Spatial generalized linear mixed-effects methods are popularly used to model spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of binary, count, or continuous types, at each location. Methods that allow joint modeling of such mixed-type multivariate spatial responses are rare. Using latent multivariate Gaussian processes (GPs), we present a class of Bayesian spatial methods that can be employed for any combination of exponential family responses. Since multivariate GP-based methods can suffer from computational bottlenecks when the number of spatial locations is high, we further employ a computationally efficient Vecchia approximation for fast posterior inference and prediction. Key theoretical properties of the proposed model, such as identifiability and the structure of the induced covariance, are established. Our approach employs a Markov chain Monte Carlo-based inference method that utilizes elliptical slice sampling in a blocked Metropolis-within-Gibbs sampling framework. We illustrate the efficacy of the proposed method through simulation studies and a real-data application on joint modeling of wildfire counts and burnt areas across the United States.

翻译：空间广义线性混合效应方法被广泛用于建模空间索引的单变量响应。然而，随着现代技术的发展，在每个空间位置上观测到向量值的混合类型响应（例如，二值型、计数型或连续型数据的组合）已很常见。允许对此类混合类型多元空间响应进行联合建模的方法却很少见。利用潜多元高斯过程，我们提出了一类贝叶斯空间方法，可适用于指数族响应的任意组合。由于基于多元高斯过程的方法在空间位置数量较多时可能面临计算瓶颈，我们进一步采用了一种计算高效的Vecchia近似方法，以实现快速的后验推断与预测。本文建立了所提出模型的关键理论性质，如可识别性及诱导协方差的结构。我们的方法采用了一种基于马尔可夫链蒙特卡洛的推断方法，该方法在分块Metropolis-within-Gibbs抽样框架中利用了椭圆切片抽样。我们通过模拟研究以及一项关于美国全境野火发生次数与过火面积联合建模的实际数据应用，展示了所提出方法的有效性。