Editing Expectation–maximization algorithm (section)

== Applications ==
*EM is frequently used for [[parameter estimation]] of [[mixed model]]s,<ref>{{cite journal |doi=10.1080/01621459.1988.10478693 |title=Newton—Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data |journal=Journal of the American Statistical Association |volume=83 |issue=404 |pages=1014 |year=1988 |last1=Lindstrom |first1=Mary J |last2=Bates |first2=Douglas M }}</ref><ref>{{cite journal |doi=10.2307/1390614 |jstor=1390614 |title=Fitting Mixed-Effects Models Using Efficient EM-Type Algorithms |journal=Journal of Computational and Graphical Statistics |volume=9 |issue=1 |pages=78–98 |year=2000 |last1=Van Dyk |first1=David A }}</ref> notably in [[quantitative genetics]].<ref>{{cite journal |doi=10.1111/anzs.12208 |title=A new REML (parameter expanded) EM algorithm for linear mixed models |journal=Australian & New Zealand Journal of Statistics |volume=59 |issue=4 |pages=433 |year=2017 |last1=Diffey |first1=S. M |last2=Smith |first2=A. B |last3=Welsh |first3=A. H |last4=Cullis |first4=B. R |doi-access=free |hdl=1885/211365 |hdl-access=free }}</ref>
*In [[psychometrics]], EM is an important tool for estimating item parameters and latent abilities of [[item response theory]] models.
*With the ability to deal with missing data and observe unidentified variables, EM is becoming a useful tool to price and manage risk of a portfolio.{{Citation needed|date=November 2017}}
*The EM algorithm (and its faster variant [[ordered subset expectation maximization]]) is also widely used in [[medical imaging|medical image]] reconstruction, especially in [[positron emission tomography]], [[single-photon emission computed tomography]], and x-ray [[computed tomography]]. See below for other faster variants of EM.
*In [[structural engineering]], the Structural Identification using Expectation Maximization (STRIDE)<ref>Matarazzo, T. J., and Pakzad, S. N. (2016). “STRIDE for Structural Identification using Expectation Maximization: Iterative Output-Only Method for Modal Identification.” Journal of Engineering Mechanics.http://ascelibrary.org/doi/abs/10.1061/(ASCE)EM.1943-7889.0000951</ref> algorithm is an output-only method for identifying natural vibration properties of a structural system using sensor data (see [[Operational Modal Analysis]]).
*EM is also used for [[data clustering]]. In [[natural language processing]], two prominent instances of the algorithm are the [[Baum–Welch algorithm]] for [[hidden Markov models]], and the [[inside-outside algorithm]] for unsupervised induction of [[probabilistic context-free grammar]]s.
*In the analysis of intertrade [[waiting time]]s i.e. the time between subsequent trades in [[share (finance)|shares of stock]] at a [[stock exchange]] the EM algorithm has proved to be very useful.<ref>{{Cite journal|last1=Kreer|first1=Markus|last2=Kizilersu|first2=Ayse|last3=Thomas|first3=Anthony W.|date=2022|title=Censored expectation maximization algorithm for mixtures: Application to intertrade waiting times|journal=Physica A: Statistical Mechanics and Its Applications|volume=587|issue=1|pages=126456|doi=10.1016/j.physa.2021.126456|bibcode=2022PhyA..58726456K |s2cid=244198364 |issn=0378-4371|url=https://www.sciencedirect.com/science/article/pii/S0378437121007299}}</ref>