Table 8.

A comparison of the values of $n$, $\alpha$ and $\alpha {\sigma }_a^n$ obtained using the input ‘experimental’ data in table 1 (subscript inp), the Bayesian-type statistical approach with HTS data from §6a(i)(ii) (subscript Bayes), HT data with equation (6.7) (subscript BFNO), and HT data with equation (6.8) (subscript GNP). The subscript ${(\hspace{0.17em})}_{\mathrm{nf}}$ denotes noise-free data and the subscript ${(\hspace{0.17em})}_{0.01}$ denotes values averaged of predictions over 100 realizations with ${\eta }_{\mathrm{h}}={\eta }_{\mathrm{s}}=0.01$. Also shown is the value of $\alpha {\sigma }_a^n$ where for each material, ${\sigma }_a$ is the applied stress in equation (6.1). The values of $n$ used in equations (6.7) and (6.8) were obtained from a least-squares fit to the steady-state portions of the ‘experimental’ indentation depth versus time responses.

	Se	${\mathrm{CsHSO}}_4$	Sn
$n_{\mathrm{inp}}$	1.15	3.59	6.60
${\alpha }_{\mathrm{inp}}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$1.04\times {10}^{-12}$	$9.89\times {10}^{-16}$	$9.97\times {10}^{-47}$
${\alpha }_{\mathrm{inp}}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.50\times {10}^{-5}$	$2.57\times {10}^{-4}$	$2.44\times {10}^{-5}$
$n_{\mathrm{Bayes},\mathrm{nf}}$	1.16	3.58	6.46
${\alpha }_{\mathrm{Bayes},\mathrm{nf}}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.898\times {10}^{-12}$	$10.6\times {10}^{-16}$	$86.7\times {10}^{-47}$
${\alpha }_{\mathrm{Bayes},\mathrm{nf}}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.53\times {10}^{-5}$	$2.56\times {10}^{-4}$	$2.81\times {10}^{-5}$
$n_{\mathrm{Bayes},0.01}$	1.16	3.59	6.59
${\alpha }_{\mathrm{Bayes},0.01}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.895\times {10}^{-12}$	$9.53\times {10}^{-16}$	$19.1\times {10}^{-47}$
${\alpha }_{\mathrm{Bayes},0.01}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.52\times {10}^{-5}$	$2.48\times {10}^{-4}$	$4.04\times {10}^{-5}$
$n_{\mathrm{BFNO},\mathrm{nf}}$	1.17	3.57	6.66
${\alpha }_{\mathrm{BFNO},\mathrm{nf}}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.813\times {10}^{-12}$	$11.6\times {10}^{-16}$	$3.91\times {10}^{-47}$
${\alpha }_{\mathrm{BFNO},\mathrm{nf}}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.78\times {10}^{-5}$	$2.60\times {10}^{-4}$	$2.27\times {10}^{-5}$
$n_{\mathrm{BFNO},0.01}$	1.17	3.57	6.66
${\alpha }_{\mathrm{BFNO},0.01}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.832\times {10}^{-12}$	$11.8\times {10}^{-16}$	$4.59\times {10}^{-47}$
${\alpha }_{\mathrm{BFNO},0.01}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.89\times {10}^{-5}$	$2.65\times {10}^{-4}$	$2.67\times {10}^{-5}$
$n_{\mathrm{GNP},\mathrm{nf}}$	1.17	3.57	6.66
${\alpha }_{\mathrm{GNP},\mathrm{nf}}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.769\times {10}^{-12}$	$5.09\times {10}^{-16}$	$12.3\times {10}^{-47}$
${\alpha }_{\mathrm{GNP},\mathrm{nf}}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.52\times {10}^{-5}$	$1.14\times {10}^{-4}$	$7.15\times {10}^{-5}$
$n_{\mathrm{GNP},0.01}$	1.17	3.57	6.66
${\alpha }_{\mathrm{GNP},0.01}\hspace{0.17em}({\mathrm{Pa}}^{-n}\hspace{0.17em}{\mathrm{s}}^{-1})$	$0.790\times {10}^{-12}$	$5.18\times {10}^{-16}$	$14.2\times {10}^{-47}$
${\alpha }_{\mathrm{GNP},0.01}{\sigma }_a^n\hspace{0.17em}({\mathrm{s}}^{-1})$	$4.65\times {10}^{-5}$	$1.16\times {10}^{-4}$	$8.25\times {10}^{-5}$