用Poisson-Lognormal滤波器从星系分布恢复非线性密度场
Recovering the nonlinear density field from the galaxy distribution with a Poisson-Lognormal filter
摘要：
我们提出了一个一般表达式的对数正态滤波器给定的任意非线性星系的偏见。我们推导出这个过滤器作为最大的后验解决方案，假设一个对数正态先验分布的物质场与一个给定的平均场和模型所观察到的星系分布的泊松过程。我们已经进行了一个三维的实施，这个过滤器与一个非常有效的牛顿-克雷洛夫反演方案。此外，我们已经测试了它与暗物质N体模拟假设一个单位星系的偏见关系，并与以前的密度场估计，如逆加权方案和维纳滤波的结果进行比较。我们的研究结果表明，即使在δ ~1000以上的超密度下，与潜在的暗物质场也有很好的一致性，这超过了对数正态分布预期有效的一个数量级。原因在于，对于我们的滤波器，对数正态假设作为先验分布函数进入，但最大后验解也以数据为条件。我们发现，对数正态滤波器是优于以前的过滤方案在更高的相关系数和更小的欧氏距离的底层物质场。我们还展示了它是如何能够恢复的正尾的物质密度场分布的单位偏置关系下降到约>~2 Mpc/h的规模。
英文摘要：
We present a general expression for a lognormal filter given an arbitrary nonlinear galaxy bias. We derive this filter as the maximum a posteriori solution assuming a lognormal prior distribution for the matter field with a given mean field and modeling the observed galaxy distribution by a Poissonian process. We have performed a three-dimensional implementation of this filter with a very efficient Newton-Krylov inversion scheme. Furthermore, we have tested it with a dark matter N-body simulation assuming a unit galaxy bias relation and compared the results with previous density field estimators like the inverse weighting scheme and Wiener filtering. Our results show good agreement with the underlying dark matter field for overdensities even above delta~1000 which exceeds by one order of magnitude the regime in which the lognormal is expected to be valid. The reason is that for our filter the lognormal assumption enters as a prior distribution function, but the maximum a posteriori solution is also conditioned on the data. We find that the lognormal filter is superior to the previous filtering schemes in terms of higher correlation coefficients and smaller Euclidean distances to the underlying matter field. We also show how it is able to recover the positive tail of the matter density field distribution for a unit bias relation down to scales of about >~2 Mpc/h.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
