Dear Hakwan,
Yes, you are essentially correct.
Bayesian inferences in this context are effectively the same
as the interval estimation framework of classical inference (rather
than the point estimation framework).
The conceptual difference is that in interval estimation the random variables
are the lower and upper interval points whereas in Bayesian inference the
random variable is the variable itself (eg. regression coefficient).
However, when Bayesian inferences are combined with informative
priors and Bayesian estimation procedures, the results can be
very different. Essentially the mean and variance of the
distribution will be in different places.
And if the priors are right, the mean will be estimated more
accurately.
So, Bayesian inferences concerning the null are
potentially more sensitive than the interval estimation methods.
See eg. the discussion of shrinkage priors on page 479 on
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/bayes1.pdf
for more info.
Best,
Will.
Hakwan Lau wrote:
> Hi Will,
>
> I've been considering possibilities of using Bayesian statistics to
> solve the notorious problem of confirm the null hypothesis that a
> certain measure (say a difference in reaction times in two conditions;
> let's call it beta) is 0. Ideally, I'd like to be able to make the
> claim that P(beta = 0 | the observed data) > 0.95 (or so). Having think
> about it for a while, I realise that I can't do much better than a
> classical frequentist approach. Obviously, however narrow is my
> estimated probability distribution, the probability at beta exactly
> equals zero would still be much lower than 0.95. Which means I still
> have to specify something similar to an effect size, i.e. a range of
> possible values (say -0.1 to 0.1), and say that this range falls with
> 95% of the area under the probability distribution. Then I don't see
> how it is much better than the classical Cohen approach of estimating
> sufficient power to prove the null, beyond gaining the
> semantic/philosophical credit in a Bayesian framework.
>
> Am I correct? Or is there some clever Bayesian way of dealing with this
> problem? If there's any (or things in a similar direction), would you
> mind pointing me to the references?
>
> Many thanks,
> Hakwan
>
>
>
--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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