As we saw in Getting started, to create a MultiNorm object, you pass a mean vector, a covariance matrix (both as Numpy arrays) and optionally a list of parameter names:

from multinorm import MultiNorm
mean = [10, 20, 30]
covariance = [[1, 0, 0], [0, 4, 0], [0, 0, 9]]
names = ["a", "b", "c"]
mn = MultiNorm(mean, covariance, names)

But where do these things come from?

On this page, we look at the most common scenarios.

Create from fit

TODO: show example using scipy.optimize.curve_fit

To use multinorm, we first need to fit some parameterised model to obtain a best-fit parameter vector and covariance matrix.

Let’s use scipy.optimize.curve_fit to fit some data.

TODO: show example using iminuit

Create from publication

TODO: show example how to take covar (or par errors) from a publication or blog post, i.e. as inputs.

Create from samples

A common way to analyse likelihood or in Bayesian analyses the posterior probability distributions is to use MCMC methods that sample the distribution. E.g. emcee or pymc are Python packages that generate this kind of output.

Estimating the multivariate normal distribution from samples well can be difficult, there are many methods with different trade-offs. We recommend using a different package for this task, e.g. sklearn.covariance.

That said, there is a method MultiNorm.from_samples that calls numpy.std to compute the mean vector, and numpy.cov to compute what’s sometimes called the “empirical” multivariate normal estimate.

Samples should always be given as 2-dimensional arrays with shape (n_dim, n_samples).

>>> samples = mn.sample(size=100, random_state=0)
>>> MultiNorm.from_samples(samples, names=mn.names)
MultiNorm with n=3 parameters:
           mean       error
a      9.875816  0.980901
b     20.212505  1.973948
c     30.301562  3.093609

From stack

TODO: document MultiNorm.from_stack

From product

TODO: document MultiNorm.from_product

Make example

TODO: document MultiNorm.make_example