The curve fitting problem: A bayesian approach

Philosophy of Science 63 (3):272 (1996)
In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship between simplicity of a theory and its predictive accuracy
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DOI 10.1086/289960
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Prasanta S. Bandyopadhyay & Gordon Brittan (2010). Two Dogmas of Strong Objective Bayesianism. International Studies in the Philosophy of Science 24 (1):45 – 65.
Rhonda Martens (2009). Harmony and Simplicity: Aesthetic Virtues and the Rise of Testability. Studies in History and Philosophy of Science Part A 40 (3):258-266.
Jan Sprenger (2013). The Role of Bayesian Philosophy Within Bayesian Model Selection. European Journal for Philosophy of Science 3 (1):101-114.

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