I am trying to a handle on how to use a some of the theano math functions within a probability model. My first effort was to reconstruct the parameters of a single unknown sinusoid in white Gaussian noise, which is a very common introductory problem in astrostatistics. It also has the advantage of …

I get perfect results running the model exactly as you specified it: t = np.linspace(0, 10) x = np.sin(2*np.pi * t * 0.1) x += np.random.randn(*x.shape) with pm.Model() as model: amplt = pm.Normal('amplt', mu=1, sd=1) freq = pm.Uniform('freq', 0, 0.5) mu_x = amplt * pm.math.sin(2*np.pi…

I don’t see anything wrong with what you’re doing here, or how you’re thinking about it. For many straightforward things you can pretty much use theano as you would numpy, just replace np with tt. Have you tried running this model? Do you get reasonable results?

Because the above model runs surprisingly slow, I decided to simplify the model further to be amplt = pm.Normal(‘amplt’, mu=1, sd=1) freq = pm.Uniform(‘freq’, 0, 0.5) mu_x = amplt * pm.math.sin(2*pi * t * freq) X_obs = pm.Normal(‘X_obs’, mu=mu_x, sd=1, observed=x) and it still took 18:40 to t…

Following up with a longer run, the results are actually even worse. In the ADVI computation at the beginning, the average ELBO is -861.43, which I presume is pretty poor. The posterior estimates are awful. I am curious if anyone else has the same problem given this is such a simple model. As I have…

Not sure where exactly I was going wrong but @aplavin has ironed out whatever it was. Many thanks. And now to see if I can expand the above model to include phase, unknown noise variance and then more sinusoids.

Just to let you know, you can do a fft in theano. So if you have equally spaced observations and your prior can be expressed reasonably on the discrete frequency domain, than looking into that might make sense.

I was a bit curious what prior one could possibly use on the frequency and experimented a little. It seems that if we set a uniform prior on the angle, and a strong shrinkage prior on each individual magnitude, we get an interesting prior on the functions. import numpy as np from scipy import stat…

Working in the Fourier domain will definitely be helpful when I start to move away white Gaussian noise, as the Covariance Matrix can get pretty complex if there is any underlying frequency structure. If my hunch is right, this also requires me to include the frequency response of a boxcar time-doma…

About 1: Using a uniform distribution on [0, 2pi) for the phase is trouble. The problem is the different topology of angles and intervals, you need to somehow include the wrapping behaviour of angles, ie 0 is the same as 2pi. If you don’t, the sampler will have a hard time and your posterior could e…

Oh, and if you have frequencies with very different orders of magnitude, then maybe it is better to use VanMiseslength with some arbitraty length distribution that the sampler likes (say pm.Normal.dist(mu=4, sd=1) or so), then just ignore the second output and introduce a separate variable for the a…

How to model sinusoids in white gaussian noise

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How to model sinusoids in white gaussian noise

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