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Model. Generalized linear mixed models are generally defined such that, conditioned on the random effects , the dependent variable is distributed according to the exponential family with its expectation related to the linear predictor via a link function : . Here and are the fixed effects design matrix, and fixed effects respectively; and are ...
Generalized additive model. In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert ...
Model predictive control. Model predictive control ( MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models [ 1 ...
Autoregressive model. In statistics, econometrics, and signal processing, an autoregressive ( AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc. The autoregressive model specifies that the output variable depends linearly on its own ...
Vector autoregression(VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic processmodel. VAR models generalize the single-variable (univariate) autoregressive modelby allowing for multivariate time series.
Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), relying solely on the input-output behavior. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points.
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
e. In statistics, linear regression is a statistical model which estimates the linear 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 ...