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We present in this paper a way to transform a constrained statisticalinference problem into an unconstrained one in order to be able to use moderncomputational methods, such as those based on automatic differentiation, GPUcomputing, stochastic gradients with mini-batch.  Unlike the parametrizations classically used in Machine Learning, theparametrizations introduced here are all bijective and are evendiffeomorphisms, thus allowing to keep the important properties from astatistical inference point of view, first of all identifiability.  This cookbook presents a set of recipes to use to transform a constrainedproblem into a unconstrained one.  For an easy use of parametrizations, this paper is at the same time acookbook, and a Python package allowing the use of parametrizations with numpy,but also JAX and PyTorch, as well as a high level and expressive interfaceallowing to easily describe a parametrization to transform a difficult problemof statistical inference into an easier problem addressable with modernoptimization tools.

Parametrization Cookbook: A set of Bijective Parametrizations for using Machine Learning methods in Statistical Inference