STATISTICAL COMPUTING

STATISTICAL COMPUTING (60 Hours)

Objectives:

  • To learn the probability distributions and density estimations to perform analysis of various kinds of data.
  • To explore the statistical analysis techniques using Python and R programming languages.
  • To expand the knowledge in R and Python to use it for further research.

Probability Theory: Sample Spaces- Events - Axioms – Counting - Conditional Probability and Bayes’ Theorem – The Binomial Theorem – Random variable and distributions : Mean and Variance of a Random variable-Binomial-Poisson-Exponential and Normal distributions. Curve Fitting and Principles of Least Squares- Regression and correlation.

Sampling Distributions & Descriptive Statistics: The Central Limit Theorem, distributions of the sample mean and the sample variance for a normal population, Sampling distributions (Chi-Square, t, F, z). Test of Hypothesis- Testing for Attributes – Mean of Normal Population – One-tailed and two-tailed tests, F-test and Chi-Square test - - Analysis of variance ANOVA – One way and two way classifications.

Tabular data- Power and the computation of sample size- Advanced data handling- Multiple regression- Linear models- Logistic regression- Rates and Poisson regression- Nonlinear curve fitting.

Density Estimation- Recursive Partitioning- Smoothers and Generalised Additive Models - Survivals Analysis- Analysing Longitudinal Data- Simultaneous Inference and Multiple Comparisons- Meta-Analysis- Principal Component Analysis- Multidimensional Scaling- Cluster Analysis.

Introduction to R- Packages- Scientific Calculator- Inspecting Variables- Vectors- Matrices and Arrays- Lists and Data Frames- Functions- Strings and Factors- Flow Control and Loops- Advanced Looping- Date and Times. Introduction to Python- Packages- Fundamentals of Python- Inserting and Exporting Data- Data Cleansing- Checking and Filling Missing Data- Merging Data- Operations- Joins.

Outcomes:

Students will be able to:

  • Implement statistical analysis techniques for solving practical problems.
  • Perform statistical analysis on variety of data.
  • Perform appropriate statistical tests using R and visualize the outcome.