In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression. They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed.
Ordinary linear regression predicts the expected value of a given unknown quantity (the response variable, a random variable) as a linear combination of a set of observed values (predictors). This implies that a constant change in a predictor leads to a constant change in the response variable (i.e. a linear-response model). This is appropriate when the response variable can vary, to a good approximation, indefinitely in either direction, or more generally for any quantity that only varies by a relatively small amount compared to the variation in the predictive variables, e.g. human heights.
However, these assumptions are inappropriate for some types of response variables. For example, in cases where the response variable is expected to be always positive and varying over a wide range, constant input changes lead to geometrically (i.e. exponentially) varying, rather than constantly varying, output changes. As an example, suppose a linear prediction model learns from some data (perhaps primarily drawn from large beaches) that a 10 degree temperature decrease would lead to 1,000 fewer people visiting the beach.
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This course explains the mathematical and computational models that are used in the field of theoretical neuroscience to analyze the collective dynamics of thousands of interacting neurons.
This course explains the mathematical and computational models that are used in the field of theoretical neuroscience to analyze the collective dynamics of thousands of interacting neurons.
This course covers statistical methods that are widely used in medicine and biology. A key topic is the analysis of longitudinal data: that is, methods to evaluate exposures, effects and outcomes that
This course aims to introduce the basic principles of machine learning in the context of the digital humanities. We will cover both supervised and unsupervised learning techniques, and study and imple
Statistics lies at the foundation of data science, providing a unifying theoretical and methodological backbone for the diverse tasks enountered in this emerging field. This course rigorously develops
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family.
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).
Covers Generalized Linear Models, likelihood, deviance, link functions, sampling methods, Poisson regression, over-dispersion, and alternative regression models.
A novel approach for linear parameter-varying (LPV) controller synthesis for adaptive rejection of time-varying sinusoidal disturbances is proposed. Only the frequency response data of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) sys ...
2024
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Background :Sensory reafferents are crucial to correct our posture and movements, both reflexively and in a cognitively driven manner. They are also integral to developing and maintaining a sense of agency for our actions. In cases of compromised reafferen ...
2024
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Here we provide the neural data, activation and predictions for the best models and result dataframes of our article "Task-driven neural network models predict neural dynamics of proprioception". It contains the behavioral and neural experimental data (cu ...