Spatial generalized linear mixed-effects models are popularly used to analyze 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 for jointly modeling such mixed-type multivariate spatial responses are rare. Using multivariate Gaussian processes (GPs) in the latent layer, we present a class of Bayesian spatial methods applicable to 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 uses elliptical slice sampling within 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模型常用于分析空间索引的单变量响应。然而，随着现代技术的发展，在每个位置观测到向量形式的混合类型响应（例如二元、计数或连续类型的组合）已较为普遍。针对此类混合类型多元空间响应进行联合建模的方法尚不多见。通过在潜层中引入多元高斯过程，我们提出了一类适用于任意指数族响应组合的贝叶斯空间方法。由于基于多元高斯过程的方法在空间位置数量较大时可能面临计算瓶颈，我们进一步采用计算高效的Vecchia近似来实现快速后验推断与预测。本文建立了所提出模型的关键理论性质，例如可识别性及诱导协方差结构。我们的方法采用基于马尔可夫链蒙特卡洛的推断技术，在分块Metropolis-within-Gibbs采样框架中结合椭圆切片采样。通过模拟研究及对美国全境野火次数与过火面积联合建模的实际数据应用，我们验证了该方法的有效性。