标题： 多类函数数据的贝叶斯分类 显示英文标题

标题： Bayesian Classification of Multiclass Functional Data

摘要： 我们提出了一种贝叶斯方法来估计多元函数模型中的参数。考虑了无序多项式 probit 模型、有序多项式 probit 模型和多项式逻辑模型。在这三个多项式模型中，我们使用基于适当基（如 B 样条）的有限随机级数先验，并利用贝叶斯规则对函数数据进行分类。我们根据从马尔可夫链蒙特卡洛（MCMC）输出估计的边际似然对模型进行平均。计算了这三个多项式模型的后验收缩率。我们还研究了对原始函数数据应用函数主成分技术得到的多元数据上的贝叶斯线性判别分析和二次判别分析。进行了模拟研究以比较不同类型数据上的这些方法。我们还将这些方法应用于语音音素数据集。 显示英文摘要

摘要： We propose a Bayesian approach to estimating parameters in multiclass functional models. Unordered multinomial probit, ordered multinomial probit and multinomial logistic models are considered. We use finite random series priors based on a suitable basis such as B-splines in these three multinomial models, and classify the functional data using the Bayes rule. We average over models based on the marginal likelihood estimated from Markov Chain Monte Carlo (MCMC) output. Posterior contraction rates for the three multinomial models are computed. We also consider Bayesian linear and quadratic discriminant analyses on the multivariate data obtained by applying a functional principal component technique on the original functional data. A simulation study is conducted to compare these methods on different types of data. We also apply these methods to a phoneme dataset.