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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.
The Nuova Cronica, a 14th-century history of Florence by the Florentine banker and official Giovanni Villani, includes much statistical information on population, ordinances, commerce and trade, education, and religious facilities and has been described as the first introduction of statistics as a positive element in history, [3] though neither ...
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]
A philosopher of statistics from the frequentist perspective has observed a shift from the statistical domain to philosophical interpretations of probability over the past two generations. [27] Some perceive that the successes achieved with Bayesian applications do not sufficiently justify the associated philosophical framework. [ 28 ]
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.
The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of statistics appeared. More recently, a collection of summarisation techniques has been formulated under the heading of exploratory data analysis : an example of such a ...
In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened). The random variable itself is the process dictating how the observation comes about.