Add Jax Inference Methods

[BradyPlanden]

Feature description

#481 adds the Jaxified IDAKLU solver as an experimental implementation with auto-differentiation applied to the cost/likelihood functions. This issue aims to expand this functionality with Jax inference methods such as:

• Numpyro for MCMC sampling
• Optax for frequentist/deterministic inference methods
• GPJax for Gaussian Processes
• BlackJax for sampling

Motivation

Jax offers a compiled interface for parameter optimisation with lowering to both GPU/TPU. This can enable both performance improvements for PyBOP's methods, as well as removing the need for manual definition of gradients from cost/likelihoods.

Possible implementation

Design outlines and discussion needs to occur to ensure an integrated development into PyBOP's predefined design.

Additional context

No response