View plots of the log posterior around the posterior mode for each parameter. In the plots of the log posterior around the mode, YADA evaluates the log posterior based on a grid whose parameters are determined on the Optimization frame on the Settings tab. The procedure is based on fixing all the other parameters at the mode, thus providing a plot of the conditional log posterior for the parameter in question.
To evaluate the usefulness of various inverse Hessian estimators, YADA plots the normal approximation using the conditional standard deviation from the inverse Hessian that the optimization routine provides. In addition, YADA estimates the standard deviation which provides the best fit to the log posterior in a mean squared sense. This standard deviation provides a basis for modifying the inverse Hessian.
In addition, YADA provides plots of the log posterior around the mode alongside plots of the log likelihood. The latter function is scaled such that its value at the mode is equal to the value of the log posterior. That is, the value of the log prior at the mode is added to the value of the log likelihood. The graph gives an idea about how far away a maximum likelihood estimate of the parameters is from the posterior mode estimate, i.e., how much weight is given to the prior.
Additional Information
• | A more detailed description about checking the optimum can also be found in Sections 7.1 and 7.2 of the YADA Manual. |
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