![\"copula](\"copula_schematic.png\")
\n",
"\n",
"Schematic of a 2D Gaussian copula. Our complex distribution P(a, b) in observation space (bottom) is modelled as being generated by a 2D Gaussian copula in multivariate normal space (top). Mapping from multivariate normal space to observation space (downwards) is done by the normal cumulative density function and then the inverse cumulative density function of the marginal distributions. The reverse, inference, process (upwards) can be done through the cumulative density function of the marginal distributions followed by an inverse cumulative density function of the normal distribution.\n",
":::"
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"This notebook will describe how to make inferences about copulas based on bivariate data with rich correlational structure. We at [PyMC Labs](https://www.pymc-labs.com) completed this work as part of a larger project with the [Gates Foundation](https://www.gatesfoundation.org), some of which has also been outlined {ref}`here