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首页> 外文期刊>International Journal of Statistics and Probability >Bayesian Simultaneous Intervals for Small Areas: An Application to Variation in Maps
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Bayesian Simultaneous Intervals for Small Areas: An Application to Variation in Maps

机译：小区域的贝叶斯同时间隔：在地图上变化的应用

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摘要

Bayesian inference about small areas is of considerable current interest, and simultaneous intervals for the parameters for the areas are needed because these parameters are correlated. This is not usually pursued because with many areas the problem becomes difficult. We describe a method for finding simultaneous credible intervals for a relatively large number of parameters, each corresponding to a single area. Our method is model based, it uses a hierarchical Bayesian model, and it starts with either the $100(1-lpha)$% (e.g., $lpha=.05$ for 95%) credible interval or highest posterior density (HPD) interval for each area. As in the construction of the HPD interval, our method is the result of the solution of two simultaneous equations, an equation that accounts for the probability content, $100(1-lpha)$% of all the intervals combined, and an equation that contains an optimality condition like the ``equal ordinates'' condition in the HPD interval.? We compare our method with one based on a nonparametric method, which as expected under a parametric model, does not perform as well as ours, but is a good competitor. We illustrate our method and compare it with the nonparametric method using an example on disease mapping which utilizes a standard Poisson regression model.
机译：关于小区域的贝叶斯推断是相当大的电流兴趣，并且需要对区域参数的同时间隔是相关的，因为这些参数相关。这通常不会追求，因为许多领域这个问题变得困难。我们描述了一种用于找到相对大量参数的同时可信间隔的方法，每个参数对应于单个区域。我们的方法是基于模型，它使用了分层贝叶斯模型，它以100美元（1- alpha）$ ％（例如，$ alpha = .05 $开始95 ％）可信间隔或最高后密度（HPD）每个区域的间隔。与HPD间隔的构建一样，我们的方法是两个同时等式的解决方案的结果，一个方程占概率内容，所有间隔的100美元（1- alpha）$ ％组合，以及等式其中包含HPD间隔中的“等于坐标”条件等最优性条件。？我们将基于非参数方法的方法进行比较，该方法在参数模型下的预期，不执行和我们的竞争对手。我们说明了我们的方法，并使用疾病映射的示例将其与非参数方法进行比较，该方法利用标准泊松回归模型。

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