When’s that next gamma-ray blast gonna come, already?

Phil Plait writes:

Earth May Have Been Hit by a Cosmic Blast 1200 Years Ago . . . this is nothing to panic about. If it happened at all, it was a long time ago, and unlikely to happen again for hundreds of thousands of years.

This left me confused. If it really did happen 1200 years ago, basic statistics would suggest it would occur approximately once every 1200 years or so (within half an order of magnitude). So where does “hundreds of thousands of years” come from?

I emailed astronomer David Hogg to see if I was missing something here, and he replied:

Yeah, if we think this hit us 1200 years ago, we should imagine that this happens every few thousand years at least. Now that said, if there are *other* reasons for thinking it is exceedingly rare, then that would be a strong a priori argument against believing in the result. So you should either believe that it didn’t happen 1200 years ago, or else you should believe it will happen again in the next few thousand.

So, from a Bayesian standpoint, our prior guess is that this event has very low frequency, thus conditional on the assumed data (1200 years since the most recent event), the estimated frequency should be something a bit less than 1 per 1200 years. But it’s hard to see how we’d get 1 per 300,000 years. That would require a prior that’s so strong that it would be contradicted by the data. (Or, again, perhaps the data are being misinterpreted, but the above analysis is conditional on that interpretation.)

David supplied an update:

Here is the paper and the authors of the paper say the rate is one per 375,000 yr to 3,750,000 yr. (You will enjoy the precision they use in their numbers, given their uncertainties.) Then they say that this is consistent with one event in the last 3000 yr within 2.6 sigma. (They figure the census for such events is complete back to 3000 years, and there is one event found in that census.)

I guess it all depends on how strongly you believe your prior and how strongly you believe the data.

P.S. I wrote this post in January and then put it on the queue, confident that there was no rush. After all, the probability of a major gamma ray burst in any given year is so small!

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