Related papers: Non-parametric power-law surrogates
The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the…
We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…
In recent years, neural network-based classification has been used to improve data analysis at collider experiments. While this strategy proves to be hugely successful, the underlying models are not commonly shared with the public and rely…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
Many human-related activities show power-law decaying interevent time distribution with exponents usually varying between 1 and 2. We study a simple task-queuing model, which produces bursty time series due to the nontrivial dynamics of the…
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
In this study we aim for a deeper understanding of the power law slope, $\alpha$, of waiting time distributions. Statistically independent events with linear behavior can be characterized by binomial, Gaussian, exponential, or Poissonian…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into account how the past events influence the occurrence of future…