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Promoting widespread use of Bayesian analysis

Keith Arnaud (CRESST/UMd/GSFC)

As the Goddard representative at this session I would like to start by noting
that Alanna's PhD thesis was a search for fast transients in the HEAO-1 A2
database. The field of time domain astronomy is becoming increasingly important
so this is another example where Alanna was ahead of her time.

Alanna is one of the people who have inspired me to take statistical issues
more seriously. I think it is incumbent on those of us who are authors of
widely-used software to be statistically sophisticated. It should be our aim to
make the default behavior of our users statistically correct.

As an example of this, and again inspired by Alanna, my aim is to move the XSPEC
community towards Bayesian methods. This requires surmounting a number of
challenges. Firstly, this must be as easy for the scientist as the current
analysis. If people have to do much more than type 'fit' followed by 'error' it
will hard to change their behavior. Secondly, the code needs to be "PhD-proof"
so it will do the correct thing even when the scientist uses it in unexpected
ways. Finally, the Bayesian method should ideally provide extra capabilities
not available using the current frequentist analysis. A good example of this
last case may well be handling of calibration uncertainties.

The current status of Bayesian methods in XSPEC is the following. A few types
of priors can be defined on individual parameters. I would like to generalize
this to allow more types of priors and joint priors on parameters. The
Metropolis-Hastings method used for MCMC in XSPEC is not simple since it
requires the choice of a proposal distribution and this has discouraged use.
I think the addition of the new affine invariant ensemble sample from Goodman
and Weare is a major advance and should make MCMC methods in XSPEC more popular.
The output probability density function is incorporated into XSPEC output. For
instance, using the 'error' command after running MCMC means that the output
chain is used to estimate the credible interval. However, I don't think this
is enough. I think we should find ways to publish our MCMC chains.