3 - Probability theory
Published online by Cambridge University Press: 06 July 2010
Summary
THE PROBABILITY OF AN EVENT
Our aim throughout the next four chapters is to explicate and justify the Law of Small Probability (LSP). To accomplish this aim, let us start by identifying the conception of probability we shall be using. Conceptions of probability abound. Typically they begin with a full theoretical apparatus determining the range of applicability as well as the interpretation of probabilities. In developing our conception of probability, I want to reverse this usual order, and instead of starting with a full theoretical apparatus, begin by asking what minimally we need in a conception of probability to make the design inference work.
One thing that becomes clear immediately is that we do not need a full-blown Bayesian conception of probability. Within the Bayesian conception propositions are assigned probabilities according to the degree of belief attached to them. Given propositions E and H, it makes sense within the Bayesian conception to assign probabilities to E and H individually (i.e., P(E) and P(H)) as well as to assign conditional probabilities to E given H and to H given E (i.e., P(E | H) and P(H | E)). If E denotes evidence and H denotes a hypothesis, then of particular interest for the Bayesian probabilist is how believing E affects belief in the hypothesis H.
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- The Design InferenceEliminating Chance through Small Probabilities, pp. 67 - 91Publisher: Cambridge University PressPrint publication year: 1998
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