Estimating the parameters of compact binaries which coalesce and produce gravitational waves is a challenging Bayesian inverse problem. Gravitational-wave parameter estimation lies within the class of multifidelity problems, where a variety of models with differing assumptions, levels of fidelity, and computational cost are available for use in inference. In an effort to accelerate the solution of a Bayesian inverse problem, cheaper surrogates for the best models may be used to reduce the cost of likelihood evaluations when sampling the posterior. Importance sampling can then be used to reweight these samples to represent the true target posterior, incurring a reduction in the effective sample size. In cases when the problem is high dimensional, or when the surrogate model produces a poor approximation of the true posterior, this reduction in effective samples can be dramatic and render multifidelity importance sampling ineffective. We propose a novel method of tempered multifidelity importance sampling in order to remedy this issue. With this method the biasing distribution produced by the low-fidelity model is tempered, allowing for potentially better overlap with the target distribution. There is an optimal temperature which maximizes the efficiency in this setting, and we propose a low-cost strategy for approximating this optimal temperature using samples from the untempered distribution. In this paper, we motivate this method by applying it to Gaussian target and biasing distributions. Finally, we apply it to a series of problems in gravitational wave parameter estimation and demonstrate improved efficiencies when applying the method to real gravitational wave detections.

翻译：估计致密双星并合产生引力波的参数是一个具有挑战性的贝叶斯反演问题。引力波参数估计属于多保真度问题范畴，其中存在多种具有不同假设、保真度水平和计算成本的模型可供推理使用。为加速贝叶斯反演问题的求解，可采用最佳模型的廉价替代模型来降低后验采样过程中似然评估的计算成本。随后可利用重要性采样对这些样本进行重新加权，以表示真实的目标后验分布，但这会导致有效样本量的减少。在高维问题中，或当替代模型对真实后验的近似效果较差时，这种有效样本的减少可能非常显著，从而导致多保真度重要性采样失效。为解决这一问题，我们提出了一种新颖的基于温度调节的多保真度重要性采样方法。该方法对低保真度模型产生的偏置分布进行温度调节，从而可能获得与目标分布更好的重叠度。在此设置下存在一个最大化效率的最优温度，我们提出了一种利用非温度调节分布样本近似该最优温度的低成本策略。本文通过将该方法应用于高斯目标分布与偏置分布来阐明其原理。最后，我们将其应用于一系列引力波参数估计问题，并证明该方法在应用于实际引力波探测时能有效提升计算效率。