Considerate approaches to constructing summary statistics for ABC model selection
Considerate approaches to constructing summary statistics for ABC model selection
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DOI：
10.1007/s11222-012-9335-7
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发表时间：
2012-11-01
影响因子：
2.2
通讯作者：
Thorne, Thomas
中科院分区：
文献类型：
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作者：
Barnes, Chris P.;Filippi, Sarah;Thorne, Thomas
对于几乎任何具有挑战性的科学问题，评估可能性都是有问题的，如果不是不可能的话。近似贝叶斯计算（ABC）允许我们采用整个贝叶斯形式主义的问题，我们可以使用模拟模型，但不能直接评估的可能性。当比较真实的和模拟数据的汇总统计量时-而不是直接比较数据-信息丢失，除非汇总统计量足够。然而，充分的统计数据并不常见，但如果没有统计数据，ABC推理中的统计推断应谨慎考虑。以前，其他作者曾试图联合收割机不同的统计，以建立（大约）足够的统计使用搜索和信息分析。在这里，我们采用了一个信息理论框架，可以用来构建适当的（近似足够的）统计数据，通过组合不同的统计数据，直到信息的损失最小化。我们从潜在的大量不同的统计数据开始，并选择捕获（几乎）与完整集合相同信息的最小集合。然后，我们证明，这样的统计集可以构建参数估计和模型选择问题，我们将我们的方法应用到一系列的说明性和现实世界的模型选择问题。
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared-rather than the data directly-information is lost, unless the summary statistics are sufficient. Sufficient statistics are, however, not common but without them statistical inference in ABC inferences are to be considered with caution. Previously other authors have attempted to combine different statistics in order to construct (approximately) sufficient statistics using search and information heuristics. Here we employ an information-theoretical framework that can be used to construct appropriate (approximately sufficient) statistics by combining different statistics until the loss of information is minimized. We start from a potentially large number of different statistics and choose the smallest set that captures (nearly) the same information as the complete set. We then demonstrate that such sets of statistics can be constructed for both parameter estimation and model selection problems, and we apply our approach to a range of illustrative and real-world model selection problems.