Vocabulary for Chapter 4
Chapter 4 covers how to generate both finite and infinite mixture models from various distributions. It introduces a number of terms relating to these models. The vocabulary words for Chapter 4 are:
| finite mixture | in the context of statistic, when the distribution of interest is a combination of a few different probability distributions |
| infinite mixture | in the context of statistic, when the distribution of interest is a combination of many probability distributions (as many or more probability distributions as observations) |
| mixture model | a model for a combination of two or more different probability distributions |
| probability density function | a function giving the relative likelihood that a continuous random variable is equal to a given value. When this function is integrated over the sample space, it equals 1. |
| bimodal distribution | a distribution comprised of two modes |
| expectation-maximization (EM) algorithm | an algorithm that allows for parameter estimation in probabilistic models with incomplete data |
| data augmentation | adding variables that are not measured (latent variables) to the data |
| latent variables | variables not measured in the data |
| bivariate distribution | a combined distribution made of two random variables |
| mixture fraction | a fraction used to describe the inhomogeneity in the mixture composition |
| identifiability | an issue where there can be several explanations for the same observed values; occurs when there are too many degrees of freedom in parameters |
| marginal likelihood | the sum of the marginal distributions |
| expectation function | a function that calculates the average of all possible values of the group that an observation belongs to |
| maximization step | a step to optimize the parameters of a model |
| soft averaging | the process in which observations are not assigned to groups, rather they are added to multiple groups by using probabilities of memberships as weights |
| model averaging | the process of using several models and combining them together into a weighted model |
| zero-inflated data | data that contains a large number of zero counts |
| ChIP-Seq data | sequencing data that identifies DNA binding sites for proteins |
| chromosome | a DNA molecule that contains the genetic material of an organism |
| binding site | in the context of molecular biology, a specific region to which a macromolecule binds |
| deoxyribonucleotide monophosphate | a single phosphate group in a unit of DNA |
| gene expression measurement | the measurement of a functional gene product (i.e., protein or RNA) |
| microarray | a laboratory tool used to detect gene expression |
| promoter | in the context of genetics, a region of DNA that initiates transcription of a gene |
| point mass | a finite probabiliity concentrated at a point in the proability mass distribution at which there is a discontinuous segment in probability density function |
| sampling distribution | the probability distribution calculated from a random sample |
| empirical cumulative distribution function (ECDF) | a step distribution function based on empirical data measurements |
| density | in the context of probability distributions, the derivitive of the distribution function |
| bootstrap | an approximation of the true sampling distribution; created by drawing new samples from the empirical distribution of the original sample |
| non-parametric method | a statistical method that does not make assumptions about population distribution or sample size |
| nonparametric bootstrap | an approximation of the true sampling distribution not based off of a specific assumption or a particular model |
| Laplace distribution | a distribution that shows differences between two independent variates with identical exponential distributions |
| gamma distribution | a distribution that is positively valued and continuous with two parameters: shape and scale |
| negative binomial distribution/ gamma-Poisson distubtion | the probability distribution of the number of failures before the kth success in a sequence of Bernoulli trials |
| dispersion | the amount by which a set of observations deviate from their mean |
| variance-stabilizing transformations | transformations designed to give approximate independence between mean and variance |
| heteroscedasticity | the variance of the data is different in different regions of the data |
| delta method | a calculus procedure that uses random variables to approximate the expected value and variance of a function |
Sources consulted or cited
Some of the definitions above are based in part or whole on listed definitions in the following sources.
- Holmes and Huber, 2019. Modern Statistics for Modern Biology. Cambridge University Press, Cambridge, United Kingdom.
- Everitt and Skrondal, 2010. The Cambridge Dictionary of Statistics (Fourth Edition). Cambridge University Press, Cambridge, United Kingdom.
- Zero-Inflated Poisson Regression. Institute for Digital Research and Education Statistical Consulting. https://stats.idre.ucla.edu/r/dae/zip/.
- Berrar, 2019. Introduction to Non-parametric Bootstrap. Research Gate. https://www.researchgate.net/
- Do and Batzoglou, 2008. What is the expectaion maximization algorithm?. Nature Biotechnology.
- Wikipedia: The Free Encylcopedia. https://en.wikipedia.org/wiki/Main_Page
- Google Oxford American Dictionary. https://www.google.com
- d’Auzay, et al., 2019. Statistics of progress variable and mixture fraction gradients in an open turbulent jet spray flame. Fuel.
- Brownlee, 2019. A Gentle Introduction to Expectation-Maximization (EM Algorithm). Machine Learning Mastery. https://www.machinelearningmastery.com
- Non-parametric Methods. R tutorial. https://www.r-tutor.com
- Precise analysis of DNA–protein binding sequences. Illumina. https://www.illumina.com
- Microarray. Nature. https://www.nature.com
Practice
Amy Fox
Graduate Student in Microbiology, Immunology, and Pathology
She's interested in using computational tools to answer biological questions.