Obvious noise fitting about celerite HOT 4 CLOSED

You must be fitting a white noise component in the GPyTorch model! In celerite, you should include a JitterTerm.

Even so, it's not obvious to me that a stationary GP is a good choice for your particular data set.

from celerite.

(I should mention that I know this because without a white noise term, the model will exactly go through every data point by construction...)

from celerite.

Ok thank you for the quick answer it does give a similar result now !

Yes I was trying to compare GPyTorch and celerite on random data with a random kernel. Now I have data for my work on which I am trying to do a Gaussian regression using celerite and might want some help. These data come from different orders of a spectrograph on which I was forgetting to add a jitter and was getting this result :

Final log-likelihood: -34152.13490724329
OrderedDict([('kernel:log_sigma', 7.880630186965559), ('kernel:log_rho', -3.6806385290403085), ('mean:alpha', -15196058.545724938), ('mean:beta', 20969.494149527465), ('mean:gamma', -7.232764975132396)])

And once I add the jitter I still get :

Final log-likelihood: -34136.52418631356
OrderedDict([('kernel:terms[0]:log_sigma', 7.932584498094634), ('kernel:terms[0]:log_rho', -3.6436370800533444), ('kernel:terms[1]:log_sigma', -2.758714124608422), ('mean:alpha', -15196058.545724858), ('mean:beta', 20969.494266574093), ('mean:gamma', -7.232530879898518)])

I am fitting a second orderl polynomial model

class MeanModel(Model):
    parameter_names = ("alpha", "beta", "gamma")

    def get_value(self, t):
        return self.alpha + self.beta * t + self.gamma * t * t


    def compute_gradient(self, t):
        dalpha = np.ones(len(t))
        dbeta = t
        dgamma = t*t
        return np.array([dalpha, dbeta, dgamma])

and a simple Matern32 kernel

    rho = .03
    sigma = np.var(y)
    kernel = terms.Matern32Term(log_sigma = np.log(sigma),log_rho = np.log(rho))
    #kernel += terms.JitterTerm(log_sigma = np.log(sigma))

This is the spectrum of a Fabry-Pérot and I wish it could retrieve the sharp lines of the spectrum as in this paper [https://arxiv.org/abs/1912.09563]

Following this paper, it would be normal to have an obvious noise fitting for a Matern32 kernel but would not happen using a Matern52 kernel. So here is my next question, is there an existing robust way to implement a Matern52 kernel ? I was thinking to use

for small ε but I figured I might as well ask how you do it :)

Thank you !

from celerite.

I'm happy to chat about this via email after the holidays. Send me an email (should be easy enough to find!) and I'll get back to you in the new year.

from celerite.