用英语回答,Fisher信息量是什么?如何理解?
时间: 2024-05-30 17:08:14 浏览: 12
The Fisher information is a measure of how much information a random variable X carries about an unknown parameter θ of a probability distribution. It is defined as the expected value of the square of the derivative of the log-likelihood function with respect to the parameter θ.
In other words, the Fisher information quantifies the sensitivity of the log-likelihood function to changes in the parameter θ. A higher Fisher information indicates that small changes in θ will have a larger impact on the log-likelihood function, and therefore provide more information about the parameter.
Intuitively, we can think of the Fisher information as a measure of the precision with which we can estimate a parameter based on a given amount of data. A higher Fisher information means that we can estimate the parameter more precisely, while a lower Fisher information means that our estimates will be more uncertain.
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