Synthetic likelihood (SL) is a strategy for parameter inference when the likelihood function is analytically or computationally intractable. In SL, the likelihood function of the data is replaced by a multivariate Gaussian density over summary statistics of the data. SL requires simulation of many replicate datasets at every parameter value considered by a sampling algorithm, such as MCMC, making the method computationally-intensive. We propose two strategies to alleviate the computational burden imposed by SL algorithms. We first introduce a novel MCMC algorithm for SL where the proposal distribution is sequentially tuned and is also made conditional to data, thus it rapidly "guides" the proposed parameters towards high posterior probability regions. Second, we exploit strategies borrowed from the correlated pseudo-marginal MCMC literature, to improve the chains mixing in a SL framework. Our methods enable inference for challenging case studies when the chain is initialised in low posterior probability regions of the parameter space, where standard samplers failed. Our guided sampler can also be potentially used with MCMC samplers for approximate Bayesian computation (ABC). Our goal is to provide ways to make the best out of each expensive MCMC iteration, which will broaden the scope of likelihood-free inference for models with costly simulators. To illustrate the advantages stemming from our framework we consider four benchmark examples, including estimation of parameters for a cosmological model and a stochastic model with highly non-Gaussian summary statistics.

翻译：合成可能性( SL) 是当概率函数在分析上或计算上难以掌握时进行参数推断的一种策略。 在 SL 中,数据的可能性功能被数据汇总统计的多变高斯密度取代。 SL 需要模拟由抽样算法(如MCMC)考虑的每个参数值中的许多复制数据集,使方法计算密集。 我们提出了两个战略来减轻 SL 算法的计算负担。 我们首先为 SL 引入了一个新的 MC 算法算法。 我们首先为 SL 引入了一个新的 MC 算法算法, 其建议分布按顺序调整, 并且也以数据为条件, 从而迅速“ 指导” 数据被提议的参数替换为高远似概率区域。 其次, 我们利用从相关假相负的 MMC 文献中提取的战略, 来改进SL 框架的混合链。 我们的方法可以推导出在参数空间的低后种概率模型区域进行初始化的案例研究, 标准采样员也有可能与 MC 采样员一起使用, 快速“ 指南 ”, 将 Bayesian combers 计算出我们的目标范围框架, 包括成本缩缩缩缩算法 。