ⓘ Doubly stochastic model
In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling timeseries and stochastic processes.
The basic idea for a doubly stochastic model is that an observed random variable is modelled in two stages. In one stage, the distribution of the observed outcome is represented in a fairly standard way using one or more parameters. At a second stage, some of these parameters often only one are treated as being themselves random variables. In a univariate context this is essentially the same as the wellknown concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a timeseries or stochastic model are simultaneously affected by the underlying parameters, either by using a single parameter affecting many outcome variates, or by treating the underlying parameter as a timeseries or stochastic process in its own right.
The basic idea here is essentially similar to that broadly used in latent variable models except that here the quantities playing the role of latent variables usually have an underlying dependence structure related to the timeseries or spatial context.
An example of a doubly stochastic model is the following. The observed values in a point process might be modelled as a Poisson process in which the rate the relevant underlying parameter is treated as being the exponential of a Gaussian process.
 and stochastic process as two different objects such that a point process is a random object that arises from or is associated with a stochastic process
 where it can be considered as a stochastic process. In this setting, it is used, for example, in queueing theory to model random events, such as the arrival
 R. 2011 State  dependent doubly weighted stochastic simulation algorithm for automatic characterization of stochastic biochemical rare events Journal
 Asmussen, Soren Glynn, Peter W. 2007 Stochastic Simulation: Algorithms and Analysis. Stochastic Modelling and Applied Probability. 57. Springer. Atzberger
 copula models are outlined below. Two  dimensional copulas are known in some other areas of mathematics under the name permutons and doubly  stochastic measures
 proof for existence is similar with Birkhoff von Neumann theorem for doubly stochastic matrix. Here is an example that illustrates the existence and non  uniqueness
 beyond the Standard Model BSM refers to the theoretical developments needed to explain the deficiencies of the Standard Model such as the strong CP
 by an arriving customer. The property also holds for the case of a doubly stochastic Poisson process where the rate parameter is allowed to vary depending
 diffraction  limited output. S. Kawakami, S. Nishida 1974 Characteristics of a doubly clad optical fiber with a low  index inner cladding IEEE Journal of Quantum
 Supersymmetric Standard Model MSSM is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers
 limit of the infinitely long temporal evolution and the model can be said to exhibit the stochastic generalization of the butterfly effect. From a more
Latent variable model 
Dynamic unobserved effects model 
Factor regression model 
Firstdifference estimator 
Nuisance variable 
Partial least squares regression 
Film 
Television show 
Game 
Sport 
Science 
Hobby 
Travel 
Technology 
Brand 
Outer space 
Cinematography 
Photography 
Music 
Literature 
Theatre 
History 
Transport 
Visual arts 
Recreation 
Politics 
Religion 
Nature 
Fashion 
Subculture 
Animation 
Award 
Interest 
Users also searched:
...
