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uq [2018/12/03 11:06] – [The Ensemble Method] slongbottomuq [2018/12/03 11:08] – [Hessian Bracketing Algorithm] slongbottom
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 **Only use this if you know what you are doing! ** **Only use this if you know what you are doing! **
  
-If ''hess_pert = -1'' the parameter perturbations used in the finite difference calculation of the hessian are found individually. This algorithm can be used as a diagnostic tool to understand the curvature on the length scale of the sampling temperature. However care should be taken when analysing the information as many assumptions about the cost minimum are inherently made (e.g. that the landscape at the sampling temperature height is harmonic). Each parameter is perturbed to bracket the perturbation value yielding a the cost set by the sampling temperature - $C_T = C_0 + T = C_0 +\frac{2\alpha C_0}{N}$. When the bracketing interval is within 5% of $C_T$, a drawn between the two bounds and the gradient is used to choose the perturbation value estimated to give a cost of $C_T$.+If ''hess_pert = -1'' the parameter perturbations used in the finite difference calculation of the hessian are found individually. This algorithm can be used as a diagnostic tool to understand the curvature on the length scale of the sampling temperature. However care should be taken when analysing the information as many assumptions about the cost minimum are inherently made (e.g. that the landscape at the sampling temperature height is harmonic). Each parameter is perturbed to bracket the perturbation value yielding a the cost set by the sampling temperature - $C_T = C_0 + T = C_0 +\frac{2\alpha C_0}{N}$. When the bracketing interval is within 5% of $C_T$, a line is drawn between the two bounds and the gradient is used to choose the perturbation value estimated to give a cost of $C_T$.
  
 If the landscape at this scale is not harmonic, the eigenvalues of the hessian will be negative. In this case a reduced sampling temperature may be required and the user should think about improving the reference data being fit to, as well as the suitability and possible limitations of the potential model being used. If the landscape at this scale is not harmonic, the eigenvalues of the hessian will be negative. In this case a reduced sampling temperature may be required and the user should think about improving the reference data being fit to, as well as the suitability and possible limitations of the potential model being used.
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 ^ **hess_pert** | float | 0.00001 | ^ **hess_pert** | float | 0.00001 |
-| Percentage parameter perturbation in Hessian finite difference calculation. (If ''hess_pert = -1'' a bracketing algorithm is used to find individual parameter perturbation values, see [[hessian bracketing algorithm]] - only use this is you know what you are doing!) |||+| Percentage parameter perturbation in Hessian finite difference calculation. (If ''hess_pert = -1'' a bracketing algorithm is used to find individual parameter perturbation values, see explanation above - only use this is you know what you are doing!) |||
  
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