A growing arsenal of option models has emerged that extend the same underlying methodology beyond the basic formula, incorporating more variables and more-robust assumptions for specialized applications.
Numerical results support that our proposed method is computationally efficient, produces more accurate estimates than those commonly used and the estimates are more robust to model assumptions.
Such an estimator may be more robust to model assumptions and/or be diagnostic for data that deviates from the model.
By taking into account evolutionary history, coalescent-based estimates are more robust to model assumptions and allow us to determine factors influencing the observed patterns (see below).
Another solution is to use, generalized estimating equations (GEE) [ 31], an alternative method that is (in our experience, slightly) more robust to this assumption failure.
This assumes that frame shifts never happen, and statistical alignment approaches using codon models may be more robust to this assumption.
By taking into account these variables, the resulting time estimates are more robust and have fewer assumptions.
The uncorrelated lognormal (UCLN) model draws its rates from a lognormal distribution and appears to be more robust to violation of assumptions about clock rate variation, and a better fit to simulated and empirical datasets, than are strict or autocorrelated clock models [ 11, 12].
These case studies contribute to a more robust basis for the assumption that many, if not all, toxicological effects exhibit biological thresholds and provide guidance on research needs to further address this question.
The Bayesian bootstrap (BB) is quite similar to conventional frequentist bootstrap (Efron 1979), except that it provides a method for simulating the posterior distribution of the parameters of interest rather than the sampling distribution of parameters of interest, and as such, is more robust to violations of distributional assumptions associated with the posterior distribution.
