Intractable Likelihood: New Challenges from Modern Applications (ILike)

在大多数统计环境中，人们认识到，基于似然函数的推断方法通常是选择的方法。然而，这些方法并不总是容易实现。例如，在通常具有大量数据集的复杂问题中，有时甚至完全不可能评估似然函数。20世纪90年代的计算统计学革命为进行基于似然性的推断提供了强大的方法，包括马尔可夫链蒙特卡罗方法，EM算法，许多相关的似然性优化技术，和序贯蒙特卡罗方法。虽然这些方法已经并非常成功地使可能性-基于推理的方法可以处理几乎所有科学和技术领域的广泛问题，我们现在对它们的局限性有了更好的理解，例如在高维问题和海量数据集方面。因此，许多具有挑战性的统计推断问题的21世纪世纪不能使用现有的基于似然的方法来解决。本项目的实例来自遗传学、基因组学、传染病流行病学、生态学、商业和文献计量学。然而，最近在计算和统计方法方面取得了各种突破，包括伪边缘和粒子MCMC，无似然方法，如近似贝叶斯计算，合成和伪似然，新的模拟方法，迄今棘手的随机模型，自适应蒙特卡罗方法。这些进步加上GPU等多核计算技术的发展，为扩展似然方法以应对现代科学问题的最困难挑战提供了巨大的潜力。然而，需要一种统一的方法来实现我们实现可能性的能力的一步变化。Ilike工作计划最初将涉及对10个项目的调查，所有项目都将结合两个或更多的突破领域。该项目的后半部分将涉及一个类似的工作计划，该工作计划将以最初项目的成果为基础。

In most statistical contexts, it is recognised that inference methodology based on the likelihood function are usually methods of choice. However such methods are not always easy to implement. For instance, in complex problems often with massive data sets, it can sometimes be completely impossible to even evaluate the likelihood function. The computational statistics revolution of the 1990s provided powerful methodology for carrying out likelihood-based inference, including Markov chain Monte Carlo methods, the EM algorithm, many associated optimisation techniques for likelihoods, and Sequential Monte Carlo methods.Although these methods have been and are highly successful in making likelihood-based inference accessible to a wide range of problems from virtually every area of science and technology, we now have a far better understanding of their limitations, for example in high-dimensional problems and for massive data sets. Thus many challenging statistical inference problems of the 21st century cannot be addressed using existing likelihood-based methods. Examples which motivate the current project come from genetics, genomics, infectious disease epidemiology, ecology, commerce, and bibliometrics.However there have been various recent breakthroughs in computational and statistical approaches to intractable likelihood problems, including pseudo-marginal and particle MCMC, likelihood-free methods such as Approximate Bayesian Computation, composite and pseudo-likelihoods, new simulation methods for hitherto intractable stochastic models, and adaptive Monte Carlo methods. These advances coupled with developments in multi-core computational technologies such as GPUs, have enormous potential for extending likelihood methods to meet the most difficult challenges of modern scientific questions.All these new areas have demonstrated considerable promise. However, a unified approach is required to deliver a step change in our capability to implement likelihood. The Ilike workplan will initially involve the investigation of 10 projects all combining two or more of the about breakthrough areas. The second half of the project will involve a similar workplan informed by the outcomes of the initial projects.