Conclusions

This section describes the conclusions, obtained from the Bayesian inference process, about the parameters in the two models, and about which model is correct.

1. The electrostatic potential in the sample, as a function of cobalt thickness, in the null model, is as shown in figure 5.8.

   Figure: A Graph of the Inferred Electrostatic Potential in the Sample, in the Null Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.

   

2. The electrostatic potential in the sample, as a function of cobalt thickness, in the main model, is as shown in figure 5.9.

   Figure: A Graph of the Inferred Electrostatic Potential in the Sample, in the Main Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.

   

3. The magnetic flux density in the sample, as a function of cobalt thickness, in the main model, is as shown in figure 5.10.

   Figure: A Graph of the Inferred Magnetic Flux Density in the Sample, in the Main Model, against $Co$ Thickness. The Conversion factor between the Units of Thickness on the Horizontal Axis, and More Conventional Thickness Units, Is (appendix B) $(78\pm{}11)\,\mathrm{\mu{}m}\,\mathrm{A}^{-1}\,\mathrm{s}^{-1}$.

   

4. The posterior probability of the null model, in which cobalt ferro-magnetism is not detected, is estimated at $0.34\times{}10^{-2014444631}$ , and that of the main model, in which cobalt ferro-magnetism is detected, at $0.1\times{}10^{1}$ .

At first glance, the precision of the inferred electrostatic potentials and magnetic flux densities appears a rather unimpressive return on the experimental effort involved in obtaining the measurements. In addition, a comparison (tables 5.4, 5.5) of the beliefs held about all of the parameters, including those concerned with instrumental calibration and with transient instrumental characteristics, before and after the data in chapter 5, along with the published calibration data (figures 5.6, 5.7,) have been taken into account, shows a broadening, rather than the narrowing that one might expect, of the probability distribution over the parameter set, due to the data.

However, the very decisive choice of model with successful detection of the Weiss field as the better model supplies a greater reward.

Table 5.4: The Effect of the Experimental Evidence on Beliefs about Parameters in the Null (Non-Magnetic Cobalt) Model. The Parameters Are Described in Tables 5.6 and 5.7

Parameter	Prior Value	Posterior Value
$a$	$0.5\pm{}0.29$	$-0.03\pm{}0.53$
$P_{10}$	$1\pm{}0.05$	$0.8\pm{}3.1$
$P_{11}$	$1\pm{}0.05$	$0.6\pm{}3$
$P_{12}$	$1\pm{}0.05$	$0.9\pm{}3.7$
$P_{13}$	$1\pm{}0.05$	$1.14\pm{}0.82$
$P_{14}$	$1\pm{}0.05$	$0.6\pm{}3.5$
$P_{15}$	$1\pm{}0.05$	$0.8\pm{}5.1$
$P_{16}$	$1\pm{}0.05$	$1.17\pm{}0.97$
$P_{17}$	$1\pm{}0.05$	$0.7\pm{}1.8$
$P_{20}$	$1\pm{}0.05$	$0.8\pm{}3.1$
$P_{21}$	$1\pm{}0.05$	$0.8\pm{}2.9$
$P_{22}$	$1\pm{}0.05$	$0.8\pm{}3.8$
$P_{23}$	$1\pm{}0.05$	$1.23\pm{}0.67$
$P_{24}$	$1\pm{}0.05$	$1.1\pm{}3.3$
$P_{25}$	$1\pm{}0.05$	$0.9\pm{}5.1$
$P_{26}$	$1\pm{}0.05$	$1.34\pm{}0.73$
$P_{27}$	$1\pm{}0.05$	$1.4\pm{}1.4$
$\Gamma_0$	$0.5\pm{}0.29$	$-0.4\pm{}4.4$
$\Gamma_1/\,\mathrm{fJ}^{-1}$	$0\pm{}6.2$	$20\pm{}170$
$\Gamma_2/\,\mathrm{fJ}^{-2}$	$0\pm{}39$	$-100\pm{}1200$
$\Gamma_3/\,\mathrm{fJ}^{-3}$	$0\pm{}240$	$-600\pm{}3100$
$\Gamma_4/\,\mathrm{fJ}^{-4}$	$0\pm{}1500$	$-4000\pm{}19000$
$\Gamma_5/\,\mathrm{fJ}^{-5}$	$0\pm{}9500$	$30000\pm{}170000$
$S_0$	$0\pm{}0.58$	$0\pm{}15$
$S_1/\,\mathrm{fJ}^{-1}$	$0\pm{}12$	$-10\pm{}730$
$S_2/\,\mathrm{fJ}^{-2}$	$0\pm{}78$	$-100\pm{}2000$
$S_3/\,\mathrm{fJ}^{-3}$	$0\pm{}490$	$-2000\pm{}24000$
$S_4/\,\mathrm{fJ}^{-4}$	$0\pm{}3000$	$20000\pm{}240000$
$S_5/\,\mathrm{fJ}^{-5}$	$0\pm{}19000$	$-60000\pm{}680000$
$\eta_1$	$0.835\pm{}0.032$	$0.79\pm{}0.56$
$\eta_2$	$0.835\pm{}0.032$	$0.81\pm{}0.76$
$V_0/\,\mathrm{V}$	$-0.55\pm{}0.31$	$-0.5\pm{}4.2$
$V_1/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1\pm{}3.3$
$V_2/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1.1\pm{}3.4$
$V_3/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-0.1\pm{}5$
$V_4/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-0.5\pm{}4$
$V_5/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1.1\pm{}6.9$
$V_6/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1\pm{}11$
$V_7/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1.5\pm{}4.7$

Parameter	Prior Value	Posterior Value
$a$	$0.5\pm{}0.29$	$0.06\pm{}0.38$
$P_{10}$	$1\pm{}0.05$	$1.27\pm{}0.93$
$P_{11}$	$1\pm{}0.05$	$1.8\pm{}2.1$
$P_{12}$	$1\pm{}0.05$	$-0.3\pm{}2.8$
$P_{13}$	$1\pm{}0.05$	$1.3\pm{}2.3$
$P_{14}$	$1\pm{}0.05$	$-0.3\pm{}3.2$
$P_{15}$	$1\pm{}0.05$	$0.8\pm{}2$
$P_{16}$	$1\pm{}0.05$	$0.4\pm{}1.6$
$P_{17}$	$1\pm{}0.05$	$0.2\pm{}2.5$
$P_{20}$	$1\pm{}0.05$	$0.3\pm{}1.5$
$P_{21}$	$1\pm{}0.05$	$0.6\pm{}2.7$
$P_{22}$	$1\pm{}0.05$	$1.3\pm{}2.6$
$P_{23}$	$1\pm{}0.05$	$0.5\pm{}2.5$
$P_{24}$	$1\pm{}0.05$	$1.5\pm{}2.8$
$P_{25}$	$1\pm{}0.05$	$1.8\pm{}1.1$
$P_{26}$	$1\pm{}0.05$	$0.4\pm{}1.6$
$P_{27}$	$1\pm{}0.05$	$0.8\pm{}2.4$
$\Gamma_0$	$0.5\pm{}0.29$	$-0.5\pm{}2.8$
$\Gamma_1/\,\mathrm{fJ}^{-1}$	$0\pm{}6.2$	$25\pm{}100$
$\Gamma_2/\,\mathrm{fJ}^{-2}$	$0\pm{}39$	$-260\pm{}600$
$\Gamma_3/\,\mathrm{fJ}^{-3}$	$0\pm{}240$	$1500\pm{}3000$
$\Gamma_4/\,\mathrm{fJ}^{-4}$	$0\pm{}1500$	$-2000\pm{}12000$
$\Gamma_5/\,\mathrm{fJ}^{-5}$	$0\pm{}9500$	$-9000\pm{}95000$
$S_0$	$0\pm{}0.58$	$-0.3\pm{}7.4$
$S_1/\,\mathrm{fJ}^{-1}$	$0\pm{}12$	$70\pm{}200$
$S_2/\,\mathrm{fJ}^{-2}$	$0\pm{}78$	$-500\pm{}1100$
$S_3/\,\mathrm{fJ}^{-3}$	$0\pm{}490$	$-700\pm{}9700$
$S_4/\,\mathrm{fJ}^{-4}$	$0\pm{}3000$	$-20000\pm{}62000$
$S_5/\,\mathrm{fJ}^{-5}$	$0\pm{}19000$	$170000\pm{}530000$

Table 5.5: The Effect of the Experimental Evidence on Beliefs about Parameters in the Main (Magnetic Cobalt) Model. The Parameters Are Described in Tables 5.6 and 5.7

$\eta_1$	$0.835\pm{}0.032$	$0.5\pm{}0.71$
$\eta_2$	$0.835\pm{}0.032$	$0.71\pm{}0.38$
$V_0/\,\mathrm{V}$	$-0.55\pm{}0.31$	$1.2\pm{}8.5$
$V_1/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-1\pm{}4.3$
$V_2/\,\mathrm{V}$	$-0.9\pm{}0.32$	$1.5\pm{}6.6$
$V_3/\,\mathrm{V}$	$-0.9\pm{}0.32$	$1\pm{}5.4$
$V_4/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-0.4\pm{}5.8$
$V_5/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-2.1\pm{}5.2$
$V_6/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-0.4\pm{}4.4$
$V_7/\,\mathrm{V}$	$-0.9\pm{}0.32$	$-2.4\pm{}6.5$
$B_1/\,\mathrm{T}$	$0\pm{}1000$	$1000\pm{}10000$
$B_2/\,\mathrm{T}$	$0\pm{}1000$	$0\pm{}16000$
$B_3/\,\mathrm{T}$	$0\pm{}1000$	$-4000\pm{}22000$
$B_4/\,\mathrm{T}$	$0\pm{}1000$	$1000\pm{}22000$
$B_5/\,\mathrm{T}$	$0\pm{}1000$	$7000\pm{}21000$
$B_6/\,\mathrm{T}$	$0\pm{}1000$	$-5000\pm{}30000$
$B_7/\,\mathrm{T}$	$0\pm{}1000$	$-6000\pm{}24000$