Appendix A: Program comparison

Comparison of thermobarometric inversion programs, AvPT+ [Green2025], Bingo-Antidote [Duesterhoeft2020], MCMC [Mackay2025], and mc_fit. The comparison is restricted to programs that match observed mineral assemblages directly to thermodynamic models computed by free energy minimization. This restriction, somewhat artificially, excludes the LinaForma [Mackay2024] and IntersecT [Nerone2025] programs in that these programs find the best match between observational data and a pre-computed phase diagram section. In terms of capabilities and limitations, LinaForma and IntersecT are similar to Bingo-Antidote in that they require knowledge of the bulk composition of the system of interest. The more recent contributions ([Mackay2024], [Nerone2025]) have adopted this approach to the simplified problem of minimizing the misfit between observed and predicted in a calculated phase diagram section. mc_fit and avPT+ use Monte Carlo sampling strategies to seek the global minimum of the objective function. MCMC is the only program to implement a Bayesian Markov-Chain Monte Carlo algorithm.

Program	Requires bulk composition	Unmeasured components	Misfit minimizer	Thermodynamic minimizer	Bayesian Option	Thermodynamic Uncertainty[1]	Thermodynamic parameter inversion
AvPT+	No	No	local	local[2]	No	No	No
Bingo-Antidote	Yes	Yes	local	global	No	No	No
MCMC	Yes[3]	Yes	global	global	Yes	No	No
mc_fit	No	Yes	global	global	Yes[4]	Yes	Yes

[1]

MCMC, AvPT+, and mc_fit have the capacity to assess analytical uncertainties.

Bingo-Antidote reports the covariance of the misfit function as a measure of uncertainty. This measure accounts for neither analytical nor thermodynamic uncertainties and is primarily a measure of the shape of the misfit function. This is equivalent to the unfiltered central model covariance ellipse

(Fig. 4, see also

the Nelder-Mead covariance option) reported by mc_fit.

[2]

Use of a local minimizer has the consequence that the stability of the observed phase assemblage is not rigorously tested.

[3]

MCMC is in development, limitations noted here may have changed.

[4]

mc_fit does not do true Bayesian inversion, but the Bayes option permits use of Bayesian-scoring to select the best-fit model.