INFERENCE

in statistics, the process of drawing conclusions about a particular parameter of a statistical distribution. One principal approach of statistical inference is the Bayesian estimation, in which conclusions are based upon posterior judgments about the parameter given an experimental outcome (that is, prior judgments about the parameter and about the chances of the experimental outcome conditional to values of the parameter are assumed). A second is the likelihood approach, in which all conclusions are based upon the likelihood function of the parameter given the experimental outcomethat is, the emphasis is on the distribution function of the experimental outcome conditioned on the parameter considered as a function of the possible parameter values, instead of considering the distribution function as a function of the experimental outcome. In nonparametric inference, estimators of information about the distribution function do not depend on the mathematical form of the distribution function; hence they are called nonparametric in contrast to parametric estimators, which are used to estimate parameter values of an unknown distribution having an unknown functional form. in logic, derivation of conclusions from given information or premises by any acceptable form of reasoning. Inferences are commonly drawn (1) by deduction, which, by analyzing valid argument forms, draws out the conclusions implicit in their premises, (2) by induction, which argues from many instances to a general statement, (3) by probability, which passes from frequencies within a known domain to conclusions of stated likelihood, and (4) by statistical reasoning, which concludes that, on the average, a certain percentage of a set of entities will satisfy the stated conditions. See also deduction; implication.