The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing substantial biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

科学假设的命运通常取决于计算模型解释数据的能力，这些能力在现代统计方法中通过似然函数进行了量化。对数似然性是参数估计和模型评估的关键要素。但是，在计算生物学和神经科学等领域中，复杂模型的对数似然性通常难以分析或数值计算。在这种情况下，研究人员通常只能通过将观察到的数据与模型模拟生成的综合观察结果进行比较来估计对数似然率。通过模拟近似可能性的标准技术要么使用数据的摘要统计，要么有可能在估计中产生大量偏差。在这里，我们探索另一种方法，逆二项式采样（IBS），它可以有效地估计整个数据集的对数似然率，而不会产生偏差。对于每次观察，IBS都会从模拟器模型中抽取样本，直到与观察值匹配为止。然后，对数似然估计是抽取的样本数的函数。该估计量的方差是有界的，为无偏估计量实现了最小方差，并且我们可以计算方差的校准估计量。我们提供了支持IBS的理论论据，并提供了基于仿真模型的最大似然估计方法的经验评估。作为案例研究，我们从计算和认知神经科学中解决了三个模型拟合问题，这些问题越来越复杂。在所有问题上 与具有相同平均样本数的替代采样方法相比，IBS通常在估计参数和最大对数似然值方面产生的误差较小。我们的结果表明，在没有确切的技术可用时，IBS可能是一种实用，可靠且易于实现的对数似然评估方法。