Spatial Random Field Models Inspired from Statistical Physics with Applications in the Geosciences

Power-law size distributions in geoscience revisited

The size or energy of diverse structures or phenomena in geoscience appears to follow power-law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power-law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially…

探索受牛顿法几何解释启发的过程输出的统计特性

Exploring the Statistical Properties of Outputs from a Process Inspired by Geometrical Interpretation of Newton's Method

本文研究特定情形下牛顿法算法输出的统计特性，证明其概率密度服从柯西分布，提出生成均匀分布的新方法，经统计检验验证结果，并推导连续输出距离分布的变换求解方法。

一种通过序贯蒙特卡洛与统计物理启发技术的贝叶斯优化方法

A Bayesian Optimization through Sequential Monte Carlo and Statistical Physics-Inspired Techniques

本文提出一种结合序贯蒙特卡洛与统计物理概念的贝叶斯优化方法，借助NumPyro和JAX实现跨CPU、GPU、TPU的高性能并行优化，为多种优化问题提供了低门槛且有前景的技术方向。

A statistical physics perspective on criticality in financial markets

Stock markets are complex systems exhibiting collective phenomena and particular features such as synchronization, fluctuations distributed as power-laws, non-random structures and similarity to neural networks. Such specific properties suggest that markets operate at a very special point. Financial markets are believed to be critical by analogy to physical systems but few statistically founded evidence have been given. Through a data-based methodology and comparison to simulations inspired by statistical physics of complex systems, we show that the Dow Jones and indices sets are not rigorousl…

Temporal statistical analysis on human article creation patterns

Inspired by previous works on human dynamics, we collect the temporal statistics of the article creation by three Western scientists and an Eastern writer. We investigate the distributions of the time intervals between the creations of every two consecutive articles. All four time distributions are found to be deviate from the Poisson statistics, and show an approximate power-law distribution. The power-law exponents are different with respect to individual, indicating that there is no universally shared article creation pattern.

A new ordering principle for the classical statistical analysis of Poisson processes with background

Inspired by the recent proposal by Feldman and Cousins of a ``unified approach to the classical statistical analysis of small signals'' based on a choice of ordering in Neyman's construction of classical confidence intervals, I propose a new ordering principle for the classical statistical analysis of Poisson processes with background which minimizes the effect on the resulting confidence intervals of the observation of less background events than expected. The new ordering principle is applied to the calculation of the confidence region implied by the recent null result of the KARMEN neutrino…