petrelharp
commented
10 years ago So, (1) and (3) seem straightforward.
For (2): I'm not really motivated by the PCA notion of that post, but the general framework seems fairly well worked out; here's some references. The horseshoe prior seems well-justified: parameters are Normal, with variances half-Cauchy (with independent variances for each parameter). A drawback is that we'd then have to also MCMC over the variances, since there isn't a nice expression for the posterior. (I think this is what they do? I can't quite tell. Maybe there is more info in this paper.
Also, that approach allows the parameters to be positive or negative. So far, I've been constraining the rates to be positive; although we could allow higher-order mutation rates to be negative, as long as the sum of relevant terms was nonnegative (i.e. G->T + GC -> TC should be nonnegative). I still think having nonnegative rates is the right way to go, but I could imagine a situation when allowing negative corrections would end up with a more parsimonious model.
The last question: I'm imagining mutation rates built up with rules of increasing complexity, explaining as much as possible with single-base rates, like in the CpG example. That's why things are set up allowing for patterns of arbtrary length, so the rate for CG -> CT adds to the rate for G -> T. This way we can have a nice, interpretable representation for the spectrum, putting as much emphasis as possible on single-base rates.
matsen
We won't be able to do number 2 fully, but perhaps it's a framework to start from?
I'd like to understand if you are thinking of all mutations as coming from these context-dependent processes, or if they are sitting on top of some base mutation process, like in your CpG example.