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I am beginning to learn statistics and made some searches in Internet about statistics. Most of the articles I found says that there are two different approaches (or schools, or methods) in statistics Frequentist and Bayesian. But one article says that there are also Information-Theoretic and Likelihood. So how many different approaches (or schools, or methods) are in statistics, 2, 3, 4 or may be more?

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    $\begingroup$ Velcome to the site! $\endgroup$ – kjetil b halvorsen Jun 3 '14 at 12:48
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    $\begingroup$ Don't think there's a definite answer: how different does one approach have to be from another before it forms a separate "school"? The frequentist school could be divided into one for design-based inference & one for model-based inference. The latter might well be divided into decision theorists (headed by say Wald) vs likelihoodlums (headed by say Sprott). Bayesians can choose to adhere to the subjective school or take their pick from among the objective schools using different types of reference prior. $\endgroup$ – Scortchi - Reinstate Monica Jun 3 '14 at 14:40
  • $\begingroup$ Reading these would give a useful introduction to many of the issues: Geisser (2006), Modes of Parametric Statistical Inference; Barnett (1999), Comparative Statistical Inference; & Gillies (2000), Philosophical Theories of Probability. $\endgroup$ – Scortchi - Reinstate Monica Jun 3 '14 at 14:49
  • $\begingroup$ I voted to close this question pending edits that would clarify what a "school" or "method" is and how one is supposed to distinguish among them. $\endgroup$ – whuber May 11 '15 at 13:55