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What about data with very small or large values of $T$?

Data with many small or large $T_i$ cause no problems with the method in theory. Moreover, data like these produce estimates with very narrow bounds (since the tomography lines cut off the top right or bottom left corner of the plot). This is good news for estimation, although if the difference between, say, $\beta_i^b=0.01$ and $\beta_i^b=0.005$ is substantively large (as for mortality rates), what might otherwise be considered ``narrow'' bounds (such as [0,0.05]) could in some cases still be too wide for particular substantive purposes, so be careful about interpretation. To read the graphs, it is helpful to zoom in on the relevant regions, by setting globals such as _eigraph_Xlo, _eigraph_BBhi, etc. Be sure to check and probably reduce the global _EnumTol, since the default value (0.0001) would define some data sets as unanimous ($T_i=0,1$) for too many observations. Beware also of other numerical problems with data like these (by verifying the fit of the contours to the data with eigraph's tomogS and fit), since the contours must be fit to a very small area of the tomography plot and so calculating the cdf of the truncated bivariate normal can be imprecise. It is often necessary to use better starting values (see _Estval) and search constraints (_Ebounds) than the defaults. The grid search procedure can also be helpful (_Estval). Since odds are you want to distinguish between very small differences in the quantities of interest, you will probably also wish to increase the number of simulations substantially (_Esims). Finally, posterior densities from EI are rarely normal or symmetric in the presence of rare events, and in this situation mean posterior point estimates are not good summaries of EI's inference in these situations. Better would be to use a density estimate of the simulations, such as eigraph's post option.