Create¶
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
http://www.statsmodels.org/devel/examples/notebooks/generated/chi2_fitting.html https://github.com/cdeil/pyfit/blob/master/fitting_tutorial/src/tests/chi2_example.py https://lmfit.github.io https://iminuit.readthedocs.io https://sherpa.readthedocs.io
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
name
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