Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation
Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation
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DOI：
10.1109/tci.2019.2913108
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发表时间：
2018-09
影响因子：
5.4
通讯作者：
Safa C. Medin;John Murray-Bruce;D. Castañón;Vivek K Goyal
中科院分区：
文献类型：
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作者：
Safa C. Medin;John Murray-Bruce;D. Castañón;Vivek K Goyal
估计伯努利过程的参数出现在许多应用中，包括光子有效的主动成像，其中每个照明周期被视为单个伯努利试验。当多个伯努利过程（例如，多个像素）的兴趣，我们制定的平均值的约束下，作为一个最优的资源分配问题的试验分配。一个甲骨文辅助的试验分配表明，可以有一个显着的优势，从不同的分配不同的进程，并激发了一个简单的试验分配增益量的介绍。在本文中，我们提出了一个基于网格的框架来表示和优化停止规则。考虑到方便的情况下，Beta先验，三个可实现的停止规则具有类似的性能进行了探索，其中最简单的是渐近实现的甲骨文辅助试验分配。这些方法进一步扩展到估计函数的伯努利参数。在模拟的灵感来自现实的主动成像的情况下，我们表现出显着的均方误差改善高达4.36 dB的估计$p$和高达1.86 dB的估计$\log p$。
Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, in this paper, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of $p$ and up to 1.86 dB for the estimation of $\log p$.