.. _book_fig_chapter5_fig_posterior_gaussgauss:


Gaussian Distribution with Gaussian Errors
------------------------------------------
Figure 5.8

The solid lines show marginalized posterior pdfs for :math:`\mu` (left) and
:math:`\sigma` (right) for a Gaussian distribution with heteroscedastic
Gaussian measurement errors (i.e., integrals over :math:`\sigma` and
:math:`\mu` for the two-dimensional distribution shown in figure 5.7). For
comparison, the dashed histograms show the distributions of approximate
estimates for :math:`\mu` and :math:`\sigma` (the median and given by eq. 5.68,
respectively) for 10,000 bootstrap resamples of the same data set. The true
values of :math:`\mu` and :math:`\sigma` are indicated by the vertical dotted
lines.



.. image:: ../images/chapter5/fig_posterior_gaussgauss_1.png
    :scale: 100
    :align: center


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