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MAL7060: Statistics for Data Science

Autumn 2026–27 (Semester I) · IIT Jodhpur
Core course for Executive M.Tech. (Data and Computational Science) students in their 1st year

L-T-P-D (C): 2-0-0-0 (2)
Prerequisite: Basic probability and statistics

Syllabus

Objectives

The instructor will provide an understanding of some of the statistical concepts and their real-life applications.

Learning outcomes

The students are expected to have the ability to:

  1. perform hypothesis testing and estimation of the parameters for a given parametric family of distributions;
  2. gain the basic knowledge of association, correlation, mixture models, latent models and stochastic processes;
  3. gain the knowledge of Markov chains and sequence models.

Contents

Statistical inference (14 lectures):
  1. Probability Models and Sampling Techniques (3 lectures)
    • Normal, chi-square, and \(t\) distributions
    • Basic concepts of random sampling, sampling from a normal distribution
    • Properties of the sample mean and sample variance
  2. Estimation (5 lectures)
    • Point estimation: maximum likelihood estimator, Bayes estimator
    • Methods of evaluating estimators: unbiasedness, mean squared error
    • Interval estimation: confidence intervals for the mean and the variance of a normal population using the pivot technique
  3. Testing of Hypotheses (6 lectures)
    • Basic concepts of statistical hypothesis testing, simple and composite hypotheses, critical regions
    • Type-I and Type-II errors, size and power of a test
    • UMP tests, Neyman–Pearson lemma
    • Tests for one-sample and two-sample problems from normal populations
Statistical techniques (14 lectures):
  1. Association and Correlation Analysis (6 lectures)
    • Categorical data, consistency of data, independence and association of attributes
    • Measures of association: Pearson's and Yule's measures, Goodman–Kruskal's \(\gamma\), odds ratio
    • Properties of the product moment correlation coefficient, Spearman's rank correlation coefficient
  2. Mixture Models and Latent Models (3 lectures)
    • Basic ideas, finite mixtures, continuous mixtures, conditional mixing distributions
    • Latent models
  3. Stochastic Processes (5 lectures)
    • Definition and classification of general stochastic processes
    • Poisson processes: interarrival and waiting time distributions, NHPP, compound Poisson process
    • Renewal theory: distribution of \(N(t)\), Wald's equation, renewal reward processes
    • Random walks

Textbooks

Reference Books

Online Course Material

Lectures

Classes are held online in Slot YQ:

There is no separate tutorial slot. Please note timetable adjustments as per the Academic Calendar. Doubt clarifications will be scheduled at the mutual convenience of the instructor and students.

Lecture updates will be posted on Google Classroom.

A calendar of lectures and assessment dates is maintained for this course [Google Calendar]. Sign in with your IIT Jodhpur account to view or subscribe.

Evaluation

Attendance

Attendance in lectures is compulsory. If you miss lectures for valid reasons (e.g., medical), please inform the instructor promptly. Students who do not meet the 80% attendance requirement will be awarded an F grade. [Google Sheets]

Assessments

Course materials

Check the Google Classroom page for updates.