Dear All,
Some quick comments. Apologies if they seem a little grumpy, but I
really thought that this was a very poor set of comments. For me, the
giveaway is "One technique which answers all these problems is the
Bayesian approach to statistics". This isn't science - its salesmanship.
For the record, although I have some issues with Bayesian approaches, I
generally think that they are interesting, and have some real potential,
both in clinical decision-making (which I am assuming the readers of
this list are familiar with) and also in clinical trials. Those
interested might want to read: Bayesian Approaches to Clinical Trials
and Health-care Evaluation (Statistics in Practice) by Spiegelhalter (or
see his page at
http://www.mrc-bsu.cam.ac.uk/BSUsite/AboutUs/People/davids/davids_Research.shtml)
> The major limitation of the "frequentist" statistical approaches is that
> they makes assumptions on the nature of the data rather than on the
> processes that are being studied.
Bayesian approaches make assumptions about the processes (e.g. that they
are conditionally independent).
In addition, techniques used
> frequentist statistics are based on asymptotic principles and are
> applicable to normally distributed data.
> The only data I know which is truly /normalI/ is measurement error. No
> real world data is normal. The techniques work because when there are
> large numbers, the results asymptotically approach that of truly normal
> data.
Which means that for large samples, we can treat them as normally
distributed. The issue of no real world data fitting a theoretical
distribution is not unique to the normal distribution - it is a feature
of real-world data vs. theoretical distributions.
> Such techniques therefore are not suitable when our interest is centred
> on the sample size of one that you are talking about.
> To make predictions at the individual level, one needs to create models
> which realistically capture all the sources of variation at the
> individual level.
Which is going to be impossible; From the frequentist POV because we can
never do enough studies to get the data; from the bayesian because we
can't guarantee the independence of variables. In reality, therefore, we
use a smaller subset of the variables and hope that they are suitable
as a surrogate for what we want to measure.
> One technique which answers all these problems is the Bayesian approach
> to statistics. Individuals when they make decisions (including
> physicians) use Bayesian techniques.
No they don't; Some people would say that they /should/ but there is
ample work (Kaheman & Tversky) which shows that humans don't apply
bayesian reasoning.
> Unlike frequentist statistics, all estimates in Bayesian statistics are
> arrived by Monte Carlo simulation.
I do hope not; Monte Carlo simulations are nice, and interesting, but
since one can apply bayes theorem, they are also a little unnecessary
for many situations (but not all). I quick flick through Sackett et al.s
Clinical Epidemology book will show you how to use Bayes without Monte
Carlo simulation.
[Most real world data are gamma distributed].
I'd like to see a reference for this; I suspect it is very heavily
dependent on the domain.
> When the numbers are large, conventional statistics and Bayesian
> statistics give generally equivalent results ( when they differ,
> Bayesian results are more correct under equivalent assumptions).
I have no idea what this means - correct WRT what?
> One example. Suppose you are studying the prevalence of lupus in a
> district in Malaysia. You have surveyed 10,000 individuals and found none.
> Can you give an upper limit on the prevalence of lupus from the above data.
> Frequentist statistics fail because you will encounter infinite variance
> (which is far from the truith). You can give a valid confidence limit
> (only the upper limit is valid) using Bayesian statistics.
See other post for comments on this.
> I have been working on it for more than an year now.
I'll let this speak for itself.
Matt
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