However, velocity model calibration for location with surface instruments is difficult for several reasons: well log measurements are often inaccurate or incomplete, yielding intractable models; origin times of perforation shots are not always accurate; and the non-uniqueness of velocity models obtained by inversion becomes especially problematic when only perforation shots are used.
Taking this issue on the grounds of how models can be integrated under a coherent framework that is both flexible and plausible [48], we believe that rational analyses that arrive at wildly worst-case intractable models should not be a big concern because worst cases are uncommon.
However complex problems may entitle intractable models, and approximations of the biological scenario become a prerogative.
Conversely, if the sampling rate is too high it can be computationally intractable to model far enough into the future (i.e. high model order m) to capture interactions.
These data have been widely used, for example, to predict properties of populations retrospectively or prospectively according to mathematically intractable genetic models, and to assist the validation, statistical inference and power analysis of a variety of statistical models.
Currently, many physicists are pursuing such "quantum simulations" because the experiments may provide the best hope for solving such intractable mathematical models, which themselves are abstractions of the far messier physics of electrons whizzing around in solids.
At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions.
Consequently, a general proof of existence appears intractable in this model but existence can be demonstrated within the special case where s → 0. Here, the model collapses to some standard search models and so we can apply previous results.
In this circumstance, MCS requires a potentially burdensome (if not computationally intractable) number of model evaluations to obtain a credible estimate of the global statistics.
Under the analytic approach used here, continuous distribution of "immune-types" would inevitably make the model intractable.
