I have a reference vector, with a mean and standard deviation for each of its n elements. I want to compute the probability that a test vector is different than the reference vector.
For a single element, it's easily calculated from the number of standard deviations away from the mean. How can the probability be calculated for the whole vector?
Context: The vector is energy bins from a radiation spectragram. The difference is for early detection of the appearance of radioactive isotopes (e.g. in a nuclear power plant) to raise a warning before lethal levels are reached.
Elements in the test and reference vectors rarely are exactly the same, even for a close match, so the joint probability will be near zero over the 3,000 vector elements. What's needed is some kind of similarity metric between the vectors.
Thanks, Alan
I may be misunderstanding your set-up, but if the elements are independent, that the joint probability would be the product of the individual probabilities, unless there are some additional subtle factors in your problem. I hope this helps.