Table 2.

Comparison of ABC methods for the enzyme kinetics model inference problem. Estimates of the posterior mean are given along with the $95\text{\%}$ CIs. Signed relative errors are shown for the confidence interval limits with respect to the true parameter values k₁ = 0.001, k₂ = 0.005 and k₃ = 0.01. Computations are performed using an Intel^® Core^TM i7-5600U CPU (2.6 GHz).

method	posterior mean estimate	relative error	compute time
ABC rejection	${\hat{k}}_1=1.0098\times {10}^{-3}\pm 1.7011\times {10}^{-4}$	$[-16.0\text{\%},18.0\text{\%}]$	2037 (s)
sampler	${\hat{k}}_2=7.7203\times {10}^{-3}\pm 7.3490\times {10}^{-4}$	$[39.7\text{\%},69.1\text{\%}]$
	${\hat{k}}_3=1.5164\times {10}^{-2}\pm 2.1201\times {10}^{-3}$	$[30.4\text{\%},72.8\text{\%}]$
ABCMCMC	${\hat{k}}_1=3.0331\times {10}^{-4}\pm 7.5670\times {10}^{-5}$	$[-77.2\text{\%},-62.1\text{\%}]$	2028 (s)
	${\hat{k}}_2=5.8106\times {10}^{-3}\pm 7.9993\times {10}^{-4}$	$[0.2\text{\%},32.2\text{\%}]$
	${\hat{k}}_3=3.3865\times {10}^{-2}\pm 3.0187\times {10}^{-3}$	$[208.5\text{\%},268.8\text{\%}]$
ABCSMC	${\hat{k}}_1=9.8972\times {10}^{-4}\pm 1.4630\times {10}^{-4}$	$[-15.7\text{\%},13.6\text{\%}]$	342 (s)
	${\hat{k}}_2=9.2680\times {10}^{-3}\pm 9.1997\times {10}^{-4}$	$[67.0\text{\%},103.8\text{\%}]$
	${\hat{k}}_3=1.3481\times {10}^{-2}\pm 1.3278\times {10}^{-3}$	$[21.5\text{\%},48.1\text{\%}]$
ABCMLMC	${\hat{k}}_1=1.0859\times {10}^{-3}\pm 6.7058\times {10}^{-5}$	$[1.9\text{\%},15.3\text{\%}]$	795 (s)
	${\hat{k}}_2=6.8111\times {10}^{-3}\pm 3.2107\times {10}^{-4}$	$[29.9\text{\%},42.6\text{\%}]$
	${\hat{k}}_3=1.3663\times {10}^{-2}\pm 1.0729\times {10}^{-3}$	$[25.9\text{\%},47.4\text{\%}]$