12,732 research outputs found
On the Independence Jeffreys prior for skew--symmetric models with applications
We study the Jeffreys prior of the skewness parameter of a general class of
scalar skew--symmetric models. It is shown that this prior is symmetric about
0, proper, and with tails under mild regularity conditions.
We also calculate the independence Jeffreys prior for the case with unknown
location and scale parameters. Sufficient conditions for the existence of the
corresponding posterior distribution are investigated for the case when the
sampling model belongs to the family of skew--symmetric scale mixtures of
normal distributions. The usefulness of these results is illustrated using the
skew--logistic model and two applications with real data
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
A note on marginal posterior simulation via higher-order tail area approximations
We explore the use of higher-order tail area approximations for Bayesian
simulation. These approximations give rise to an alternative simulation scheme
to MCMC for Bayesian computation of marginal posterior distributions for a
scalar parameter of interest, in the presence of nuisance parameters. Its
advantage over MCMC methods is that samples are drawn independently with lower
computational time and the implementation requires only standard maximum
likelihood routines. The method is illustrated by a genetic linkage model, a
normal regression with censored data and a logistic regression model
Coherent frequentism
By representing the range of fair betting odds according to a pair of
confidence set estimators, dual probability measures on parameter space called
frequentist posteriors secure the coherence of subjective inference without any
prior distribution. The closure of the set of expected losses corresponding to
the dual frequentist posteriors constrains decisions without arbitrarily
forcing optimization under all circumstances. This decision theory reduces to
those that maximize expected utility when the pair of frequentist posteriors is
induced by an exact or approximate confidence set estimator or when an
automatic reduction rule is applied to the pair. In such cases, the resulting
frequentist posterior is coherent in the sense that, as a probability
distribution of the parameter of interest, it satisfies the axioms of the
decision-theoretic and logic-theoretic systems typically cited in support of
the Bayesian posterior. Unlike the p-value, the confidence level of an interval
hypothesis derived from such a measure is suitable as an estimator of the
indicator of hypothesis truth since it converges in sample-space probability to
1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly
extended to vector parameters of interest. The derivation of upper and lower
confidence levels from valid and nonconservative set estimators is formalize
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