I don''t know why the email became destroyed. Here I give extra carriage
returns between then lines. The two program calls were:
20 5 0 deduce 10
and
20 5 0 predict 10
The output lines were
8 2 0
1 1 0
and
7.5 2.14286 0.357143
1.56745 1.48533 0.671764
Thanks!
Bo.
Den 16:23 tirsdag den 29. marts 2016 skrev Devon McCormick
<[email protected]>:
Bo - your J examples came out garbled on my end, so I'm unsure what the
right-hand arguments are to both "deduce" and "predict". Simply cutting
and pasting from your e-mail gives a result containing a complex number for
your first example and an error ("ill-formed number") for your second one.
On Tue, Mar 29, 2016 at 7:55 AM, 'Bo Jacoby' via Programming <
[email protected]> wrote:
> Thank you for the links!
> One trouble about Bayesian statistics is the naming of probability. It is
> problematic to talk about the probability of life on Mars, because we do
> not have a big population of Marsplanets such that we can count the
> proportion of Marsplanets containing life.
> Life on Mars is a hypothesis. Hypotheses do not have probabilities.
> Hypotheses have credibilities. It makes sense to talk about the credibility
> that there is life on Mars.
> This tiny change of wording may help accepting the Bayesian approach.
> Secondly, the notation P(A|B) for the conditional probability of event A,
> given hypothesis B, can be simplified by omitting the letter P and writing
> simply (A|B). The unconditional probability of A is then written (A|0), and
> Bayes' rule reads
> (A|B)(B|0) = (A|0)(B|A)
> meaning that the conditional probability times the prior credibility
> equals the unconditional probability times the posterior credibility.
> Thirdly, consider these two J programs:
> deduce=.%~`*`:3"2@(,: (%:@* -.))@(+/@[ %~ 1 , ,:)
> predict=.(deduce~ -@>:)~
> They compute mean values and standard deviations.
> If a population contains 20 items of category 1 and 5 items of category 2
> and 0 items of category 3, then a random sample of 10 items will contain
> 8±1 items of category 1 and 1±1 items of category 2 and 0±0 items of
> category 3. This was computed with program deduce like this:
> 20 5 0 deduce 108 2 01 1 0
> If a sample contains 20 items of category 1 and 5 items of category 2 and
> 0 items of category 3, then another sample, of 10 items, will contain
> 7.5±1.6 items of category 1 and 2.1±1.5 items of category 2 and
> 0.4±0.7 items of category 3. This was computed with program predict like
> this:
> 20 5 0 predict 10 7.5 2.14286 0.3571431.56745 1.48533 0.671764
> The close relationship between deduce and predict is the main result of
> this research: Statistical induction and prediction
> Thanks. Bo.
>
>
> Den 6:39 tirsdag den 29. marts 2016 skrev Ian Clark <
> [email protected]>:
>
>
>
> You're welcome, Devon.
>
> I've quite forgotten I'd done that. I recognise the article, now I see
> it again. A bit of a Bayesian myself, I must have repaired it because
> I remember thinking at the time what a good intro to Bayesianism it
> was, with applications to human factors topics I was deeply into
> throughout the 1980s. Yes, it needs J versions of the APL functions.
>
> Amazed the APL chars have survived the migration to WikiMedia. Feel
> free to strip out my initials etc and take back ownership of your
> essay.
>
> On Tue, Mar 29, 2016 at 1:14 AM, Devon McCormick <[email protected]>
> wrote:
> > Hi - I've put up some links relating to my recent talk introducing
> Bayesian
> > statistics - http://www.sigapl.org/BayesianLinks.php .
> >
> > Thanks to Ian Clark for reviving my old APL essay on this (
> >
> http://code.jsoftware.com/wiki/User:Devon_McCormick/DynamicLinearModels/BayesianFinancialDynamicLinearModel_iac
> )
> > by fixing the broken APL characters. I may get around to re-doing this
> in
> > J one of these days.
> >
> > --
> >
> > Devon McCormick, CFA
> >
> > Quantitative Consultant
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
>
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
--
Devon McCormick, CFA
Quantitative Consultant
----------------------------------------------------------------------
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