John,
I just sent you an email regarding a question about fitting a piecewise constant curve to an approximately normal distribution. But, I thought I would post the question here as well. I need the pw const curve to have 13 pieces, but I want the knots to be freely spaced, but I noticed in your comments that pw constant curves have trouble with this. Is there any way around it?
If not, is there a way to make the last interior knot to be at the start of the flat part of the distribution (the right tail) and then the other pieces are fit to the central part of the curve where the curve is changing rapidly.
Thank you again for your great contributions! I have used your tools in several parts of my dissertation.
Thank you,
Britnee
Ron - Thanks for finding the weights bug. I'll post a new version with a fix. As far as references go, I don't really know of any. The basic philosophy is a somewhat Bayesian one, wherein one uses knowledge of the physical system to be modeled to yield a viable model consistent with your prior information. In practice, I have found it to work splendidly, and have used similar schemes for over 20 years. I've given many talks on that modeling philosophy, but no published papers. I'll argue that what makes SLM work as well as it does is the use of a simple scheme to encode your knowledge of the system into a set of well defined parameters describing the shape of the curve.
These routines are very useful. Would like to read more on the mathematical foundation of these routines. Can you recommend reading beyond the basic least square splines references?
Also, I made the following correction concerning handling of weights...
% were there any NaN or inf elements in the data?
k = isnan(x) | isnan(y) | isinf(x) | isinf(y);
if any(k)
% drop them from the analysis
x(k) = [];
y(k) = [];
prescription.Weights(k) = []; % ALSO drop corresponding weights, May 2011
n = length(x);
end
% if weights or errorbars were set, verify the sizes of these
% parameters, compared to the number of data points.
Aside from all the awfully clever (advanced) stuff, also a really handy way to find the inflection point in a piecewise linear regression. Neat =)
see: http://www.mathworks.com/matlabcentral/newsreader/view_thread/298989
It sounds like you want to allow the knots to vary, but only within set bounds? If so, I might suggest putting the call to slmengine inside a wrapper, an objective function for fmincon. Use it to vary the knot placement, with slmengine now seeing a fixed list of knots.
In fact, this is all slmengine does to vary the knots when you specify free interior knots, so one might argue that I could have offered this as yet another option for slm. The problem is, the interface would be a bit messy, coming up with a way to allow the user to specify bounds on some or all of the knots.
If you read through the code, you will see in the beginning how I call fmincon in that case. Note that I constrain the knots to be distinct.
Ask again if I am mistaken about your goal here.
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