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bimodal data distribution


From: Dupuis
Subject: bimodal data distribution
Date: Mon, 24 Aug 2009 06:22:29 -0700 (PDT)

Hello,
I'm trying to extract parameters of a two levels signal described as
x = N(m1, s1) with probability p
x = N(m2, s2) with probability (1-p)
|m1-m2| >> sqrt(s1^2+s2^2)

The operation is similar to MatLab 'gmdistribution', identifying the
parameters of a mixture of gaussian signals. I implemented the search like
this: 
1) use 'statistics' to get a number of indicators; 
2) [p0, obj0, info0, iter0, nf0, lambda0] = sqp(p , 'bimodal_func', [], [],
lb,ub); where the vector p contains 5 members: the ratio p defined above,
m1, s1, m2, s2. Those values were initialised from the indicators: m1 and m3
are the first and third quartiles, p is set to 0.5, s1 and s2 are sqrt(2) *
the standard deviation. 'lb' and 'ub' provides constraints on the result: 0
<= p <= 1; 0<= s1, s2 <= standard deviation, ...
The bimodal_func is included, I have a few concerns. How could I correct
them ?
- data are passed through a global, I didn't see how to pass a supplemental
parameter through sqp call 
- if I used gradient and hessian, it converges quadratically ... close to
the minimum, and diverges otherwise. Is is possible with sqp to only use
hessian close to the minimum, in the convergence region ? A practical
criterion is that all eigenvalues should be > 0
- I'm also trying to the the Fisher information matrix at the solution. The
definition on wikipedia is not clear; am I right in postulating that it is
equal to hessian(p0)/length(x), where p0 is the optimal point ?

Regards

Pascal http://www.nabble.com/file/p25116016/bimodal_func.m bimodal_func.m 
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