论文标题
使用步骤功能进行直接采样
Direct Sampling with a Step Function
论文作者
论文摘要
Walker等人提出的直接采样方法。 （JCGS 2011）可以从加权分布中产生抽签，这可能具有棘手的归一化常数。该方法可能是在需要从陌生分布中绘制的情况的有用工具。但是，在某些情况下，原始算法很难产生抽签。目前的工作将注意力限制在单变量设置中，其中加权目标密度的重量函数和基本分布符合某些标准。在这里，提出了直接采样器的变体，该变体使用阶梯函数来近似该方法基于的特定增强随机变量的密度。可以从战略上放置步骤函数的结，以确保近似值接近基础密度。然后可以可靠地生成变体，同时在很大程度上避免了需要进行手动调整或拒绝的需求。基于步骤函数的拒绝采样器允许从目标生成精确的绘制，而拒绝概率较低，以换取增加的计算。提出的采样器的一些应用说明了以下方法：从Conway-Maxwell Poisson分布中生成绘制，这是一种Gibbs Sampler，它在带有条件自动化结构的随机效应模型中绘制了依赖性参数，以及绘制与T-Distribed Order的Recressionss in Repreedom参数的GIBBS Sampler。
The direct sampling method proposed by Walker et al. (JCGS 2011) can generate draws from weighted distributions possibly having intractable normalizing constants. The method may be of interest as a useful tool in situations which require drawing from an unfamiliar distribution. However, the original algorithm can have difficulty producing draws in some situations. The present work restricts attention to a univariate setting where the weight function and base distribution of the weighted target density meet certain criteria. Here, a variant of the direct sampler is proposed which uses a step function to approximate the density of a particular augmented random variable on which the method is based. Knots for the step function can be placed strategically to ensure the approximation is close to the underlying density. Variates may then be generated reliably while largely avoiding the need for manual tuning or rejections. A rejection sampler based on the step function allows exact draws to be generated from the target with lower rejection probability in exchange for increased computation. Several applications of the proposed sampler illustrate the method: generating draws from the Conway-Maxwell Poisson distribution, a Gibbs sampler which draws the dependence parameter in a random effects model with conditional autoregression structure, and a Gibbs sampler which draws the degrees-of-freedom parameter in a regression with t-distributed errors.
