In statistics, the restricted (or residual, or reduced) maximum likelihood (REML) approach is a particular form of maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a transformed set of data, so that nuisance parameters have no effect. In the case of variance component estimation, the original data set is replaced by a set of contrasts calculated from the data, and the likelihood function is calculated from the probability distribution of these contrasts, according to the model for the complete data set. In particular, REML is used as a method for fitting linear mixed models. In contrast to the earlier maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters. The idea underlying REML estimation was put forward by M. S. Bartlett in 1937. The first description of the approach applied to estimating components of variance in unbalanced data was by and of the University of Edinburgh in 1971, although they did not use the term REML. A review of the early literature was given by Harville. REML estimation is available in a number of general-purpose statistical software packages, including Genstat (the REML directive), SAS (the MIXED procedure), SPSS (the MIXED command), Stata (the mixed command), JMP (statistical software), and R (especially the lme4 and older nlme packages),as well as in more specialist packages such as MLwiN, HLM, ASReml, BLUPF90, wombat, Statistical Parametric Mapping and CropStat. REML estimation is implemented in Surfstat, a Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric neuroimaging data using linear mixed effects models and random field theory, but more generally in the fitlme package for modeling linear mixed effects models in a domain-general way. (Wikipedia).
Maximum and Minimum Values (Closed interval method)
A review of techniques for finding local and absolute extremes, including an application of the closed interval method
From playlist 241Fall13Ex3
Maximum Likelihood Estimation Examples
http://AllSignalProcessing.com for more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files. Three examples of applying the maximum likelihood criterion to find an estimator: 1) Mean and variance of an iid Gaussian, 2) Linear signal model in
From playlist Estimation and Detection Theory
Extreme Value Theorem Using Critical Points
Calculus: The Extreme Value Theorem for a continuous function f(x) on a closed interval [a, b] is given. Relative maximum and minimum values are defined, and a procedure is given for finding maximums and minimums. Examples given are f(x) = x^2 - 4x on the interval [-1, 3], and f(x) =
From playlist Calculus Pt 1: Limits and Derivatives
Extreme Value Statistics: Peak over Threshold methods
From playlist Extreme Value Statistics
What is the max and min of a horizontal line on a closed interval
π Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Maximum Likelihood For the Normal Distribution, step-by-step!!!
Calculating the maximum likelihood estimates for the normal distribution shows you why we use the mean and standard deviation define the shape of the curve. NOTE: This is another follow up to the StatQuests on Probability vs Likelihood https://youtu.be/pYxNSUDSFH4 and Maximum Likelihood: h
From playlist StatQuest
(ML 4.1) Maximum Likelihood Estimation (MLE) (part 1)
Definition of maximum likelihood estimates (MLEs), and a discussion of pros/cons. A playlist of these Machine Learning videos is available here: http://www.youtube.com/my_playlists?p=D0F06AA0D2E8FFBA
From playlist Machine Learning
EXTRA MATH 11C: The LS estimates are also Maximum Likelihood Estimates
Forelæsning med Per B. Brockhoff. Kapitler:
From playlist DTU: Introduction to Statistics | CosmoLearning.org
Lecture 14.5 β RBMs are infinite sigmoid belief nets [Neural Networks for Machine Learning]
Lecture from the course Neural Networks for Machine Learning, as taught by Geoffrey Hinton (University of Toronto) on Coursera in 2012. Link to the course (login required): https://class.coursera.org/neuralnets-2012-001
From playlist [Coursera] Neural Networks for Machine Learning β Geoffrey Hinton
Lecture 14E : RBMs are Infinite Sigmoid Belief Nets
Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] Lecture 14E : RBMs are Infinite Sigmoid Belief Nets
From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]
DeepMind x UCL | Deep Learning Lectures | 11/12 | Modern Latent Variable Models
This lecture, by DeepMind Research Scientist Andriy Mnih, explores latent variable models, a powerful and flexible framework for generative modelling. After introducing this framework along with the concept of inference, which is central to it, Andriy focuses on two types of modern latent
From playlist Learning resources
Lecture 14/16 : Deep neural nets with generative pre-training
Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] 14A Learning layers of features by stacking RBMs 14B Discriminative fine-tuning for DBNs 14C What happens during discriminative fine-tuning? 14D Modeling real-valued data with an RBM 14E RBMs are Infinite Sigmoid Beli
From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]
Lecture 15F : Shallow autoencoders for pre-training
Neural Networks for Machine Learning by Geoffrey Hinton [Coursera 2013] Lecture 15F : Shallow autoencoders for pre-training
From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]
Lecture 15.6 β Shallow autoencoders for pre-training [Neural Networks for Machine Learning]
Lecture from the course Neural Networks for Machine Learning, as taught by Geoffrey Hinton (University of Toronto) on Coursera in 2012. Link to the course (login required): https://class.coursera.org/neuralnets-2012-001
From playlist [Coursera] Neural Networks for Machine Learning β Geoffrey Hinton
Statistical modeling and missing data - Rod Little
Virtual Workshop on Missing Data Challenges in Computation, Statistics and Applications Topic: Statistical modeling and missing data Speaker: Rod Little Date: September 8, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Find the max and min from a quadratic on a closed interval
π Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points
From playlist Extreme Value Theorem of Functions
Howard Bondell - Bayesian inference using estimating equations via empirical likelihood
Professor Howard Bondell (University of Melbourne) presents "Do you have a moment? Bayesian inference using estimating equations via empirical likelihood", 22 October 2021.
From playlist Statistics Across Campuses