1. Today (2/16/16) Learning objectives (Sections 5.1, 5.2, and 5.3):
Apply the method of maximum likelihood to determine the most probable set of parameters in a linear fit.
Be able to perform both weighted and unweighted linear fits.
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2. Worked problem
Consider the following attempt to quantify the intensity and offset in a fluorescence lifetime according to the linear equation below.
Import the data in the file named “y-data.dat”, which are Poisson-distributed. Using the measured counts as initial estimates for the variance, write a MathCad file to invert the problem and solve for the best-fit values of a0 and a1.
Refine your estimates for the variance based on the equation above rather than the experimental values of y.
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3. Worked problem
Consider the following attempt to quantify the intensity and offset in a fluorescence lifetime according to the linear equation below.
Refine your estimates for the variance based on the equation above rather than the experimental values of y. Substitute your new values of the coefficients and update the new expression for  until a0 and a1 stop changing with additional iterations.
Compare your result based on Poisson weighting of the measurements with what you would get if you instead performed an unweighted fit (i.e., assumed each measurement has identical variance), consistent with most software packages (Excel, Mathcad, etc.)?
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4. Next time
Introduction to 2-space.
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