The power-law distribution plays a crucial role in complex networks as well
as various applied sciences. Investigating whether the degree distribution of a
network follows a power-law distribution is an important concern. The commonly
used inferential methods for estimating the model parameters often yield biased
estimates, which can lead to the rejection of the hypothesis that a model
conforms to a power-law. In this paper, we discuss improved methods that
utilize Bayesian inference to obtain accurate estimates and precise credibility
intervals. The inferential methods are derived for both continuous and discrete
distributions. These methods reveal that objective Bayesian approaches return
nearly unbiased estimates for the parameters of both models. Notably, in the
continuous case, we identify an explicit posterior distribution. This work
enhances the power of goodness-of-fit tests, enabling us to accurately discern
whether a network or any other dataset adheres to a power-law distribution. We
apply the proposed approach to fit degree distributions for more than 5,000
synthetic networks and over 3,000 real networks. The results indicate that our
method is more suitable in practice, as it yields a frequency of acceptance
close to the specified nominal level.

通过改进方法，利用贝叶斯推断来获得准确的估计和可信区间，以提高拟合度分布检验的可靠性。探究了网络或其他数据集是否遵循幂律分布，并将该方法应用于合成网络和实际网络的分析中。结果表明该方法更加适用于实际情况。

无标度网络：改进的推理

Scale-free networks: improved inference

This work offers a broad perspective on probabilistic modeling and inference
in light of recent advances in probabilistic programming, in which models are
formally expressed in Turing-complete programming languages. We consider a
typical workflow and how probabilistic programming languages can help to
automate this workflow, especially in the matching of models with inference
methods. We focus on two properties of a model that are critical in this
matching: its structure---the conditional dependencies between random
variables---and its form---the precise mathematical definition of those
dependencies. While the structure and form of a probabilistic model are often
fixed a priori, it is a curiosity of probabilistic programming that they need
not be, and may instead vary according to random choices made during program
execution. We introduce a formal description of models expressed as programs,
and discuss some of the ways in which probabilistic programming languages can
reveal the structure and form of these, in order to tailor inference methods.
We demonstrate the ideas with a new probabilistic programming language called
Birch, with a multiple object tracking example.

本文介绍了基于概率编程中的最新进展，以广阔的概率建模和推断为视角，探讨了概率编程语言如何自动匹配模型和推断方法，强调了模型的结构和形式对这种匹配的至关重要性，并通过 Birch 进行实例演示。

使用概率编程语言 Birch 进行自动化学习

Automated learning with a probabilistic programming language: Birch

Birnbaum and Saunders introduced a two-parameter lifetime distribution to
model fatigue life of a metal, subject to cyclic stress. Since then, extensive
work has been done on this model providing different interpretations,
constructions, generalizations, inferential methods, and extensions to
bivariate, multivariate and matrix-variate cases. More than two hundred papers
and one research monograph have already appeared describing all these aspects
and developments. In this paper, we provide a detailed review of all these
developments and at the same time indicate several open problems that could be
considered for further research.

本文详细回顾了二参数寿命分布模型的各种解释、推导方法、推广及扩展到双变量、多变量和矩阵变量情况，并指出了一些可供进一步研究的问题。