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. (shrink)

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. (shrink)

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. (shrink)

I advance a decision principle called the "weak dominance principle" (WDP) based on the interval notion of probability to deal with the Ellsberg type paradox (ETP). Given ETP, I explain three things: (i) Why WDP is a better principle than many principles e.g. Kyburg's principle and Gardenfors and Sahlin's principle, (ii) Why one should not, contrary to many principles, expect a unique solution in ETP, and (iii) What is the relationship between WDP and the principles mentioned above. I prove also (...) that WDP induces a strict partial ordering on the intervals to which it is applied. (shrink)