Statistical Methods for Scientists and Engineers (Prof. Somesh Kumar, IIT Kharagpur) | Mathematics

Statistical Methods for Scientists and Engineers

Statistical Methods for Scientists and Engineers. Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course introduces some important topics in statistical methods used in science and engineering. Topics include: basic concepts of probability and distributions; parametric methods - point estimation, interval estimation, testing of hypotheses; multivariate analysis - multivariate normal distribution, Wishart and Hotelling's T-squared Distributions and their applications, classification of observations, principal component analysis; nonparametric methods - empirical distribution function, single sample problems, problems of location, Wilcoxon signed rank statistics, two sample problems, Mann-Whitney-Wilcoxon tests, scale problems, Kolmogorov-Smirnov two sample criterion, Hoeffding's U-statistics. (from nptel.ac.in)

Foundations of Probability

Review of Probability and Distributions

Lecture 01 - Foundations of Probability

Lecture 02 - Laws of Probability

Lecture 03 - Random Variables

Lecture 04 - Moments and Special Distributions

Lecture 05 - Moments and Special Distributions (cont.)

Lecture 06 - Special Distributions (cont.)

Lecture 07 - Special Distributions (cont.)

Lecture 08 - Sampling Distributions

Parametric Methods

Lecture 09 - Point Estimation: Unbiasedness, Consistency, UMVUE

Lecture 10 - Point Estimation: Completeness, Method of Moments, Maximum Likelihood

Lecture 11 - Point Estimation: Properties of Maximum Likelihood Estimation, Method of Scoring

Lecture 12 - Interval Estimation: Confidence Intervals

Lecture 13 - Interval Estimation: Confidence Intervals for proportions

Lecture 14 - Testing of Hypotheses

Lecture 15 - Testing of Hypotheses (cont.)

Multivariate Analysis

Lecture 16 - Multivariate Normal Distribution

Lecture 17 - Multivariate Normal Distribution and its Properties

Lecture 18 - Multivariate Normal Distribution and its Properties (cont.)

Lecture 19 - Random Sample from a Multivariate Normal Population, Noncentral Chi-squared Distribution

Lecture 20 - Wishart and Hotelling's T-squared Distributions and their Applications

Lecture 21 - Wishart and Hotelling's T-squared Distributions and their Applications (cont.)

Lecture 22 - Multivariate Central Limit Theorem, Problem of Classification of Observations

Lecture 23 - Classification of Observations (cont.)

Lecture 24 - Classification Procedures for Two Multivariate Normal Populations

Lecture 25 - Classifying an Observation into One of Two Multivariate Normal Populations

Lecture 26 - Classifying an Observation into One of Several Populations

Lecture 27 - Principal Component Analysis

Nonparametric Methods

Lecture 28 - Distribution-free Methods, Order Statistics

Lecture 29 - Order Statistics (cont.)

Lecture 30 - Bounds on Expected Values, Asymptotic Distributions of Order Statistics

Lecture 31 - Quantiles, Tolerance Intervals, Coverages, Empirical Distribution Function

Lecture 32 - Empirical Distribution Function (cont.)

Lecture 33 - Empirical Distribution Function (cont.), Prediction Intervals

Lecture 34 - Goodness of Fit Test, Kolmogorov?Smirnov One Sample Statistics, Single Sample Location Problems

Lecture 35 - Single Sample Location Problems: Wilcoxon Signed-rank Statistics

Lecture 36 - Single Sample Location Problems (cont.), Intro to Two Sample Problems

Lecture 37 - Two Sample Problems (cont.)

Lecture 38 - Mann-Whitney-Wilcoxon Test, Scale Problems

Lecture 39 - Sukhatme Test, Consistency of Statistical Tests, Consistency of Mann-Whitney Test

Lecture 40 - General Two Sample Problem, Efficiency of Tests, Hoeffding's U-statistics

References

Statistical Methods for Scientists and Engineers
Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur. This course introduces some important topics in statistical methods used in science and engineering.