Bayesian Adaptive Exploration
Bayesian Adaptive Exploration
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贝叶斯自适应探索
DOI：
10.1063/1.1751377
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
T. Loredo
中科院分区：
文献类型：
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作者：
T. Loredo
我们描述了一个框架，自适应天文学探索的基础上迭代的观测-推理-设计周期，允许调整的假设和观测协议，以响应观测的结果在飞行中，收集数据。该框架在推理和设计阶段使用统一的贝叶斯方法：贝叶斯推理来量化我们从现有数据中学到的东西;贝叶斯决策理论来确定哪些新观察会教我们最多。在设计阶段，可能的未来观测的效用取决于它们预期为当前推断添加多少信息，这些信息由所涉及的概率分布的（负）熵来衡量。这种贝叶斯方法的实验设计可以追溯到20世纪70年代，但大多数现有的工作集中在线性模型。我们使用一个简单的非线性问题-规划观测以最好地确定太阳系外行星的轨道-来说明该方法，并证明它可以显着提高观测效率（即，以比熟悉的“root-N”规则更快的速率减小不确定性）。我们强调需要进一步研究的开放问题，包括对模型规范的依赖，概括观察的效用（例如，包括观察“成本”）和计算问题。
We describe a framework for adaptive astronomical exploration based on iterating an Observation-Inference-Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data are gathered. The framework uses a unified Bayesian methodology for the inference and design stages: Bayesian inference to quantify what we have learned from the available data; and Bayesian decision theory to identify which new observations would teach us the most. In the design stage, the utility of possible future observations is determined by how much information they are expected to add to current inferences as measured by the (negative) entropies of the probability distributions involved. Such a Bayesian approach to experimental design dates back to the 1970s, but most existing work focuses on linear models. We use a simple nonlinear problem—planning observations to best determine the orbit of an extrasolar planet—to illustrate the approach and demonstrate that it can significantly improve observing efficiency (i.e., reduce uncertainties at a rate faster than the familiar “root-N” rule) in some situations. We highlight open issues requiring further research, including dependence on model specification, generalizing the utility of an observation (e.g., to include observing “costs”), and computational issues.