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2.2 Multiple observations. ... Bayesian inference (/ ... Solomonoff's Inductive inference is the theory of prediction based on observations; for example, ...
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery". A stated confidence level generally applies only to each test considered individually, but often it is desirable to have a confidence level for the whole family of simultaneous tests. [ 4 ]
A Mastermind player uses abduction to infer the secret colors (top) from summaries (bottom left) of discrepancies in their guesses (bottom right).. Abductive reasoning (also called abduction, [1] abductive inference, [1] or retroduction [2]) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations.
For example, one might argue that it is valid to use inductive inference in the future because this type of reasoning has yielded accurate results in the past. However, this argument relies on an inductive premise itself—that past observations of induction being valid will mean that future observations of induction will also be valid.
Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling.Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model.
The importance of the statistical syllogism was urged by Henry E. Kyburg, Jr., who argued that all statements of probability could be traced to a direct inference. For example, when taking off in an airplane, our confidence (but not certainty) that we will land safely is based on our knowledge that the vast majority of flights do land safely.
As a consequence, what matters is not solely the quantity of observations, but the quality and manner of observations. [5] [6] By using Bayesian probability, it may be possible to make strong causal inferences from a small sliver of data through process tracing. [5] [7] As a result, process tracing is a prominent case study method. [8]