Intractable Likelihood: New Challenges from Modern Applications (ILike)

在大多数统计背景下，人们认识到，基于似然函数的推理方法通常是可选择的方法。然而，这样的方法并不总是容易实现的。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实现基于似然的推理提供了强大的方法论，包括马尔科夫链蒙特卡罗方法、EM算法、许多相关的似然优化技术和序贯蒙特卡罗方法。尽管这些方法已经并非常成功地使基于似然的推理可以应用于几乎所有科学和技术领域的广泛问题，但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上。因此，21世纪的许多具有挑战性的统计推断问题不能用现有的基于可能性的方法来解决。推动这项计划的例子来自遗传学、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上对棘手的似然问题取得了各种突破，包括伪边际和粒子MCMC，近似贝叶斯计算、合成和伪似然等无似然方法，迄今难以处理的随机模型的新模拟方法，以及自适应蒙特卡罗方法。这些进展加上图形处理器等多核计算技术的发展，为扩展似然方法以满足现代科学问题最困难的挑战提供了巨大的潜力。所有这些新领域都展示了相当大的前景。然而，需要一种统一的方法来实现我们实施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，所有这些项目都结合了两个或两个以上的突破性领域。该项目的后半部分将涉及一项类似的工作计划，以初步项目的结果为依据。

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.