Manuel Ebert wrote: > Dear list, > > who's got aesthetic advice for the following problem? I've got some > joint probabilities of two distinct events Pr(X=x, Y=y), stored in a > list of lists of floats, where every row represents a possible outcome > of X and every float in a row a possible outcome of Y (which I will now > call my matrix, altough I can't use numpy or numeric for this), so e.g. > m = [[0.2, 0.4, 0.05], [0.1, 0.05, 0.2]]. All lists in the list are > equally long and the values of the flattened list add up to 1.0, i.e. > sum([sum(row) for row in m]) == 1. In practice, this 'matrix' is about > 20x40, i.e. a list with 20 lists รก 40 floats each. > > Now the task is to select one outcome for X and Y based on the joint > probabilites, and afterwards check that the outcomes fullfill certain > criteria. If it doesn't fulfill some criteria a new pair of outcomes has > to be selected, for other criteria it will still be selected with a > certain probability. My approach was to choose a random number, and then > walk through the list adding the values together until the accumulated > sum is greater than my random threshold: >
[snip] For a list of cumulative probabilities you could use the bisect module to find the insertion point for a 0,1 uniform variate (which you could then map back to a cell index). Alternatively you could use an alias table, http://amath.colorado.edu/courses/7400/2004fall/002/Web/SS-10.ppt. You could produce a probability table that takes into account your criteria, so that you don't need to check them. i.e. Each cell that does not satisfy criterion a has probability 0 of being selected. Each other cell has a probability of being selected proportional to its original value if it satisfies criterion b, or its original value * p otherwise. Normalise the resulting values to sum to 1 and you're done with the need to check against criteria. So, preprocess your table, create a corresponding list of cumulative probabilities and use the bisect model (is one possibility). Duncan -- http://mail.python.org/mailman/listinfo/python-list
