In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series 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 well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series or stochastic model are simultaneously affected by the underlying parameters, e
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| - Modelo doblemente estocástico (es)
- Doubly stochastic model (en)
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| - In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series 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 well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series or stochastic model are simultaneously affected by the underlying parameters, e (en)
- En estadística y teoría de la probabilidad, un modelo doblemente estocástico es un tipo de modelo que surge en muchos contextos, pero en particular en la modelización de series temporales y procesos estocásticos. Un ejemplo de modelo deoblemente estocástico es el siguiente. Los valores observados en un proceso puntual puede ser modelado por un proceso de Poisson en que la intensidad del proceso (el parámetro subyacente relevante) se trata como la exponencial de un . (es)
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| - In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series 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 well-known concept of compounded distributions. For the more general case of doubly stochastic models, there is the idea that many values in a time-series 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 time-series 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 time-series 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. (en)
- En estadística y teoría de la probabilidad, un modelo doblemente estocástico es un tipo de modelo que surge en muchos contextos, pero en particular en la modelización de series temporales y procesos estocásticos. La idea básica de un modelo doblemente estocástico es que la variable aleatoria observada se modeliza en dos estadios. En un primer estadio, se busca la distribución de un resultado observado se representa de una manera estándar usando uno o más parámetros. En un segundo estadiom algunos de estos parámetros (frecuentemente solamente uno) son tratados en sí mismos como variables aleatorias. En el contexto univariado, esto es esencialmente lo mismo que el concepto bien conocido de . Para un caso más general de modelos doblemente estocásticos, se tiene la idea de que muchos valores en una serie temporal o modelo estocástico se ven afectados por los parámetros subyacentes, o bien usando un único parámetro que afecta a los resultados, o tratando el parámetro subyacentes como una serie temporal o un proceso estocástico en sí mismo. La idea básica, por tanto, es esencialmente idéntica a los modelos ampliamente usados llamados excepto que aquí las cantidades desempeñan un papel de variable latente. Un ejemplo de modelo deoblemente estocástico es el siguiente. Los valores observados en un proceso puntual puede ser modelado por un proceso de Poisson en que la intensidad del proceso (el parámetro subyacente relevante) se trata como la exponencial de un . (es)
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