论文标题
非高斯可能性的分区功能方法：虚弱非高斯宇宙学推断的形式主义和扩展
Partition function approach to non-Gaussian likelihoods: Formalism and expansions for weakly non-Gaussian cosmological inference
论文作者
论文摘要
非高斯的可能性，无处不在的整个宇宙学，是物理模型中非线性的直接结果。他们的治疗需要蒙特卡洛马尔可夫链或更先进的采样方法来确定置信度轮廓。作为替代方案，我们构建规范分区作为贝叶斯证据的拉普拉斯转变的作用，MCMC方法从中可以采样微骨。后分布的订单$ n $的累积量按对数分区功能的直接$ n $折叠率遵循，以二阶恢复了经典的Fisher-Matrix形式。我们将这种方法连接起来，将这种方法用于微弱的非高斯和革兰氏阴性扩展，并以宇宙学参数$ω_m$和$ w $的超新星类似性证明了有效性。我们评论规范分区函数的扩展，以包括动能能量，以桥接汉密尔顿蒙特 - 卡洛采样，以及集合马尔可夫链方法，因为它们会根据化学势过渡到大型殖民分区的功能。最后，我们证明了分区函数方法与Cramér-Rao边界和信息熵的关系。
Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of confidence contours. As an alternative, we construct canonical partition functions as Laplace-transforms of the Bayesian evidence, from which MCMC-methods would sample microstates. Cumulants of order $n$ of the posterior distribution follow by direct $n$-fold differentiation of the logarithmic partition function, recovering the classic Fisher-matrix formalism at second order. We connect this approach for weakly non-Gaussianities to the DALI- and Gram-Charlier expansions and demonstrate the validity with a supernova-likelihood on the cosmological parameters $Ω_m$ and $w$. We comment on extensions of the canonical partition function to include kinetic energies in order to bridge to Hamilton Monte-Carlo sampling, and on ensemble Markov-chain methods, as they would result from transitioning to macrocanonical partition functions depending on a chemical potential. Lastly we demonstrate the relationship of the partition function approach to the Cramér-Rao boundary and to information entropies.
