Instructions: you must type in your solutions and submit them to the blackboard. The assignment is to be completed by a group of two. Name the solutions file as Assign1_FirstName1_FirstName2. You only need to submit both the problem set & programming exercises.
Instructions: you must type in your solutions and submit them to the blackboard. Only PDF format is accept ed. The assignment is to be complete d by a group of two. Name the solutions file as Assign1_FirstName1_FirstName2. You only need to submit both the problem set & programming exercises.
I- Curve fitting problem
PS-I-1: Assume the curve fitting problem is solved using the polynomial function
The problem of finding the curve that best fits a number of data points. The philosophical interest lies in justifying any particular trade-off of simplicity, accuracy, and boldness, that may commend itself. The problem of induction can be represent graphically as a curve-fitting problem.
Much of scientific inference involves fitting numerical data with a curve, or functional relation. The receive view is that the fittest curve is the curve which best balances the conflicting demands of simplicity and accuracy, where simplicity is measurement by the number of parameters in the curve. The problem with this view is that there is no commonly accept justification for desiring simplicity. This paper presents a measure of the stability of equations. It is that the fittest curve is the curve which best balances stability and accuracy. The received view is defend with a proof that simplicity corresponds to stability, for linear regression equations.
Tables of contents for recent issues of The British Journal for the Philosophy of Science are available at http://www3.oup.co.uk/phisci/contents/. Authorized users may be able to access the full text articles at this site. The British Journal for the Philosophy of Science encourages the application of philosophical techniques to issues raised by the natural and human sciences. These include general questions of scientific knowledge and objectivity, as well as more particular problems arising within specific disciplines. Topics currently being discussed in the journal include: scientific realism, causation, the logic of natural selection, the interpretation of quantum mechanics, the direction of time, probability and confirmation.
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