We compare the results of fitting a physiologically-based pharmacokinetic (PBPK) model to a classical theophylline dataset [1] with frequentist parametric and non-parametric asymptotic methods (QRPEM: Quasi Random Parametric EM [2, 3] and NPAG: Non-parametric Adaptive Grid [4]), and two Bayesian numerical samplers: Metropolis-Hastings Markov chain Monte Carlo (MCMC) [5] and Hamiltonian Markov chain Monte Carlo (HMCMC) [6]. QRPEM and NPAG, as implemented in the Simcyp Simulator version 19, gave consistent population and individual parameter estimates and were in reasonable agreement with HMCMC or MCMC estimates. The run-times of both QRPEM and NPAG estimations were similar to those with HMCMC. MCMC simulations ran much faster, partly because they were not tasked with estimating the full population covariance matrix.