Lecture

Understanding Statistics & Experimental Design

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In course

BIO-449: Understanding statistics and experimental design

This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental design and to avoid common pitfalls of statistical reason ...

Description

This lecture covers various topics in statistics, including basic probability theory, signal detection theory, ANOVA, experimental design, correlations, PCA, and meta-statistics. It discusses the importance of planning multiple tests in advance, the power of ANOVA compared to other methods, and the challenges of multiple comparisons. The instructor emphasizes the need for simplicity in experimental design and the importance of power analysis. The lecture also explores examples related to tree heights, brain training programs, and orientation discrimination tasks.

Instructor

Michael Herzog

Teaching & PhD PhD Students Sandrine Brikh, Melissa Mohamad Allouche, Ece Yatikçi, Melissa Faggella, Elsa Scialom, Marie Isabelle Holdsworth, Martina Morea, Pierre Merret, Sandali Nisansa Liyanagoonawardena Past EPFL PhD Students Frank Scharnowski, Thomas Otto, Toni Saarela, Elisa Tartaglia, Bilge Sayim, Johannes Rüter, Marco Boi, Kristoffer Aberg, Yvonne Evelina Thunell, Mauro Manassi, Vitaly Chicherov, Lukasz Grzeczkowski, Marc Michael Lauffs, Ophélie Favrod, Janir Nuno Ramos da Cruz, Adrien Doerig, Lei

Official source

Related concepts (32)

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Probability axioms

The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .

Bayesian probability

Bayesian probability (ˈbeɪziən or ˈbeɪʒən ) is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief. The Bayesian interpretation of probability can be seen as an extension of propositional logic that enables reasoning with hypotheses; that is, with propositions whose truth or falsity is unknown.

Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event consisting of only a single outcome is called an or an ; that is, it is a singleton set. An event is said to if contains the outcome of the experiment (or trial) (that is, if ).

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