Publications by Minerva Mukhopadhyay
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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Deterministic Approx
Background In Bayesian paradigm `probability is regarded as a subjective measure of belief’. Let \(\{ p({\bf y}\mid \boldsymbol{\theta}); \boldsymbol{\theta} \in \Theta\}\) be the model, i.e., the data \(\mathcal{Y}\) is coming from the conditional distribution \(p({\bf y}\mid \boldsymbol{\theta})\) conditioned on \(\boldsymbol{\theta} \in \Th...
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MTH211A: Introduction
MTH211A: Theory of Statistics Author Minerva Mukhopadhyay Course policy: See the first course handout. Prerequisite: MSO201A or MSO205A. What is the idea of this course? The basic idea of this course is to learn to infer about an underlying truth from the data. Example: Salt experiment “During the communal riots in Delhi in 1947, many pe...
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MTH211A: Lecture 1
Descriptive Statistics Author Minerva Mukhopadhyay The term “descriptive statistics” refers to the analysis, summary, and presentation of findings related to a data set derived from a sample or the entire population. Lecture 1: (I) Data collection One meaning of Statistics is “data”. The subject Statistics teaches the tool of obtaini...
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MTH211A: Today's Lecture
Table of contents Lecture 2: Methods of Sampling (I) Simple Random Sampling: (II) Simple Random Sampling With and Without Replacement: Simple random sampling with replacement (SRSWR): Simple random sampling without replacement (SRSWOR): (III) How accurate is the simple random sample estimate when we are interested in the population mean of a ...
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PCA_demo
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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Factor Analysis Demonstration
We will understand the methods of factor analysis using the Boston housing data set. \[\\[.02 in]\] Boston Housing Data Boston housing data contains information collected by the U.S Census Service concerning housing in the area of Boston Mass. It has been used extensively throughout the literature to benchmark algorithms. The dataset has 506 cas...
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