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In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function). It is a sample-based version of the Fisher information.
The definition can be further expanded upon to include the systematic difference between what is observed due to variation in observers, and what the true value is. [ 2 ] Observer bias is the tendency of observers to not see what is there, but instead to see what they expect or want to see.
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statistics, but has some adherents and applications. The central idea of likelihoodism is the likelihood principle : data are interpreted as evidence , and the strength of the evidence is measured by the likelihood function.
Specific sampling features, such as station, specimen, transect, section, are used in many application domains, and common processing and visualization tools are used. The standard defines a common set of sampling feature types classified primarily by spatial dimension, as well as samples for ex situ observations.
The former is based on deducing answers to specific situations from a general theory of probability, meanwhile statistics induces statements about a population based on a data set. Statistics serves to bridge the gap between probability and applied mathematical fields. [10] [5] [11]
Some examples of statistics are: "In a recent survey of Americans, 52% of women say global warming is happening." In this case, "52%" is a statistic, namely the percentage of women in the survey sample who believe in global warming.
In some specific fields of science, the results of observation differ depending on factors that are not important in everyday observation. These are usually illustrated with apparent " paradoxes " in which an event appears different when observed from two different points of view, seeming to violate "common sense".