Physiologically-based pharmacokinetic (PBPK) models usually include a large number of parameters whose values are obtained using in vitro to in vivo extrapolation. However, such extrapolations can be uncertain and may benefit from inclusion of evidence from clinical observations via parametric inference. When clinical interindividual variability is high, or the data sparse, it is essential to use a population pharmacokinetics inferential framework to estimate unknown or uncertain parameters. Several approaches are available for that purpose, but their relative advantages for PBPK modeling are unclear. We compare the results obtained using a minimal PBPK model of a canonical theophylline dataset with quasi-random parametric expectation maximization (QRPEM), nonparametric adaptive grid estimation (NPAG), Bayesian Metropolis-Hastings (MH), and Hamiltonian Markov Chain Monte Carlo sampling. QRPEM and NPAG gave consistent population and individual parameter estimates, mostly agreeing with Bayesian estimates. MH simulations ran faster than the others methods, which together had similar performance. Study Highlights WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?No single software platform allows practitioners to compare parametric and nonparametric estimates of calibrated physiologically-based pharmacokinetic (PBPK) model parameters. WHAT QUESTION DID THIS STUDY ADDRESS?How do a maximum likelihood parametric (quasi-random parametric expectation maximization) and nonparametric (nonparametric adaptive grid estimation) algorithms, and two Bayesian numerical methods (Hamiltonian Markov Chain Monte Carlo and MH) compare in results and timing for calibration of a PBPK model?