相关论文: Problems with Fitting to the Power-Law Distributio…

Multivariate goodness-of-fit and two-sample tests are important components of many nuclear and particle physics analyses. While a variety of powerful methods are available if the dimensionality of the feature space is small, such tests…

Deep energy-based models (EBMs), which use deep neural networks (DNNs) as energy functions, are receiving increasing attention due to their ability to learn complex distributions. To train deep EBMs, the maximum likelihood estimation (MLE)…

Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum…

Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…

When comparing two distributions, it is often helpful to learn at which quantiles or values there is a statistically significant difference. This provides more information than the binary "reject" or "do not reject" decision of a global…

Modeling sparse data such as microbiome and transcriptomics (RNA-seq) data is very challenging due to the exceeded number of zeros and skewness of the distribution. Many probabilistic models have been used for modeling sparse data,…

A new method for calculation of goodness of multidimensional fits in particle physics experiments is proposed. This method finds the smallest and largest clusters of nearest neighbors for observed data points. The cluster size is used to…

Investigating the power density spectrum of fluctuations in Rayleigh-Taylor (RT) interfacial mixing is a means of studying characteristic length- and time-scales, anisotropies and anomalous processes. Guided by group theory, analysing the…

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…

The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension…

The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article,…

Relational models generalize log-linear models to arbitrary discrete sample spaces by specifying effects associated with any subsets of their cells. A relational model may include an overall effect, pertaining to every cell after a…

It has been observed that many complex real-world networks have certain properties, such as a high clustering coefficient, a low diameter, and a power-law degree distribution. A network with a power-law degree distribution is known as…

A common problem in physics is to fit regression data by a parametric class of functions, and to decide whether a certain functional form allows for a good fit of the data. Common goodness of fit methods are based on the calculation of the…

The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio test's null-distribution needs to…

Mixed-effects logistic regression is widely used for binary outcomes in hierarchical data, yet formal goodness-of-fit tests remain limited to random-intercept models and do not address sparse cluster settings. We extend a grouping-based…

We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares…

Linear mixed models (LMMs) have emerged as the method of choice for confounded genome-wide association studies. However, the performance of LMMs in non-randomly ascertained case-control studies deteriorates with increasing sample size. We…

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type 1 error…

The so-called Pareto-Levy or power-law distribution has been successfully used as a model to describe probabilities associated to extreme variations of worldwide stock markets indexes data and it has the form $Pr(X>x) ~ x**(-alpha) for…