Raftery Adrian E, Bao Le
Department of Statistics, University of Washington, Seattle, Washington 98195-4322, USA.
Biometrics. 2010 Dec;66(4):1162-73. doi: 10.1111/j.1541-0420.2010.01399.x.
The Joint United Nations Programme on HIV/AIDS (UNAIDS) has decided to use Bayesian melding as the basis for its probabilistic projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model, prevalence data, and expert opinion. Initially, the posterior distribution was approximated by sampling-importance-resampling, which is simple to implement, easy to interpret, transparent to users, and gave acceptable results for most countries. For some countries, however, this is not computationally efficient because the posterior distribution tends to be concentrated around nonlinear ridges and can also be multimodal. We propose instead incremental mixture importance sampling (IMIS), which iteratively builds up a better importance sampling function. This retains the simplicity and transparency of sampling importance resampling, but is much more efficient computationally. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging. In simulation experiments and on real data, it outperformed both sampling importance resampling and three publicly available generic Markov chain Monte Carlo algorithms for this kind of problem.
联合国艾滋病规划署（UNAIDS）已决定将贝叶斯融合作为其对广泛流行艾滋病国家的艾滋病毒流行率进行概率预测的基础。这一方法结合了一个机械流行病学模型、流行率数据和专家意见。最初，后验分布通过重要性重采样进行近似，该方法易于实现、易于解释、对用户透明，并且对大多数国家都给出了可接受的结果。然而，对于一些国家来说，这在计算上并不高效，因为后验分布往往集中在非线性脊附近，并且可能是多峰的。相反，我们提出增量混合重要性采样（IMIS），它通过迭代构建一个更好的重要性采样函数。这保留了重要性重采样的简单性和透明度，但在计算上效率更高。它还能得到一个简单的综合似然估计量，这是贝叶斯模型比较和模型平均的基础。在模拟实验和实际数据上，对于这类问题，它的表现优于重要性重采样和三种公开可用的通用马尔可夫链蒙特卡罗算法。
