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Course# MATH-236: Probability and statistics II

Summary

Linear statistical methods, analysis of experiments, logistic regression.

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Lectures in this course (36)

Principal Component Analysis: Understanding Data Structure

Explores Principal Component Analysis, dimensionality reduction, data quality assessment, and error rate control.

Goodness-of-fit Tests in Statistics

Explores goodness-of-fit tests, X² tests, and independence tests in statistics, with practical examples and applications.

ANOVA and Factorial Experiments

Explores ANOVA, factorial experiments, and model evaluation techniques.

Genetic Linkage and Association Studies

Explores genetic linkage, association studies, polymorphisms, and LD in genetic mapping.

Estimation Methods: Bias-Variance Tradeoff

Explores the MSE quality measure for estimators and the bias-variance tradeoff.

Related concepts (268)

Blocking (statistics)

In the statistical theory of the design of experiments, blocking is the arranging of experimental units that are similar to one another in groups (blocks). Blocking can be used to tackle the problem of pseudoreplication. Blocking reduces unexplained variability. Its principle lies in the fact that variability which cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is confounded or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product.

Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis, a subfield of mathematics, linear prediction can be viewed as a part of mathematical modelling or optimization. The most common representation is where is the predicted signal value, the previous observed values, with , and the predictor coefficients.

Two-way analysis of variance

In statistics, the two-way analysis of variance (ANOVA) is an extension of the one-way ANOVA that examines the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA not only aims at assessing the main effect of each independent variable but also if there is any interaction between them. In 1925, Ronald Fisher mentions the two-way ANOVA in his celebrated book, Statistical Methods for Research Workers (chapters 7 and 8).

Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher (following some initial results by Francis Ysidro Edgeworth).

Tool

A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.