Lecture: Mathematical Statistics

. You treat a population as an unknown random variable and a sample as a set of independent, identically distributed (iid) random variables. Theory over Data: Many instructors, like those in the MIT OpenCourseWare Jim Corkran's series

: Use criteria like bias, variance, and mean squared error to determine if a statistical test is "good" or "efficient". mathematical statistics lecture

Statistical inference is the process of making conclusions or predictions about a population based on a sample of data from that population. Statistical inference is the process of making conclusions

Choose ( \theta ) to maximize the : [ L(\theta; x_1,\dots,x_n) = \prod_i=1^n f(x_i; \theta) ] Or equivalently maximize the log-likelihood ( \ell(\theta) = \sum \log f(x_i;\theta) ). Unlike basic statistics, which focuses on applying tests

Mathematical statistics is a theoretical discipline that uses probability theory to develop and analyze the rules behind statistical tests and confidence intervals. Unlike basic statistics, which focuses on applying tests to data, mathematical statistics explores the underlying assumptions and rigorous proofs required to create new statistical tools. Core Lecture Topics