标题： 似然比和泊松信道的贝叶斯推断 显示英文标题

标题： Likelihood ratios and Bayesian inference for Poisson channels

摘要： 近年来，无穷维方法已被引入用于高斯信道估计。 本文的目的是研究类似方法在泊松信道中的应用。 特别是我们使用似然比和离散Malliavin梯度计算泊松信道的贝叶斯估计器。 该算法适合通过蒙特卡洛方案进行数值实现。 作为应用，我们提供了一个新的证明，证明了最近由Guo、Shamai和Verduú得到的公式，该公式涉及连续时间泊松信道的输入输出互信息的一些导数与输入的条件均值估计器之间的关系。 然后将这些结果扩展到混合高斯-泊松信道。 显示英文摘要

摘要： In recent years, infinite-dimensional methods have been introduced for the Gaussian channels estimation. The aim of this paper is to study the application of similar methods to Poisson channels. In particular we compute the Bayesian estimator of a Poisson channel using the likelihood ratio and the discrete Malliavin gradient. This algorithm is suitable for numerical implementation via the Monte-Carlo scheme. As an application we provide an new proof of the formula obtained recently by Guo, Shamai and Verdu\'u relating some derivatives of the input-output mutual information of a time-continuous Poisson channel and the conditional mean estimator of the input. These results are then extended to mixed Gaussian-Poisson channels.