Period priors for trigonometric functions

[mattmoo]

Firstly, thank you for all your work on this package!

I have some time series data that seems to have an annual seasonal effect. I'm not getting a particularly satisfactory fit, and wonder whether it might be possible to set a prior for the period?

[lindeloev]

Yes, I did consider adding this. Right now, mcp just follows glm standard that only the amplitude is modelled, i.e., parameter * sin(x). But technically, it's easy to do expand the model to amplitude * sin((phase + x)/period) with appropriate priors for the two new parameters.

I lean towards doing this by default. Here's the dilemma: this would perhaps surprise some users because this would be nonstandard behavior in R. But the only cases I can think of where you wouldn't want to do this is when you know a priori that phase == 0 & period == 1, which seems rare. If you wanted this behavior anyway, you could just set prior = list(sinx_phase_1 = 0, sinx_period_1 = 1). brms has a non-linear "module" where you explicitly write the formula with parameters y ~ b_amp * sin((b_phase + x) / b_period, but I think this is beyond the scope of mcp.

Right now, with mcp v0.3, you can do a very rough fix by forcing a period of 1: simply do x = period + x / phase with you dataset and then back-transform all regressors after fitting. Here, you infer in some other way.

You can also use mcp to generate the JAGS code fit$jags_code and then add phase/period and sample it directly using JAGS/rjags. But then you manually have to do check fits/predictions/plots, etc.

[lindeloev]

Just posted a twitter poll :-)

[mattmoo]

Interesting, I think that I can eyeball this particular seasonal effect, but I can see that not being the case all the time.