Re: MLE of a restricted RV

Outlier <MTBrenneman@xxxxxxxxx> wrote in news:1187742184.834976.297520
@q3g2000prf.googlegroups.com:

I want to find the MLE for an angle, a. The sine of the angle is
normally distributed s.t.
X ~ N( sin(a0), s^2)

Let me try to recast this a bit, and see if that offers any insight. I'm
assuming your data is not circular.

Instead of thinking about the angle itself, try thinking about this as a
vector of length 1 and angle theta in the complex plane (you can cast the
problem this way with Euler's formula). Now, the Imaginary component of
this vector is sin(theta), and is distributed normally (as defined by
your problem). The real part, when the problem is constrained this way,
is a simple trig relationship to the imaginary part).

I'm dealing with a problem much like this in neuroscience-- except the
magnitude of the vector is also free to change-- and I think I have a
valid approach, which I'm writing up soon for Neuroscience Methods. I'm
doing my stats on the slope of a zero-intercept orthogonal least squares
fit to the data. The slope is related to the angle, of course, by an
arctan.

I have a prelim version of this "in press" in appedix form in
Experimental Brain Research,
http://www.springerlink.com/content/100473/?Content+Status=Accepted
doi number: 10.1007/s00221-007-1072-3 Author: Seidman
This approach uses an ordinary least squares approach, but the orthogonal
least squares is much more correct. Feel free to contact me if you need
more detail-- just remember to reverse the first part of my email addy.



--
Scott
Reverse name to reply
.

Relevant Pages

  • Re: An optimization problem
    ... and X have a non-trivial intersection, it's still unbounded, because you ... This shows that maximizing your quotient is essentially equivalent to ... minimizing the angle between Xp and Ad. ... least squares and p and d is to be optimized simultaneously. ...
    (sci.math)
  • Polar-Dual Problem.
    ... conserved symbolic determinant factors include sums of squares. ... Some polar duals with angle addition. ... Two angle conservation demonstrations are given, ...
    (sci.math.research)
  • Re: how to determine the center or foci of an ellipse from a slope
    ... perform an angular search around that point ... looking for an angle "tht" at which the slope is the same ... The center of the ellipse will lie along ... the line defined by this angle through "p". ...
    (comp.soft-sys.matlab)
  • Re: Calculate slope of a data set or trend line
    ... I have a sales data base in access with monthly sales history by ... to make future predictions I need the slope (representing ... Sum of the squares of the errors: ... answers you get no longer solve the 2 X 2 matrix equation. ...
    (comp.databases.ms-access)
  • Re: Zoom and magnify relation
    ... the focal length ratio, all the way to the widest wide angle, as long as ... number of squares visible in any direction in the image than a straight ... "On Lens Angles Of View, Magnification, And Perspective. ... The FOV goes from 62.86 ...
    (rec.photo.digital)
Loading