Direct sampling with a step function

The direct sampling method proposed by Walker et al. (JCGS 2011) can generate draws from weighted distributions possibly having intractable normalizing constants. may be of interest as a tool in situations which require drawing an unfamiliar distribution. However, the original algorithm have difficulty producing some situations. present work restricts attention to univariate setting where weight function and base distribution target density meet certain criteria. Here, variant sampler is uses step approximate particular augmented random variable on based. Knots for placed strategically ensure approximation close underlying density. Variates then generated reliably while largely avoiding need manual tuning or rejections. A rejection based allows exact with lower probability exchange increased computation. Several applications illustrate method: generating Conway-Maxwell Poisson distribution, Gibbs dependence parameter effects model conditional autoregression structure, degrees-of-freedom regression t-distributed errors.