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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.
Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively. Quantifying the evidence or making sense of it in qualitative form, a researcher can answer empirical questions, which should be clearly defined and answerable with the evidence collected (usually called data). Research ...
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.
A variety of objective means exist to empirically measure biodiversity. Each measure relates to a particular use of the data, and is likely to be associated with the variety of genes. Biodiversity is commonly measured in terms of taxonomic richness of a geographic area over a time interval. In order to calculate biodiversity, species evenness ...
A scientific theory is an explanation of an aspect of the natural world that can be or that has been repeatedly tested and has corroborating evidence in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results.
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 .
Such evidence is expected to be empirical evidence and interpretable in accordance with the scientific method. Standards for scientific evidence vary according to the field of inquiry, but the strength of scientific evidence is generally based on the results of statistical analysis and the strength of scientific controls. [citation needed]
The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally ...