Tom Adams wrote:
>
>
> On Sep 11, 1:23 am, James Annan <[EMAIL PROTECTED]> wrote:
>> Michael Tobis wrote:
>>> Yes, that's the one, thanks.
>>> Since this isn't a public talk I won't identify the frequentist in
>>> question, but he was uncomfortable with the very idea of assigning a
>>> probability to an event that "either happened or didn't". Something
>>> about babies and bathwater comes to mind.
>> I would be interested to know if he listens to (and acts upon) the
>> weather forecast :-) Tomorrow's weather is not a random repeatable
>> sample, merely an unknown deterministic event. Of course people
>> (including me) do talk about frequentist notions such as reliable
>> probabilities ("reliable" meaning that eg an event has historically
>> happened on p% of the occasions that it was forecast to happen with p%
>> probability), but I would hope that most if not all researchers would
>> agree if they thought about it carefully that in fact the probabilities
>> can only be Bayesian in nature.
>
> I disagree to some degree. The weather prediction probabilities can
> be (and are) model-based frequentist probabilities.
No.
Anyone can (and indeed frequently does) dress up a Bayesian probability
by generating an ensemble of outcomes to describe their posterior pdf.
But that doesn't make the underlying problem frequentist, it is just a
computationally and intuitively convenient method.
The standard paradigm of numerical weather prediction is that the
atmosphere is a deteministic system, which is imperfectly observed. Even
in the case of a perfect model, there is no such thing as the correct
probabilistic forecast (except perhaps pedants may point out the
degenerate case: the correct forecast is the [deterministic] output from
the perfect model run with perfect initial conditions, but we can never
hope to achieve this in reality).
The very best we could ever hope for, if there was a widely available
and agreed set of observations, is that all forecasters would generate
the same ("intersubjective") probabilities. Even this requires not only
a perfect model but also a universally agreed interpretation of all
observations, which is rather unlikely. It also requires a perfect, or
at least universally agreed, method for calculating probabilities, which
is whole other can of worms in itself.
The probability cannot be a function of the atmospheric state itself,
since the forecast will change if different observations are made. In
practice it is quite reasonable for different forecasters to give
different forecasts on any given day - and both can be "right" in the
sense of giving reliable forecasts in the long run.
James
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