Intractable Likelihood: New Challenges from Modern Applications (ILike)

在大多数统计上下文中，人们认识到基于似然函数的推理方法通常是选择的方法。然而，这样的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执行基于似然的推理提供了强大的方法，包括马尔可夫链蒙特卡罗方法、EM算法、许多相关的似然优化技术和顺序蒙特卡罗方法。尽管这些方法已经并且非常成功地使基于似然的推理可以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，例如在高维问题和大量数据集中。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似然的方法来解决。激励当前项目的例子来自遗传学、基因组学、传染病流行病学、生态学、商业和文献计量学。然而，最近在解决棘手的似然问题的计算和统计方法上取得了各种突破，包括伪边际和粒子MCMC，无似然方法，如近似贝叶斯计算，复合似然和伪似然，迄今为止棘手的随机模型的新模拟方法，以及自适应蒙特卡罗方法。这些进步与gpu等多核计算技术的发展相结合，具有扩展可能性方法以满足现代科学问题中最困难挑战的巨大潜力。所有这些新领域都显示出相当大的前景。然而，需要一个统一的方法来交付我们实现可能性的能力的阶跃变化。“我喜欢”工作计划最初将包括对10个项目的调查，这些项目都结合了两个或两个以上的突破性领域。项目的后半部分将根据最初项目的成果制定类似的工作计划。

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.