Syllabus - Advanced Statistical Analytics (Open Elective-703 (C))

Syllabus

Introduction: Population and Sample, Random Sampling from finite population (SRSWR and SRSWOR), Parameter and Statistic, Sampling distribution of as tatistic in the context of a finite population, Sampling distribution of sample mean and sample proportion whilesampling from a finite population. Random sampling from an infinite population, Sampling Distribution of sample mean and sample variance when the sample is drawn from a Normal distribution, Problems on sampling distributions of statistics from finite and infinite populations. Statement of Lyndeberg-Levy Central Limit Theorem (CLT) and its applications.

Correlation, Regression Analysis and ANOVA

Correlation, Scatter diagram, Karl Pearson’s coefficient of correlation, Spearman’s Rank correlation coefficient, Methods of least square, Simple linear Regression model, SLR assumptions and prediction Multiple linear Regression, MLR assumption and prediction, Polynomial Regression, Logistics Regression, Poisson Regression, Non-Linear Regression Analysis of Variance (One way & Two Way). Analysis of Covariance, Multivariate Analysis of Variance

Testing of Hypothesis

Testing of Hypotheses: Null and Alternative Hypothesis, Testing Procedure (Critical region), Type I and Type II errors, Level of significance & Power of a test, p-value for symmetric null distribution. Tests for mean and proportion (single sample, two sample; exact & large sample) Tests for variance (single sample and two samples), Tests for mean and correlation coefficient for paired sample (Exact & Large sample), Analysis of Variance (one way).

Parametric Point Estimation

Problem of point estimation, Criteria of a good Estimator, Unbiasedness, Consistency, Efficiency, Sufficiency Minimum Variance and Unbiasedness (Small sample) Method of moments, Method of Maximum Likelihood, Consistency & Efficiency (Large sample), Interval Estimation: Confidence Intervals of mean and proportion in large samples.

Bayesian Statistics

Introduction to Bayesian inference, Bayesian parameter estimation, Markov Chain Monte Carlo (MCMC) methods, Bayesian hierarchical models, Survival analysis, Causal inference, High-dimensional data analysis.