Pathfinder initialisation

[SamuelBrand1]

This draft PR is aimed at addressing #56 .

Implemented feature

• A "safe-mode" version of the turing model to avoid early check-out in pathfinder runs here. This is to be used internally.

Usage

The usage is being developed in script here:

Rt-without-renewal/EpiAware/test/predictive_checking/toy_model_log_infs_RW.jl

Lines 158 to 175 in 6c36e30

	safe_model = make_epi_aware(truth_data, time_horizon, Val(:safe);
	epi_model = epi_model,
	latent_model_model = rwp,
	observation_model = obs_model,
	pos_shift = 1e-6)
	mpf_result = multipathfinder(safe_model, 1000; nruns = 10)
	mpf_chn = mpf_result.draws_transformed
	@time chn = sample(model,
	NUTS(; adtype = AutoReverseDiff(true)),
	MCMCThreads(),
	250,
	4;
	drop_warmup = true,
	init_params = collect.(eachrow(mpf_chn.value[1:4, :, 1]))
	)

API goal

A wrapper function that ingests an EpiAware model specification, data and runs the whole inference from pathfinder through NUTS.