# TransportMaps¶

We use (transport) maps from \(\mathbb{R}^d\) to \(\mathbb{R}^d\) to represent transformations between probability distributions. These transformations lead to efficient algorithms for the solution of practical **inference problems**, or for the **estimation of densities from samples**.

For example, if \(Y \sim \nu_\pi\) is a complex distribution and \(X \sim \nu_\rho\) is an amenable distribution (e.g. standard normal) we look for a computable and invertible map \(T\) such that \(Y = T(X)\). This allows us to apply the following change of variables

obtaining a tractable integral from an otherwise intractable one.

The actual version of TransportMaps implements a
`taxonomy`

of maps, distributions
and likelihoods which allow for modeling many complex problems.