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Bayesian model averaging and variable selection in multivariate ecological models.

机译：多元生态模型中的贝叶斯模型平均和变量选择。

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摘要

Bayesian Model Averaging (BMA) is a new area in modern applied statistics that provides data analysts with an efficient tool for discovering promising models and obtaining estimates of their posterior probabilities via Markov chain Monte Carlo (MCMC). These probabilities can be further used as weights for model averaged predictions and estimates of the parameters of interest. As a result, variance components due to model selection are estimated and accounted for, contrary to the practice of conventional data analysis (such as, for example, stepwise model selection). In addition, variable activation probabilities can be obtained for each variable of interest;This dissertation is aimed at connecting BMA and various ramifications of the multivariate technique called Reduced-Rank Regression (RRR). In particular, we are concerned with Canonical Correspondence Analysis (CCA) in ecological applications where the data are represented by a site by species abundance matrix with site-specific covariates. Our goal is to incorporate the multivariate techniques, such as Redundancy Analysis and Canonical Correspondence Analysis into the general machinery of BMA, taking into account such complicating phenomena as outliers and clustering of observations within a single data-analysis strategy.;Traditional implementations of model averaging are concerned with selection of variables. We extend the methodology of BMA to selection of subgroups of observations and implement several approaches to cluster and outlier analysis in the context of the multivariate regression model. The proposed algorithm of cluster analysis can accommodate restrictions on the resulting partition of observations when some of them form sub-clusters that have to be preserved when larger clusters are formed.
机译：贝叶斯模型平均（BMA）是现代应用统计中的一个新领域，它为数据分析人员提供了有效的工具，以通过马尔可夫链蒙特卡洛（MCMC）发现有前景的模型并获得其后验概率的估计。这些概率可以进一步用作模型平均预测和目标参数估计的权重。结果，与常规数据分析的实践（例如，逐步模型选择）相反，估计并考虑了由于模型选择而引起的方差分量。此外，可以获得感兴趣的每个变量的变量激活概率；本论文的目的是将BMA与称为减少秩回归（RRR）的多变量技术的各种分支联系起来。特别是，我们关注生态应用中的典范对应分析（CCA），其中数据由具有物种特定共变量的物种丰度矩阵的一个位置表示。我们的目标是在单一数据分析策略中考虑诸如离群值和观测值聚类等复杂现象，将冗余技术和规范对应分析等多元技术纳入BMA的通用机制中;模型平均的传统实现与变量的选择有关。我们将BMA的方法扩展到观察子组的选择，并在多元回归模型的背景下实施几种聚类和离群分析的方法。所提出的聚类分析算法可以容纳对观测结果分区的限制，当其中一些形成子聚类时，必须在形成较大聚类时保留这些子聚类。

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  • 作者

    Lipkovich, Ilya A.;

  • 作者单位

    Virginia Polytechnic Institute and State University.;

  • 授予单位 Virginia Polytechnic Institute and State University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2002
  • 页码 165 p.
  • 总页数 165
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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