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A general simulation API should be provided, and used in CompiledModel.simulate and FitHelper's simulation functions.

Negative background data can be produced from normal distribution, which should be set to zeros when the total spectrum data follows Poisson distribution.

It is well known that profile likelihood can be biased. For W-statistics, numerical experiments showed re-binning can avoid this bias (see e.g., Giacomo's blog and Johannes's review).

For PG-statistics, a certain criteria, $\hat B/\hat\sigma_B^2 \ge \alpha(1-N/S)$, should be met so that the background will not be negative. If the criteria is not met, then the background will be truncated at zero, which introduces a similar bias like W-statistics. We should also conduct a numerical experiment to see how to avoid the bias.

When using a spectral model that includes some Xspec models (e.g., apec, phabs, ztbabs, tbfeo, tbgas, tbgrain, tbpcf, tbvarabs, and tbrel), parallel computing will fail.

As an alternative to tbabs or phabs, consider using elisa.models.mul.TBAbs or elisa.models.mul.PhAbs. For the other models, a sequential computing approach should be used.

We should implement grouping method as in ftgrouppha.

Grouping method should also take data type into consideration, i.e., for poisson data with poisson background or gaussian background, we should use Li-Ma significance or GV significance formulae to assess the SNR.

The NUTS sampling procedure is first defined by PyMC/PyTensor, and "jaxified" later. This has the issue that the finite difference wraparound for Xspec's models library will not work.

Transforming backend from PyTensor to JAX can fix this.

This inefficiency occurs when some parameters are fixed during computation. The finite differences will be computed for these fixed parameters, which are not (?) optimized by JAX.

Details about how Xspec groups the area/background array, see the OGIP_92aData::groupArrays function in this link.