Bayesian Nonparametric Regression and Density Estimation Using CAR Priors

9972598研究涉及贝叶斯分层模型和函数估计问题的几个密切相关的领域。 研究人员探索使用贝叶斯技术的功能估计和他们的频率属性，并使用这些属性来帮助选择适当的非信息先验。 他们研究的一个方面是使用条件自回归模型（CAR）及其泛化来捕获空间变异性，并作为非参数回归和密度估计问题的先验分布。 初步结果表明，贝叶斯平滑参数选择的良好性能。 利用函数估计的惩罚方法和高阶CAR模型作为先验的贝叶斯估计之间的基本关系，他们使用基于采样的技术（如马尔可夫链蒙特卡罗）来处理大量数据的问题。 回归和密度估计问题是一类特殊的递阶广义线性模型。 一个共同的特点是需要为超参数指定先验分布。 研究者为这些目的开发非信息先验，并评估其适用性。 开发这些方法的动机是运输、疾病绘图和野生动物管理方面的问题。 交通问题包括对城市居民的行为以及他们对活动和目的地的选择进行建模。 疾病分布图工作按地点、年龄和性别分层估计疾病发病率。 野生动物管理问题涉及类似的问题，估计狩猎成功率的小地区，如县。 所有这些问题都涉及空间组成部分、大型数据集和对小区域的统计推断。 目前对这些主题有很大的兴趣，但许多理论问题尚未得到解决。 正在开发的结果，以帮助理解现有方法的一些理论特性，并提出新的。 通过使用客观贝叶斯技术，正在开发新的方法来处理广泛的实际问题。 这些方法是计算机密集型的，但在最新的计算机技术下是可行的。

9972598The research deals with several closely related areas of Bayesian hierarchical models and function estimation problems. The investigators explore the use of Bayesian techniques for function estimation and their frequentist properties and use those properties to help choose appropriate noninformative priors. One aspect of their study is the use of conditional autoregressive models (CAR) and their generalizations to capture spatial variability and as prior distributions in nonparametric regression and density estimation problems. Preliminary results suggest good performance for the Bayesian smoothing parameter choice. Using the fundamental relationship between penalized methods for function estimation and Bayesian estimation with high order CAR models as priors, they use sampling-based techniques (such as Markov chain Monte Carlo) to deal with problems with large amounts of data. The regression and density estimation problems are special classes of hierarchical generalized linear models. A common feature is the need to specify prior distributions for hyperparameters. The investigators develop noninformative priors for these purposes and assess their suitability. The methods being developed are motivated by problems in transportation, disease mapping and wildlife management. The transportation problem consists of modeling the behavior of residents in a city and their choice of activities and destinations. The disease mapping work estimates disease incidence by location, age and gender strata. The wildlife management issues involve similar problems in estimating hunting success rates for small areas such as counties. All of these problems entail a spatial component, large data sets, and statistical inference to small regions. There is a great deal of current interest in these topics, but many theoretical issues have not been addressed. Results are being developed to help understand some of the theoretical properties of existing methods and to suggest new ones. By using objective Bayesian techniques, new methodology is being developed to handle a wide range of practical problems. These methods are computer intensive but feasible with the latest computer technology.