final_review - Final Exam Review - Model vs Data December...

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Final Exam Review - Model vs Data December 15, 2006 Model vs. Data In most experiments we can control a set of independent variables x and can measure the value of the dependent variable y . For such a system we can propose a model which relates the value of the dependent variable to the values of the independent variables as shown in Equation(1) y = f (x; Θ) (1) The aim of the generating a model for the system is to obtain an answer to the following three questions For what value of Θ is the deviation between model and data minimum? Is the model consistent with the data? What are the error bars on the values of parameters? In the context of models we classify models as linear or non-linear. Linear models depend on the parameters Θ linearly. For example the log of the rate of an arrhenius reaction is linear in the parameters log( A ) and E R a . This model is linear even tough log( A ) is not linearly dependent on the dependent variable temperature T . E a log( k ) = log( A ) (2) RT Usually in solving these problems we make the following two assumption 1. The dependent variable y , that is being measured is distributed nor± mally (a gaussian distribution) around its mean value. This distri± bution can be due to many factors which are not in control of the experimentalist. 2. On the other hand the independent variables x are known exactly. 1
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final_review - Final Exam Review - Model vs Data December...

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