Related papers: Power laws distributions in objective priors
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
Generalized linear mixed models (GLMMs) are commonly used to analyze correlated discrete or continuous response data. In Bayesian GLMMs, the often-used improper priors may yield undesirable improper posterior distributions. Thus, verifying…
In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in exponential family models with arbitrary centring and scaling.…
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…
In this work we apply the methodology of integral priors to handle Bayesian model selection in binomial regression models with a general link function. These models are very often used to investigate associations and risks in…
The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…
The Weibull distribution is one of the most used tools in reliability analysis. In this paper, assuming a Bayesian approach, we propose necessary and sufficient conditions to verify when improper priors lead to proper posteriors for the…
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or credible intervals to inform data-driven decision making. We propose a framework for power curve approximation with such hypothesis tests. We present a fast…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
Gibbs type priors have been shown to be natural generalizations of Dirichlet process (DP) priors used for intricate applications of Bayesian nonparametric methods. This includes applications to mixture models and to species sampling models…
We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a…
According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…