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
> 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
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
> 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
[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.