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R G
Lv 5
R G asked in Science & MathematicsMathematics · 1 decade ago

compare likelihood? (hard i think) =)?

1st whats the meaning of likelihood, just plain simple. I may have not understood its meaning...

as example: let x~N(0,1);

y=a*x+b; {a,b} constants, making y~N(b,a^2)

z=c*x+h; {c,h} constants

likelihood for y_i is....:

L_i=-0.5 (y_i-mean_y)^2/var(y)-0.5 log(var(y))-0.5log(2*pi)

how can i compare 2 likelihoods, if its possible?

My main goal is to create a threshold to get the same points of x (y(x) and z(x)), from the likelihood of y and z,

the only possible way is to threshold_y=K+0.5log(var(y)) and threshold_z=K+0.5log(var(z))? K=constant...

or its there another way....

sry for my English, and tanks for your time =)

Update:

im doing image processing....

so i calculate a variance of a pixel and its mean in 2 cases.

Then i want to decide what is the background or not, so i do

L>K is background.

oh and i also know that is possible to do the prob using the normalization of the standard deviation....

My goal was to decide if a pixel changes more than a P% is considered background, on both cases... but i cant use constants!

and i just don't know WHY! can u explain why?

1 Answer

Relevance
  • 1 decade ago
    Favorite Answer

    Likelihood is sort of a generalization of probability. The "most likely" value is the value with the maximum probability. But sometimes there's another function which is more convenient to calculate with than the actual probability distribution. If this function is monotonic with probability, so L(a) > L(b) if and only if P(a) > P(b), then you can maximize the probability by maximizing the likelihood.

    I don't understand your goal or what you mean by "compare", other than seeing which is larger.

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