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This paper proposes a new post-processing method for model data in order to improve typhoon track and rainfall forecasts. The model data used in the article include low-resolution ensemble forecasts and high-resolution forecasts. The entire improvement method contains the following three steps. The first step is to correct the typhoon track forecast: three ensemble member optimization methods are applied to the low-resolution ensemble forecasts, and then the best optimization method is selected with the principle of the smallest average distance error. The results of rainfall forecasts show that the corrected rainfall forecast performs better than the original forecasts. The second step is to derive the high-resolution probability rainfall forecast: the neighborhood method is applied to the deterministic high-resolution rainfall forecast. The last step is to correct the typhoon rainfall forecast: the low- and high-resolution forecasts are blended using the probability-matching method with two different schemes. The results show that the forecasts of the two schemes perform better than the original forecast under all rainfall thresholds and all forecast lead times. In terms of bias score, a rain forecast from one scheme corrects the rainfall deviation from observation better for light and moderate rainfall, whereas a rain forecast from another scheme corrects the rainfall deviation better for heavy and torrential rainfall. The better performance of corrected rain forecasts in the case of Typhoon Lekima and Rumbia over eastern China is demonstrated.

This present study aims to explore how forecasters can quickly make accurate predictions by using various high-resolution model forecasts. Based on three high temporal-spatial resolution (3 km, hourly) numerical weather prediction models (CMA-MESO, CMA-GD, CMA-SH3) from the China Meteorological Administration (CMA), the hourly precipitation characteristics of three model within 24 h from March to September 2020 are discussed and integrated into a single, hourly, deterministic quantitative precipitation forecast (QPF) by making use of an improved weighted moving average probability-matching method (WPM). The results are as follows: (1) In non-rainstorm forecasts, CMA-MESO and CMA-GD have similar forecast abilities. However, in rainstorm forecasts, CMA-MESO has a notable advantage over the other two models. Thus, CMA-MESO is selected as a critical factor when participating in sensitivity experiments. (2) Compared with the traditional equal-weight probability-matching method (PM), the WPM improves the different grade QPF because it can effectively reduce rainfall pattern bias by making use of the weighted moving average (WMA). Additionally, the WPM threat score in rainstorm forecast similarly improved from 0.051 to 0.056, with a 9.8% increase relative to the PM. (3) The sensitivity experiments show that an optimal rainfall intensity score (WPM-best) can further improve the QPF and overcome all single models in both rainstorm and non-rainstorm forecasts, and the WPM-best has a rainstorm threat score skill of 0.062, with an increase of 21.6% compared with the PM. The performance of the WPM-best will be better if the precipitation intensity is stronger and the valid forecast periods is longer. It should be noted that there is no need to select models before using the WPM-best method, because WPM-best can give a very low weight to the less-skillful model in a more objective way. (4) The improved WPM method is also applied to investigate the heavy-rainfall case induced by typhoon Mekkhala (2020), where the improved WPM technique significantly improves rainstorm forecasting ability compared with a single model.

We consider the construction of set estimators that possess both Bayesian credibility and frequentist coverage properties. We show that under mild regularity conditions there exists a prior distribution that induces (1 − α) frequentist coverage of a (1 − α) credible set. In contrast to the previous literature, this result does not rely on asymptotic normality or invariance, so it can be applied in nonstandard inference problems. Supplementary materials for this article are available online.

Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by the examination of the Bayesian posterior and frequentist means of this statistic. Second-order matching conditions are shown to arise from matching of the Bayesian posterior and frequentist variances of a mean-adjusted version of the signed root statistic. Conditions for conditional probability matching in ancillary statistic models are derived and discussed.

With reference to a general class of empirical-type likelihoods, we develop higher-order asymptotics for the frequentist coverage of Bayesian credible sets based on posterior quantiles and highest posterior density. These asymptotics, in turn, characterise members of the class that allow approximate frequentist validity of such sets. It is seen that the usual empirical likelihood does not enjoy this property up to the order of approximation considered here.

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of the sample size. This condition is on the model, not on the prior, and it ensures that any first-order probability matching prior in the unconditional sense automatically yields higher-order conditional probability matching. Objective Bayes methods are compared to parametric bootstrap and analytic methods for higher-order conditional frequentist inference.

Jeffreys' prior, one of the widely used noninformative priors, remains invariant under reparameterization, but does not perform satisfactorily in the presence of nuisance parameters. To overcome this deficiency, recently various noninformative priors have been proposed in the literature. This article explores the invariance (or lack thereof) of some of these noninformative priors including the reference prior of Berger and Bernardo, the reverse reference prior of J. K. Ghosh and the probability-matching prior of Peers and Stein under reparameterization. Berger and Bernardo's m-group ordered reference prior is shown to remain invariant under a special type of reparameterization. The reverse reference prior of J. K. Ghosh is shown not to remain invariant under reparameterization. However, the probability-matching prior is shown to remain invariant under any reparameterization. Also for spherically symmetric distributions, certain noninformative priors are derived using the principle of group invariance.

SUMMARY We characterise priors which match, up to O(n−1), the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function. This work extends and unifies the work of Ghosh & Mukerjee (1993) and Datta & Ghosh (1995a) on the topic of probability-matching priors. A set of necessary and sufficient conditions is obtained for the above characterisation. Some of these conditions depend only on the parametric functions and not on the prior. Examples are given where the joint probability matching is possible and where it is not possible.

SUMMARY We derive the differential equation that a prior must satisfy if the posterior probability of a one-sided credibility interval for a parametric function and its frequentist probability agree up to 0(n−1). This equation turns out to be identical with Stein's equation for a slightly different problem, for which also our method provides a rigorous justification. Our method is different in details from Stein's but similar in spirit to Dawid (1991) and Bickel & Ghosh (1990). Some examples are provided.

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued parametric function to match a nominal level with a remainder of O(n −1 ), where n denotes the sample size. The latter priors, first introduced by Welch and Peers, are obtained by solving a differential equation due to Peers. Finally, in the presence of several parameters of interest, a general class of priors that satisfies the matching criterion separately for each parameter is constructed, and examples are given to illustrate how reference or reverse reference priors fit within this class of priors.