Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model
Scalable Bayesian Inference for the Inverse Temperature of a Hidden Potts Model
复制标题
隐藏 Potts 模型温度逆的可扩展贝叶斯推理
作者：
M. Moores;G. Nicholls;A. Pettitt;K. Mengersen
Potts模型的逆温度参数控制着空间凝聚力的强度，因此对结果的模型拟合有很大的影响。困难在于难以处理的归一化常数依赖于该参数的值，因此不存在直接从后验分布抽样的闭合形式的解。在不计算归一化常数的情况下，从后验采样有多种计算方法，包括交换算法和近似贝叶斯计算(ABC)。这些算法的一个严重缺陷是它们不能很好地扩展到具有大状态空间的模型，例如具有一百万或更多像素的图像。我们引入了一个参数代理模型，它使用一条积分曲线来逼近得分函数。我们的代理模型包含了似然的已知性质，如异方差和临界温度。我们使用合成数据和来自Landsat-8卫星的遥感图像演示了这种方法。与交换算法或ABC相比，我们在运行时间上获得了高达100倍的改进。R包“bayesImageS”中提供了我们算法的开源实现。
The inverse temperature parameter of the Potts model governs the strength of spatial cohesion and therefore has a major influence over the resulting model fit. A difficulty arises from the dependence of an intractable normalising constant on the value of this parameter and thus there is no closed-form solution for sampling from the posterior distribution directly. There are a variety of computational approaches for sampling from the posterior without evaluating the normalising constant, including the exchange algorithm and approximate Bayesian computation (ABC). A serious drawback of these algorithms is that they do not scale well for models with a large state space, such as images with a million or more pixels. We introduce a parametric surrogate model, which approximates the score function using an integral curve. Our surrogate model incorporates known properties of the likelihood, such as heteroskedasticity and critical temperature. We demonstrate this method using synthetic data as well as remotely-sensed imagery from the Landsat-8 satellite. We achieve up to a hundredfold improvement in the elapsed runtime, compared to the exchange algorithm or ABC. An open source implementation of our algorithm is available in the R package "bayesImageS."
DOI：
10.1257/aer.101.3.194
发表时间：
2011-05
期刊：
The American economic review
影响因子：
--
作者：
Henderson JV;Storeygard A;Weil DN
通讯作者：
Weil DN
AABC：大约近似贝叶斯计算，用于推断人口基因模型的推断。
影响因子：
1.4
作者：
Buzbas, Erkan O.;Rosenberg, Noah A.
通讯作者：
Rosenberg, Noah A.
影响因子：
5.8
作者：
Carpenter, Bob;Gelman, Andrew;Riddell, Allen
通讯作者：
Riddell, Allen