In the interest of brevity, I've indulged in wanton snippage, but I hope what's left yields something comprehensible. S. F. Thomas <sfrthomas@yahoo.com> wrote:> Robert Dodier wrote: >> [...] OK, now this is something I haven't heard about -- how does the >> extended likelihood calculus take loss, risk, and action into account? > > [...] Under the likelihood calculus, the same is possible, but the > fact that likelihood is a point function, not a set function, > renders the general rule for change of variable different -- > easier in fact -- from what it is under the probability calculus. > As to issues of risk and action, the notion of expected loss > consequent upon any given action, is rendered as a possibility > (or likelihood) distribution, or in effect a fuzzy set.
Suppose, then, that I have a possibility or likelihood for two different actions. Can I say that one action is preferable to the other? If so, how do I determine which is more preferable?>>> [...] But probability (over sample space) gives rise to likelihood (over >>> parameter space) and the calculi required to manipulate the two are >>> different. >> >> (i) This betrays a very limited view of what a model can be: apparently >> there are but samples and parameters. Many interesting models are not so >> simple. > > What do you mean? And how does it relate to what we are discussing?
In the world of models implicit in your statement above, there are sampling distributions for observable variables and there are parameters that govern those distributions. Some models are that simple, yes. There are many models which don't fit into this neat division of labor. Does every class of models require its own reasoning calculus?> (ii) The likelihood calculus which you state above looks >> suspiciously similar to a rule derived from laws of probability. > > It *is* derived from the laws of probability. You must have missed > large parts of the thread while feigning sleep.
Well, I have no problem with deriving fuzzy reasoning from probability, but I thought that was precisely what you were arguing against.> [...] First you claim boredom with the discussion, and say you're > going to sleep, only to re-appear, apparently wide awake and engaged.
I always feel like a million bucks after a good nap. Regards, Robert Dodier -- ``Socrates used to meditate all day in the snow, but Descartes' mind worked only when he was warm.'' -- Bertrand Russell