Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on a subspace spanned by a set of linear inequality constraints can be challenging, especially when some of the constraints might be binding leading to a lower dimensional subspace. For the general case with canonical link, it is shown that a generalized truncated multivariate normal supported on a desired subspace can be used. Moreover, it is shown that such prior distribution facilitates the construction of a general purpose product slice sampling method to obtain (approximate) samples from corresponding posterior distribution, making the inferential method computationally efficient for a wide class of GLMs with an arbitrary set of linear inequality constraints. The proposed product slice sampler is shown to be uniformly ergodic, having a geometric convergence rate under a set of mild regularity conditions satisfied by many popular GLMs (e.g., logistic and Poisson regressions with constrained coefficients). One of the primary advantages of the proposed Bayesian estimation method over classical methods is that uncertainty of parameter estimates is easily quantified by using the samples simulated from the path of the Markov Chain of the slice sampler. Numerical illustrations using simulated data sets are presented to illustrate the superiority of the proposed methods compared to some existing methods in terms of sampling bias and variances. In addition, real case studies are presented using data sets for fertilizer-crop production and estimating the SCRAM rate in nuclear power plants.
翻译:通用线性模型(GLMs)的贝叶斯统计推论显示,在限制空间上具有参数的通用直线性直线性模型(GLMs)具有普遍意义(如单调或曲线回归),但通常在一组线性不平等限制所支持的子空间内构建有效的先前分布,这具有挑战性,特别是当一些制约因素可能具有约束性,导致一个较低维度的子空间时,尤其当一些制约因素可能具有约束性,导致形成一个较低维度的亚空间时,可以使用通俗的子空间所支持的普遍脱轨多变量正常值。此外,还表明,这种先前分布有助于构建通用产品切片采样采样方法,以便从相应的远端分布中获取(近似)样本样本样本样本样本样本样本样本样本样本样本样本的样本样本样本,使广泛的GLMsmission方法具有计算效率。 拟议的产品切片采样器具有统一的直线性,在一组普通GLMMs(如,物流和Poisson Region Region Regal Reviews)中,在模拟模型中比较地使用了现有数据推算法的模型分析,这是在模拟模型中比较法系中,在模拟模型中比较了现有数据推算法法系系系系系系系现有数据法的优点。