.. _book_fig_chapter5_fig_likelihood_gaussgauss:


Gaussian Distribution with Gaussian Errors
------------------------------------------
Figure 5.7

The logarithm of the posterior probability density function for :math:`\mu`
and :math:`\sigma`, :math:`L_p(\mu,\sigma)`, for a Gaussian distribution with
heteroscedastic Gaussian measurement errors (sampled uniformly from the 0-3
interval), given by eq. 5.64. The input values are :math:`\mu = 1` and
:math:`\sigma = 1`, and a randomly generated sample has 10 points. Note that
the posterior pdf is not symmetric with respect to the :math:`\mu = 1` line,
and that the outermost contour, which encloses the region that contains 0.997
of the cumulative (integrated) posterior probability, allows solutions with
:math:`\sigma = 0`.



.. image:: ../images/chapter5/fig_likelihood_gaussgauss_1.png
    :scale: 100
    :align: center


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