Related papers: Jeffreys priors for mixture estimation: properties…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
Firth (1993, Biometrika) shows that the maximum Jeffreys' prior penalized likelihood estimator in logistic regression has asymptotic bias decreasing with the square of the number of observations when the number of parameters is fixed, which…
Mixture models are commonly used in applications with heterogeneity and overdispersion in the population, as they allow the identification of subpopulations. In the Bayesian framework, this entails the specification of suitable prior…
The notion of confidence distributions is applied to inference about the parameter in a simple autoregressive model, allowing the parameter to take the value one. This makes it possible to compare to asymptotic approximations in both the…
Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good…
The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…
Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…
We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this…
Many psychological theories that are instantiated as statistical models imply order constraints on the model parameters. To fit and test such restrictions, order constraints of the form $\theta_i \leq \theta_j$ can be reparameterized with…
It is shown that the first-order term of the asymptotic bias of the posterior mean is removed by a suitable choice of a prior density. In regular statistical models including exponential families, and linear and logistic regression models,…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…