Statistical Inference

TL;DR

This paper discusses the diverse perspectives on statistics, emphasizing its role as a mathematical engineering discipline focused on extracting reliable information from limited data for learning, prediction, and decision making under uncertainty.

Contribution

It provides an overview of statistical inference as a branch of mathematical engineering, highlighting its practical importance and varying attitudes among practitioners and theoreticians.

Findings

Statistics as a mathematical engineering discipline

Diverse attitudes towards statistical methods

Importance of reliable information extraction from limited data

Abstract

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly reporting p-values and claiming statistical significance for scientifically insignificant results. In these notes statistics is viewed as a branch of mathematical engineering, that studies ways of extracting reliable information from limited data for learning, prediction, and decision making in the presence of uncertainty. These ACM lecture notes are based on the courses the author taught at the University of Southern California in 2012 and 2013, and at the California Institute of Technology in 2016.