory in nature, there are model based techniques which use distributional assumptions extensively. Many astronomical data sets related to galaxies, globular clusters, pulsars, among others, show complicated non-Gaussian nature. For classification a common practice is to use a discriminant function based on normality assumption, which may result in severe amount of loss of accuracy if the underlying distribution is quite different from Gaussian. The present paper makes an attempt to develop a likelihood ratio based procedure for classification when the underlying data are skewed and in addition, there are some missing observations. The efficiency of the classifier has been verified on the basis of simulation and also a real data set corresponding to different parameters of Globular Clusters (GCs) of an elliptical galaxy NGC 5128. © ISOSS Publications 2016.

Journal of Applied Probability and Statistics

Classification under non-Gaussian set up: An astrostatistical problem

An allocation function, invariant under monotonic transformation, is proposed in the context of multi-arm clinical trials for a class of continuous response distributions. The aim is to skew the allocation towards the most promising treatment using the whole information about the response distributions. A response adaptive implementation based on the proposed allocation function is suggested and assessed through some useful performance measures.

GENERAL

Statistics and its Interface

An invariant allocation function for multi-treatment clinical trials

Einstein, Tagore and the Nature of Reality

Preface

Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike classification, in clustering one has to first decide the optimum number of clusters and then assign the objects into different clusters. Solution of such problems for a large number of high dimensional data points is quite complicated and most of the existing algorithms will not perform properly. In the present work a new clustering technique applicable to large data set has been used to cluster the spectra of 702248 galaxies and quasars having 1,540 points in wavelength range imposed by the instrument. The proposed technique has successfully discovered five clusters from this 702,248X1,540 data matrix. © 2016 Taylor & Francis Group, LLC.

Fulltext

Communications in Statistics - Theory and Methods

Clustering large number of extragalactic spectra of galaxies and quasars through canopies

Traditionally optimal target allocation proportions for response-adaptive designs are derived by completely ignoring the actual adaptive randomization procedure. Considering efficiency of the allocation designs, we derive near efficient target proportions to balance between individual and collective ethics. Performance of the derived allocation targets are assessed numerically for binary, normal and exponential responses. Generalization for multiple treatments is also addressed. © The Author(s) 2012.

Statistical Methods in Medical Research

Near efficient target allocations in response-adaptive randomization

Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still largely in use, together with numerous mono- or bivariate classifications most often made by eye. However, a classification must be driven by the data, and sophisticated multivariate statistical tools are used more and more often. In this paper we review these different approaches in order to situate them in the general context of unsupervised and supervised learning. We insist on the astrophysical outcomes of these studies to show that multivariate analyses provide an obvious path toward a renewal of our classification of galaxies and are invaluable tools to investigate the physics and evolution of galaxies.

Frontiers in Astronomy and Space Sciences

Multivariate approaches to classification in extragalactic astronomy

In a mixture experiment, the response depends on the proportions of the mixing components. Canonical models of different degrees and also other models have been suggested to represent the mean response. Optimum designs for estimation of the parameters of the models have been investigated by different authors. In most cases, the optimum design includes the vertex points of the simplex as support points of the design, which are not mixture combinations in the true non-trivial sense. In this paper, optimum designs have been obtained when the experimental region is an ellipsoidal subspace of the entire factor space which does not cover the vertex points of the simplex. © 2013 Springer-Verlag Berlin Heidelberg.

Statistical Papers

Optimum mixture designs in a restricted region

A randomized two treatment allocation design, conducted in two stages, is proposed for a class of continuous response trials. Patients are assigned to each treatment in equal numbers in the first stage and p value of a test of equality of treatment effects based on these data is used to determine the assignment probability of second stage patients. Relevant properties of the proposed allocation design are investigated and compared with suitable competitors. © 2014, Springer-Verlag Berlin Heidelberg.

Statistical Methods and Applications

A randomized two stage allocation for continuous response clinical trials

Independent component analysis (ICA) is closely related to principal component analysis (PCA). Whereas ICA finds a set of source variables that are mutually independent, PCA finds a set of variables that are mutually uncorrelated. Here we consider an objective classification of different regions in central Iowa, USA, in order to study the pollution level. The study was part of the Soil Moisture Experiment 2002. Components responsible for significant variation have been obtained through both PCA and ICA, and the classification has been done by K-Means clustering. Result shows that the nature of clustering is significantly improved by the ICA. © 2014, Springer Science+Business Media New York.