Publications by Minerva Mukhopadhyay
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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MTH211A: Point Estimation: Part 1
Table des matières Lecture 1: What is inference? Some Definitions and Terminologies: Principles of Data Reduction Lecture 2: The Sufficiency Principle Definition: [Sufficient Statistic] Explanation: Theorem 1 (Neyman’s Factorization Theorem) Lecture 3: Minimal Sufficiency Definition: [Minimal Sufficient Statistic] Ancillary Statistics ...
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MTH211A: Measures of Association
Table of contents Lecture 1 Pearson’s correlation coefficient: Properties of correlation coefficient: Linearity: Lecture 2: Other Measures of Association Spearman’s rank correlation coefficient: Properties of Spearman’s rank correlation: Kendall’s Tau: Comparison of Pearson’s correlation coefficient and rank correlation coefficie...
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MTH211A: Module 2
Table of contents Descriptive Measures of Statistics Lecture 1: Measures of Central Tendency (I) Arithmetic Mean (AM): Some important properties of AM: (II) Geometric Mean (GM): Some important properties of GM: (III) Harmonic Mean (HM): Some important properties of HM: Comparison of AM-GM-HM: (IV) MEDIAN: Some important properties of Me...
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