(i) Estimation of model parameters
We estimate the parameters θ = {Tmin,Tmax, c, σ} using Bayesian inference methods (Gelman et al . 2013, Bolstad et al . 2016, McElreath 2016) implemented using the available data. The parameters Tmin, Tmax and c have been defined earlier. The quantity σ provides the scale factor for the width of the likelihood between observed data and model.
Our implementation of the inference strategy uses STAN (https://mc-stan.org/), a platform for statistical modelling and high-performance statistical computation. STAN performs Bayesian statistical inference with Markov Chain Monte Carlo (MCMC) sampling. It also provides diagnostic tools to evaluate the accuracy and convergence of the MCMC while allowing for posterior predictive checks.