7,343 research outputs found
Objective Bayesian analysis for the multivariate skew-t model
We perform a Bayesian analysis of the p-variate skew-t model, providing a new
parameterization, a set of non-informative priors and a sampler specifically
designed to explore the posterior density of the model parameters. Extensions,
such as the multivariate regression model with skewed errors and the stochastic
frontiers model, are easily accommodated. A novelty introduced in the paper is
given by the extension of the bivariate skew-normal model given in Liseo &
Parisi (2013) to a more realistic p-variate skew-t model. We also introduce the
R package mvst, which allows to estimate the multivariate skew-t model
Bayesian inference for the multivariate skew-normal model: a Population Monte Carlo approach
Frequentist and likelihood methods of inference based on the multivariate
skew-normal model encounter several technical difficulties with this model. In
spite of the popularity of this class of densities, there are no broadly
satisfactory solutions for estimation and testing problems. A general
population Monte Carlo algorithm is proposed which: 1) exploits the latent
structure stochastic representation of skew-normal random variables to provide
a full Bayesian analysis of the model and 2) accounts for the presence of
constraints in the parameter space. The proposed approach can be defined as
weakly informative, since the prior distribution approximates the actual
reference prior for the shape parameter vector. Results are compared with the
existing classical solutions and the practical implementation of the algorithm
is illustrated via a simulation study and a real data example. A generalization
to the matrix variate regression model with skew-normal error is also
presented
Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions
We formalise and generalise the definition of the family of univariate double
two--piece distributions, obtained by using a density--based transformation of
unimodal symmetric continuous distributions with a shape parameter. The
resulting distributions contain five interpretable parameters that control the
mode, as well as the scale and shape in each direction. Four-parameter
subfamilies of this class of distributions that capture different types of
asymmetry are discussed. We propose interpretable scale and location-invariant
benchmark priors and derive conditions for the propriety of the corresponding
posterior distribution. The prior structures used allow for meaningful
comparisons through Bayes factors within flexible families of distributions.
These distributions are applied to data from finance, internet traffic and
medicine, comparing them with appropriate competitors
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