Hi. I've just joined this list. I've just started using maxima, and to
be honest am finding it heavy going. My immediate need for maxima is
to create MLE expressions for the parameters of a number of probability
distributions. I'm not a mathematician (unfortunately I did a cellular
and molecular biology/computer science double major for my BSc, and hence
did not study as much maths as typical computer scientists).
As practice for solving MLE problems, I'm trying to derive the
expressions for a and b (as in y=ax+b) for linear regression, minimising
the squared residual errors.
First, I define an equation describing the squared difference for the
residuals of a line (described by a and b for ax+b) and a set of data points
(in arrays x[] and y[], with n data points). This looks like:
q2( x, y, n, a, b ) :=
SUM( (y[i] - (b+a*x[i])) * (y[i]-(b+a*x[i])), i, 0, n-1 );
I can differentiate this fine and get the results that I expect to find
as per web pages on the method:
(C3) diff( q2( x, y, n, a, b ), a );
n - 1
====
\
(D3) - 2 > x (y - a x - b)
/ i i i
====
i = 0
and:
(C4) diff( q2( x, y, n, a, b ), b );
n - 1
====
\
(D4) - 2 > (y - a x - b)
/ i i
====
i = 0
But, when I try and solve these as a set of linear equations, I get
nothing!
(C5) algsys( [ diff( q2( x, y, n, a, b ), b ) = 0,
diff( q2( x, y, n, a, b ), a ) = 0 ], [a, b ] );
(D5) []
So, just when I thought I'd reached the finishing line, I'm stumped. Possibly
incorrectly, I'm thinking that if I can figure out what I'm doing wrong here,
then MLE estimations for parameters of many distributions will be a cinch
(and I'm also excited about least-squares minimising fits of equations to
data). Except of course that I get [] as a result, and am stumped as to
why.
Is there something simple that I'm doing wrong? Either in terms of the
underlying math, or in my use of maxima?
Thanks in anticipation,
Ross-c