problem_set9

# problem_set9 - 10.34 Fall 2006 Homework Models vs Data Due...

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10.34 Fall 2006 Homework: Models vs. Data Due Monday November 13, 2005, 9 am. Your task is to analyze the dataset Signal( λ ,t) presented in the SVD homework. Each point in this dataset is an average of 100 repeated experiments, so you expect the uncertainties in these data to be approximately given by a Gaussian distribution. Unfortunately, the individual points from each repeat were not stored, only the average value, so you do not know the standard deviation corresponding to each point, and you do not know the expected variance in the averaged data. Before beginning, you are 100% certain that the data is of the form Signal( λ ,t) = Σ c i (t) A i ( λ ) + noise Also because of their physical meanings, concentrations c and absorption strengths A can never be negative. You are 99.9% sure the volume change during the reaction is negligible, i.e. dc i /dt = (1/V) dn i /dt is accurate to as many digits as you can measure, and you are 99.9% sure that the noise level in the instrument is the same at every wavelength and time point to the accuracy with which you can determine it. Based on the SVD analysis (see solution to homework 5), you believe that there are only two absorbing species contributing to the signal, call them B (which decays away, related to species 2 in homework 5 posted solution) and C (which is formed, related to species 1 in homework 5 posted solution). The SVD analysis appears to show two different time constants. This suggests two

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problem_set9 - 10.34 Fall 2006 Homework Models vs Data Due...

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