Thermal history modelling: HeFTy vs. QTQt

HeFTy is a popular thermal history modelling program which is named after a brand of trash bags as a reminder of the 'garbage in, garbage out' principle. QTQt is an alternative program whose name refers to its ability to extract visually appealing ('cute') time-temperature paths from complex thermochronological datasets. This paper compares and contrasts the two programs and aims to explain the algorithmic underpinnings of these 'black boxes' with some simple examples. Both codes consist of 'forward' and 'inverse' modelling functionalities. The 'forward model' allows the user to predict the expected data distribution for any given thermal history. The 'inverse model' finds the thermal history that best matches some input data. HeFTy and QTQt are based on the same physical principles and their forward modelling functionalities are therefore nearly identical. In contrast, their inverse modelling algorithms are fundamentally different, with important consequences. HeFTy uses a 'Frequentist' approach, in which formalised statistical hypothesis tests assess the goodness-of-fit between the input data and the thermal model predictions. QTQt uses a Bayesian 'Markov Chain Monte Carlo' (MCMC) algorithm, in which a random walk through model space results in an assemblage of 'most likely' thermal histories. In principle, the main advantage of the Frequentist approach is that it contains a built-in quality control mechanism which detects bad data ('garbage') and protects the novice user against applying inappropriate models. In practice, however, this quality-control mechanism does not work for small or imprecise datasets due to an undesirable sensitivity of the Frequentist algorithm to sample size, which causes HeFTy to 'break' when datasets are sufficiently large or precise. QTQt does not suffer from this problem, as its performance improves with increasing sample size in the form of tighter credibility intervals. However, the robustness of the MCMC approach also carries a risk, as QTQt will accept physically impossible datasets and come up with 'best fitting' thermal histories for them. This can be dangerous in the hands of novice users. In conclusion, the name 'HeFTy' would have been more appropriate for QTQt, and vice versa.