Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic rejection sampling ABC algorithm is to use sequential Monte Carlo (ABC SMC) to produce a sequence of proposal distributions adapting towards the posterior, instead of generating values from the prior distribution of the model parameters. Proposal distribution for the subsequent iteration is typically obtained from a weighted set of samples, often called particles, of the current iteration of this sequence. Current methods for constructing these proposal distributions treat all the particles equivalently, regardless of the corresponding value generated by the sampler, which may lead to inefficiency when propagating the information across iterations of the algorithm. To improve sampler efficiency, we introduce a modified approach called stratified distance ABC SMC. Our algorithm stratifies particles based on their distance between the corresponding synthetic and observed data, and then constructs distinct proposal distributions for all the strata. Taking into account the distribution of distances across the particle space leads to substantially improved acceptance rate of the rejection sampling. We further show that efficiency can be gained by introducing a novel stopping rule for the sequential process based on the stratified posterior samples and demonstrate these advances by several examples.

翻译：近似贝叶斯计算方法是在似然函数解析形式不可解时，用于推断复杂模型参数的标准工具。为提高基本拒绝采样ABC算法低接受率的常用方法，是采用序贯蒙特卡洛方法生成一序列自适应逼近后验的建议分布，而非从模型参数的先验分布中直接采样。后续迭代的建议分布通常由当前迭代的加权样本集（常称为粒子）获得。当前构建这些建议分布的方法对所有粒子同等对待，而不考虑采样器生成的对应数值，这可能导致算法在迭代间传播信息时效率低下。为提升采样器效率，我们提出一种改进方法——分层距离ABC SMC。该算法根据粒子对应的合成数据与观测数据之间的距离对粒子进行分层，并为所有分层分别构建不同的建议分布。考虑粒子空间中距离的分布特性，可显著提升拒绝采样的接受率。我们进一步证明，基于分层后验样本引入新颖的序贯过程停止准则能提升效率，并通过多个实例验证这些改进。