Probabilistic forecast of low-level wind shear over Jeju international airport using non-homogeneous regression model

Ensemble verification of low-level wind shear (LLWS) is an important issue in airplane landing operation and management. However, there have been few studies on the probabilistic forecasts of LLWS obtained from ensemble prediction system. In this study, we analyzed a reliability analysis to verify LLWS ensemble member forecasts and observation based on the limited grid points around Jeju International Airport in Jeju. Homogeneous and non-homogeneous regression models were used to reduce the bias and dispersion existing ensemble prediction system and to provide probabilistic forecast. Prior to applying probabilistic forecast model, reliability analysis was conducted by using rank histogram to identify the statistical consistency of LLWS ensemble forecasts and corresponding observations. Based on the results of our study, we found that LLWS ensemble forecasts had a consistent positive bias, indicating over-forecasting, and were under-dispersed for all seasons. To correct such biases, homogeneous regression and non-homogeneous regressions as EMOS (Ensemble Model Output Statistics) and EMOS exchangeable model by assuming exchangeable ensemble members were applied. The prediction skills of the methods were compared by the mean absolute error and continuous ranked probability score. We found that the prediction skills of probabilistic forecasts of EMOS exchangeable model were superior to the bias-corrected forecasts in terms of deterministic prediction.

Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models

Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to 0. Computations of the total variation distance for the distribution of the number of types in the sample suggest that the exact Moran model provides a better approximation for the sampling formula under the exact Wright-Fisher model than the Ewens sampling formula in the limit of the Kingman coalescent with nonrecurrent mutation. On the other hand, this model seems to provide a good approximation for a Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.

Recurrence Equations for the Probability Distribution of Sample Configurations in Exact Population Genetics Models

Recurrence equations for the number of types and the frequency of each type in a random sample drawn from a finite population undergoing discrete, nonoverlapping generations and reproducing according to the Cannings exchangeable model are deduced under the assumption of a mutation scheme with infinitely many types. The case of overlapping generations in discrete time is also considered. The equations are developed for the Wright-Fisher model and the Moran model, and extended to the case of the limit coalescent with nonrecurrent mutation as the population size goes to ∞ and the mutation rate to 0. Computations of the total variation distance for the distribution of the number of types in the sample suggest that the exact Moran model provides a better approximation for the sampling formula under the exact Wright-Fisher model than the Ewens sampling formula in the limit of the Kingman coalescent with nonrecurrent mutation. On the other hand, this model seems to provide a good approximation for a Λ-coalescent with nonrecurrent mutation as long as the probability of multiple mergers and the mutation rate are small enough.

A genealogical approach to variable-population-size models in population genetics

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

A genealogical approach to variable-population-size models in population genetics

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.