Some Bayesian Methods for Sequences of Discrete Observationsand for Finite Population Sampling

这一建议考虑了两个基本上不相关的问题， 贝叶斯统计。 第一个问题由来已久， 找到卡尔曼模型的易处理的非高斯模拟， 滤波算法。 这里有一个很有希望的可能性 结构的介绍，似乎产生合理的递归 离散数据的滤波算法 拟议的工作涉及 这一模式的发展和实施。 在第二种情况下， 问题的改进的区间估计的有限 人口平均数或中位数。 众所周知， 在简单随机抽样下，没有用中度替换 从偏态总体中抽样，通常的区间估计 表现不佳。 分层随机抽样也是如此 当地层中的样本量很小时。 这里 无信息贝叶斯方法，它是基于一个 推广的'波利亚后'，建议作为一种方法 用于生成改进的区间估计。 首席研究员是一个专家的理论， 有限抽样他继续使用贝叶斯方法， 在这方面的问题，并在过滤的发展 离散数据的算法是非常值得追求的。 的 理论概念有很大的潜力扩展到其他 有限抽样中的估计问题，结果应 受到相当大的关注。

This proposal considers two essentially unrelated problems in Bayesian statistics. In the first, a problem of long standing, finding tractable non-Gaussian analogs of the Kalman model and filtering algorithm, is studied. Here a promising probability structure is introduced that seems to produce sensible recursive filtering algorithms for discrete data. The proposed work involves the development and implementation of this model. In the second, the problem of finding improved interval estimates of a finite population mean or median is considered. It is well-known that under simple random sampling without replacement with a moderate sample from a skewed population, the usual interval estimates perform poorly. The same can be true in stratified random sampling when the sample sizes within the strata are small. Here a noninformative Bayesian approach, which is based on a generalization of the 'Polya posterior', is suggested as a method for generating improved interval estimates. The principal investigator is an expert in the theory of finite sampling. His continued use of the Bayesian approach to problems in this area and in the development of filtering algorithms for discrete data is well worth pursuing. The theoretical concepts have great potential for extension to other estimation problems in finite sampling and the results should receive considerable attention.