import distl
import numpy as np

Multivariate Gaussian

First we'll create a multivariate gaussian distribution by providing the means and covariances of three parameters.

mvg = distl.mvgaussian([5,10, 12], 
                       np.array([[ 2,  1, -1], 
                                 [ 1,  2,  1], 
                                 [-1,  1,  2]]),
                       allow_singular=True,
                       labels=['a', 'b', 'c'])

mvg.sample()

array([ 3.55132717,  9.78715395, 13.23582678])

mvg.sample(size=5)

array([[ 5.23033061,  9.06949021, 10.8391596 ],
       [ 5.51617199, 11.37966572, 12.86349373],
       [ 3.85260322,  8.08953995, 11.23693674],
       [ 6.14967157, 10.06814347, 10.9184719 ],
       [ 2.99347865,  9.33717474, 13.34369609]])

and plotting will now show a corner plot (if corner is installed)

fig = mvg.plot(show=True)

Multivariate Histogram

we can now convert this multivariate gaussian distribution into a multivariate histogram distribution (alternatively we could create a histogram directly from a set of samples or chains via mvhistogram_from_data.

mvh = mvg.to_mvhistogram(bins=15)

fig = mvh.plot(show=True, size=1e6)

np.asarray(mvh.density.shape)

array([15, 15, 15])

Now if we access the means and covariances, we'll see that they are slightly different due to the binning.

mvh.calculate_means()

array([ 4.96800078,  9.96608606, 11.05088341])

mvh.calculate_covariances()

array([[ 2.14976389,  1.00436435, -0.98909508],
       [ 1.00436435,  2.1466647 ,  1.00202299],
       [-0.98909508,  1.00202299,  2.12926164]])

If we convert back to a multivariate gaussian, these are the means and covariances that will be adopted (technically not exactly as they'll be recomputed from another sampling of the underlying distribution).

mvhg = mvh.to_mvgaussian()

fig = mvhg.plot(show=True)

mvhg.mean

array([ 4.96926904,  9.96608361, 11.05252993])

mvhg.cov

array([[ 2.16982623,  1.01293887, -1.00812602],
       [ 1.01293887,  2.14302785,  0.99148548],
       [-1.00812602,  0.99148548,  2.14529892]])

Take Dimensions

mvg_ac = mvg.take_dimensions(['a', 'c'])

mvg_ac.sample()

array([ 5.54537489, 10.75561886])

out = mvg_ac.plot(show=True)

out = mvh.take_dimensions(['a', 'c']).plot(show=True)

Passing a single dimension to take_dimension

If you pass a single-dimension to take_dimension, then the univariate version of the same type is returned instead. See the "Converting to Univariate" section below for examples directly calling to_univariate.

out = mvg.take_dimensions(['a']).plot(show=True)

Slicing

Slicing allows taking a single dimension while retaining all underlying covariances such that the resulting distribution can undergo math operations, and/or logic, and included in distribution collections. For more details, see the slice examples.

mvg_a = mvg.slice('a')

mvg_a.sample()

2.3793905616172655

out = mvg_a.plot(show=True)

mvg_a.multivariate

<distl.mvgaussian mean=[5, 10, 12] cov=[[ 2  1 -1]
 [ 1  2  1]
 [-1  1  2]] allow_singular=True labels=['a', 'b', 'c']>

Converting to Univariate

There are methods to convert directly to the univariate distribution of the same type as the univariate:

• Multivariate.to_univariate.
• MultivariateSlice.to_univariate.

When acting on a Multivariate, the requested dimension must be passed.

mvg.to_univariate(dimension='a')

<distl.gaussian loc=5.0 scale=1.4142135623730951 label=a>

Whereas a MultivariateSlice converts using the sliced dimension

mvg_a.to_univariate()

<distl.gaussian loc=5.0 scale=1.4142135623730951 label=a>