Multiple independent random walks with differing innovations

Questions
1

Hi all,

I’d like to declare multiple Gaussian random walks which evolve independently. Following an earlier post asking about multiple drifts (Can I instantiate multiple random walks with different drifts), I tried:

mean_sigma = pm.HalfNormal('mean_rw_sigma', 1., shape=n_tourneys)
prior_means = pm.GaussianRandomWalk('prior_means', sigma=mean_sigma, shape=(n_years-1, n_tourneys))

However, this doesn’t compile:

ValueError: Input dimension mis-match. (input[0].shape[1] = 3, input[1].shape[1] = 4)

I thought I could maybe do the MvGaussianRandomWalk with a diagonal covariance, but I’ve been unable to create a diagonal covariance matrix, so I’d be grateful for any pointers. Apologies if I’m doing something silly, I’m pretty new to pymc3!

Thanks,
Martin

2

Could you raise an issue on Github? This use to work i think, but now https://github.com/pymc-devs/pymc3/blob/2824027837931a6c2f1d4ac5f210eb36b8fdf7a7/pymc3/distributions/timeseries.py#L219-L225 makes it impossible.

1 Like
3

Using pm.MvGaussianRandomWalk:

import pymc3 as pm
import numpy as np
import theano.tensor as tt

n_timeseries, n_timepoint = 10, 100
with pm.Model():
    mean_sigma = pm.HalfNormal('mean_rw_sigma', 1., shape=n_timeseries)
    prior_means = pm.MvGaussianRandomWalk('rw', mu=np.zeros(n_timeseries), chol=tt.diag(mean_sigma), shape=(n_timepoint, n_timeseries))
1 Like
4

Thanks for your quick help Junpeng! I’ve now raised an issue: Multiple independent random walks with differing innovation sds · Issue #4409 · pymc-devs/pymc3 · GitHub . That diagonal normal version should be a good workaround. I didn’t realise we can just use theano to manipulate tensors like that, that’s really great.