Discrete data are abundant and often arise as counts or rounded data. Yet even for linear regression models, conjugate priors and closed-form posteriors are typically unavailable, which necessitates approximations such as MCMC for posterior inference. For a broad class of count and rounded data regression models, we introduce conjugate priors that enable closed-form posterior inference. Key posterior and predictive functionals are computable analytically or via direct Monte Carlo simulation. Crucially, the predictive distributions are discrete to match the support of the data and can be evaluated or simulated jointly across multiple covariate values. These tools are broadly useful for linear regression, nonlinear models via basis expansions, and model and variable selection. Multiple simulation studies demonstrate significant advantages in computing, predictive modeling, and selection relative to existing alternatives.
翻译:分解数据十分丰富,而且往往作为计数或四舍五入数据出现。但即使是线性回归模型,一般也无法获得共和前置物和封闭式后台,这就需要近似值,如用于后向推论的MCMC等近似值。对于一大类的计数和四舍四入数据回归模型,我们引入了共和前缀,以便能够进行闭合式后台推论。关键后台和预测功能是可比较分析的或通过蒙特卡洛直接模拟分析的。关键后台和预测功能是独立的,可以与数据支持相匹配的,并且可以在多个共变数值之间联合评估或模拟。这些工具对于线性回归、非线性模型通过基础扩展以及模型和变量选择大有用处。多重模拟研究显示,计算、预测型模型和选择相对于现有替代品在计算、预测性建模和选择方面具有重大优势。