论文标题
集合拒绝采样
Ensemble Rejection Sampling
论文作者
论文摘要
我们介绍了合奏拒绝采样，这是一种从一类非线性非高斯状态空间模型的潜在状态的后验分布进行精确模拟的方案。集合拒绝采样取决于使用状态样本集合构建的高维状态序列的建议。尽管该算法可以解释为作用在扩展空间上的拒绝采样方案，但我们在规律性条件下表明，获得精确样品的预期计算成本随状态序列的长度而不是指数级的标准拒绝采样来增加。我们通过根据随机波动率模型的后验分布和非线性自回归过程对准确的状态序列进行取样来证明这种方法。我们还向稀有事件模拟提供了一个应用程序。
We introduce Ensemble Rejection Sampling, a scheme for exact simulation from the posterior distribution of the latent states of a class of non-linear non-Gaussian state-space models. Ensemble Rejection Sampling relies on a proposal for the high-dimensional state sequence built using ensembles of state samples. Although this algorithm can be interpreted as a rejection sampling scheme acting on an extended space, we show under regularity conditions that the expected computational cost to obtain an exact sample increases cubically with the length of the state sequence instead of exponentially for standard rejection sampling. We demonstrate this methodology by sampling exactly state sequences according to the posterior distribution of a stochastic volatility model and a non-linear autoregressive process. We also present an application to rare event simulation.
