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The English term empirical derives from the Ancient Greek word ἐμπειρία, empeiria, which is cognate with and translates to the Latin experientia, from which the words experience and experiment are derived.
Empirical research is research using empirical evidence. It is also a way of gaining knowledge by means of direct and indirect observation or experience. Empiricism values some research more than other kinds. Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively.
Empirical evidence is essential to a posteriori knowledge or empirical knowledge, knowledge whose justification or falsification depends on experience or experiment. A priori knowledge, on the other hand, is seen either as innate or as justified by rational intuition and therefore as not dependent on empirical evidence.
The arithmetic mean of a population, or population mean, is often denoted μ. [2] The sample mean ¯ (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator).
The scientific method is an empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. The scientific method involves careful observation coupled with rigorous skepticism, because cognitive assumptions can distort the interpretation of the observation.
For example, Karl Popper once wrote that "In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory." [23] [24] Albert Einstein said: The scientific theorist is not to be envied.
In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise definition is found below. The precise definition is found below.
In probability theory, an empirical process is a stochastic process that characterizes the deviation of the empirical distribution function from its expectation. In mean field theory , limit theorems (as the number of objects becomes large) are considered and generalise the central limit theorem for empirical measures .