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Lecture

Quantifying Statistical Dependence

In course

BIO-369: Randomness and information in biological data

Biology is becoming more and more a data science, as illustrated by the explosion of available genome sequences. This course aims to show how we can make sense of such data and harness it in order to understand biological processes in a quantitative way. ...

Description

This lecture continues the discussion on maximum likelihood applications, focusing on quantifying statistical dependence. Topics covered include covariance, correlation, mutual information, and identifying coevolving sites in interacting proteins using sequence data. The lecture also delves into inferring probability distributions from data, model selection, parameter estimation, maximum entropy inference, and predicting protein structure from sequence data.

Instructor

Anne-Florence Raphaëlle Bitbol

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

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 density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

Rod cell

Rod cells are photoreceptor cells in the retina of the eye that can function in lower light better than the other type of visual photoreceptor, cone cells. Rods are usually found concentrated at the outer edges of the retina and are used in peripheral vision. On average, there are approximately 92 million rod cells (vs ~6 million cones) in the human retina. Rod cells are more sensitive than cone cells and are almost entirely responsible for night vision.

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Explores mutual information in biological data, emphasizing its role in quantifying statistical dependence and analyzing protein sequences.

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Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Probability and Statistics

Covers probability, statistics, independence, covariance, correlation, and random variables.

Variance and Covariance: Properties and Examples