Statistical Inference

This course covers the foundational aspects of statistical inference, including sampling generation, estimators and their main properties, confindence intervals, and hyotesis testing. Students will learn practical skills for working with the basis of statistics.

Instructor: Prof. Paolo Berta

Term: October-January

Location: Bulding U6

Time: see University website

Course Overview

This course provides a comprehensive introduction to foundational aspects of statistical inference. Students will be able to:

  • apply the techniques for the precise estimation and interval of the parameters of the distribution of a random variable
  • construct statistical tests to verify hypothesis about the distribution of a normal random variable and identify appropriate approximations in the case of any random variable
  • comparing tow or more population in terms of their expected mean with two-sample test and one-way ANOVA

Prerequisites

  • Analysis
  • Introductory statistics
  • Basic probability theory

Textbooks

  • Piccolo, D. (2000). Statistica, Bologna. Il Mulino.

Detailed program

Estimate interval and methods for determining the confidence interval. The pivotal quantity. Statistical verification of hypotheses. Significance tests. The main statistical tests: the Z test, the T test, the chi-square test, the F test. The basis of Neyman-Pearson’s theory. Error of first and second species. The most powerful test is Neyman-Pearson’s lemma. The most uniformly powerful tests. The tests based on the relationship of likelihood. A series of tests to compare different populations including the Analysis of Variance (ANOVA). Sampling from finite populations. Estimation of the total, average and variance of a continuous variable. Estimate of the relative frequency of a binary variable. Simple random sampling. The stratified sampling

  • Estimation theory
  • The pivotal quantity and confidence intervals
  • Significance tests
  • The basis of Neyman-Pearson’s theory
  • The main statistical tests: the Z test, the T test, the chi-square test, the F test
  • A series of tests to compare different populations including the Analysis of Variance (ANOVA)