Lecture

Quantifying Statistical Dependence

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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

I was trained in physics, and always had a strong interest in biology. I am broadly interested in understanding biological phenomena in a quantitative way, through physical concepts and mathematical and computational tools. I investigate the relative impacts of optimization and historical contingency in biological evolution, both at the scale of protein sequences and at the scale of microbial populations.Here is my research group website.Curriculum vitae Here is my complete CV. Professional experience:Since

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (29)

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.

Amacrine cell

Amacrine cells are interneurons in the retina. They are named from the Greek roots a– ("non"), makr– ("long") and in– ("fiber"), because of their short neuronal processes. Amacrine cells are inhibitory neurons, and they project their dendritic arbors onto the inner plexiform layer (IPL), they interact with retinal ganglion cells, and bipolar cells or both of these. Amacrine cells operate at inner plexiform layer (IPL), the second synaptic retinal layer where bipolar cells and retinal ganglion cells form synapses.

Photoreceptor cell

A photoreceptor cell is a specialized type of neuroepithelial cell found in the retina that is capable of visual phototransduction. The great biological importance of photoreceptors is that they convert light (visible electromagnetic radiation) into signals that can stimulate biological processes. To be more specific, photoreceptor proteins in the cell absorb photons, triggering a change in the cell's membrane potential. There are currently three known types of photoreceptor cells in mammalian eyes: rods, cones, and intrinsically photosensitive retinal ganglion cells.

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.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

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Mutual Information: Continued

Explores mutual information for quantifying statistical dependence between variables and inferring probability distributions from data.

Mutual Information in Biological Data

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

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Central Limit Theorem: Properties and Applications

Explores the Central Limit Theorem, covariance, correlation, joint random variables, quantiles, and the law of large numbers.

Dependence and Correlation