DAMP Physics, IITB

Instructor Name: Vikram Rentala  Course Type: Theory Pre-requisites: Matrix algebra, Integration and Differentiation Course Content: Probability Theory - Axioms and Bayes' Theorem Probability Density/Distribution Functions and their characteristics (mean, variance etc.) - Exponential, Gaussian, Poisson Transformation of random variables Multivariate probability density/distribution function Contour Plots Correlation, Covariance and Independence Reduction of number of variates Probability Distributions - Bernoulli, Binomial, Multinomial, Uniform Central Limit Theorem Multidimensional Gaussian random variables Chi squared distribution and fitting experimental data Measurement Errors Averaging measurements (including correlation) Statistical Inference - drawing conclusions from data Likelihood and maximum likelihood estimate Other topics covered: Books: Introduction to Statistics and Data Analysis for Physicists - G. Bohm and G. Zech Lectures: Attendance w...

Instructor Name Vikram Rentala Course Type Core for EP students Course overview Probability axioms and theorems ;  Probability distributions - Mean, variance, skewness, kurtosis, moments, characteristic function, cumulants ; Transformation of variables ; Multivariate probability distribution ; Detailed discussion of Gaussian, Poisson, Binomial and Multinomial, Chi-squared distributions ; Statistical and Systematic errors ; Error propagation ; Error ellipses ; Parameter Inference ; Confidence Intervals ; Hypothesis Testing ;  Likelihoods ;  Goodness of Fit Test ; p-value. Brief look at other distributions like exponential, gamma, Lorentz/Cauchy/Breit-Wigner, log-normal ; Generalised approach for distributions : n-dimensions ; Likelihoods associated with histograms Prerequisites No formal or informal prerequisites. Credit distribution 2 quizzes (10% each), midsem (25%), endsem (45%), assignment (10%) . Feedback on Lectures Attendance not compu...