Bayesian design requires determining the value of controllable variables in an experiment to maximise the information that will be obtained for subsequently collected data, with the majority of research in this field being focused on experiments that yield a univariate response. In this paper, a robust and computationally efficient Bayesian design approach is proposed to derive designs for experiments which yield bivariate discrete and mixed responses. To construct the joint distribution of responses, Copula models are considered, and a sequential Monte Carlo algorithm is adopted to reduce the computational effort required in deriving sequential designs. The total entropy utility function is considered to derive designs for the dual experimental goals of parameter estimation and model discrimination for Copula models. The results show that designs constructed within our framework are able to precisely estimate model parameters and that it is possible to discriminate between different competing Copula models. However, for experiments which yield binary and continuous data, it appears as though discriminating between Copula models can require a large number of data points, which may limit the general applicability of our methods and/or the range of experimental objectives that can be considered in experiments that yield multiple responses.

中文翻译：

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Copula模型的贝叶斯顺序设计

贝叶斯设计需要确定实验中可控变量的值，以最大程度地获取随后收集的数据所需要的信息，而该领域的大多数研究都集中在产生单变量响应的实验上。在本文中，提出了一种鲁棒且计算效率高的贝叶斯设计方法，以得出产生双变量离散和混合响应的实验设计。为了构建响应的联合分布，考虑了Copula模型，并采用了顺序蒙特卡洛算法来减少推导顺序设计所需的计算量。总熵效用函数被认为是为Copula模型的参数估计和模型区分的双重实验目标推导设计。结果表明，在我们的框架内构建的设计能够精确估计模型参数，并且有可能区分不同的竞争Copula模型。但是，对于产生二进制和连续数据的实验，似乎要区分Copula模型可能需要大量的数据点，这可能会限制我们方法的一般适用性和/或在以下情况下可以考虑的实验目标的范围：产生多重反应的实验。