Publications by Minerva Mukhopadhyay
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Table of contents How to find the UMVUE? Statistics 2: Topic 2 (continue) Author Minerva Mukhopadhyay Published February 13, 2025 So far we have been introduced to the concepts of unbiasness and efficiency. Naturally, one would ask if an (unbiased and) efficient estimator of \(\psi(\boldsymbol{\theta})\) is the best possible estimator for \...
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Table of contents Statistical Inference: Point Estimation (I) Key Takeaways What is the minimum possible value of the variance of an unbiased estimator? Statistics 2 Topic 2 Author Minerva Mukhopadhyay Statistical Inference: Point Estimation We learn some desirable properties of the estimators. (I) Key Takeaways Let \(X_{1}, \ldots, X_{n}\...
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Table of contents Inferring Population Characteristics from Samples Key Takeaways from Today’s Lecture Recall Problem iii - Finding \(E(X^2)\) when \(X \sim N_{[-2, 3]}(0,1)\) n = 100 n = 1000 n = 10000 n = 100000 Try the following: Statistics 2 Topic 1 Author Minerva Mukhopadhyay Inferring Population Characteristics from Samples This ...
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PCA Demonstration for Climate Change Workshop
Synthetic Data Analysis Motivation of PCA Let us first generate a (centered) data set to explain the theoretical properties of principal components. The motivation of Principal Component Analysis (PCA) is two fold: The \(1\)st principal component (PC) is the standardized linear combination (SLC), which has the maximum variance among all SLCs,...
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Bayesian Clustering
NCM Workshop on Introduction to Statistical Learning Techniques Author Minerva Mukhopadhyay Bayesian Clustering Bayesian way of clustering is mainly model based. It is assumed that the data points are conditionally iid with density \[ f(y \mid P) = \int K(y \mid \theta) d P(\theta) \] where \(K(\cdot \mid \theta)\) is a parametric density wi...
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NCM Workshop on Introduction to Statistical Learning Techniques Author Minerva Mukhopadhyay Bayesian Variable Selection in Linear Regression (A) Variable Selection in Linear Regression Regression is an approved and attractive tool in different fields of science for the investigation of linear dependencies among independent variables and a res...
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NCM_AIS_BVS
NCM Workshop on Introduction to Statistical Learning Techniques Author Minerva Mukhopadhyay Bayesian Variable Selection in Linear Regression (A) Variable Selection in Linear Regression Regression is an approved and attractive tool in different fields of science for the investigation of linear dependencies among independent variables and a res...
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AIS wrokshop June 2024
NCM Workshop on Introduction to Statistical Learning Techniques Author Minerva Mukhopadhyay Bayesian Variable Selection in Linear Regression (A) Variable Selection in Linear Regression Regression is an approved and attractive tool in different fields of science for the investigation of linear dependencies among independent variables and a res...
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Table of contents Definition: [Interval Estimate] Definition: [Confidence Coefficient] Methods of Finding Confidence Interval 1. Method of Pivots Definition: [Pivot] Remarks: 2. Test Inversion Remark: Method of Evaluating Confidence Intervals: Inference 3: Interval Estimation Sometimes providing a point estimate, or testing a hypothesis is...
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MTH211A: Today's Lecture
Table of contents Introduction Lecture 1: Some Definitions and Concepts: Definition: [Hypothesis] Definition: [Null Hypothesis] Definition: [One-sided or Two-sided alternatives] Definition: [Simple and Composite Hypotheses] Definition: [Hypothesis Test] Definition: [Critical and Acceptance Regions] Definition: [Type I and Type II errors] Definiti...
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