I INF 451 Lecture Notes - Lecture 3: Multivariate Random Variable, Markov Chain Monte Carlo, Round-Off Error
Document Summary
The mode of the probability density is the parameter value at which the peak occurs. This is often called the maximum a posteriori (map) estimate. It is often most easily found by looking for the parameter value at which the derivative of the probability (or log p) is zero. The variance can be estimated from the local curvature at the peak. For a symmetric density it is equal to the mode. The variance can be computed by calculating the expected squared deviation from the mean, or sometimes confidence intervals are defined to delineate regions of high probability. Be careful, the mode of the posterior of a parameter value will not in general correspond to the mode of a transform of that parameter! Often researchers will compute one optimal parameter and perform a transform assuming that the result is optimal. A physics example of this difficulty is a comparison of the frequency spectrum and wavelength spectrum of blackbody radiation.
