996 research outputs found
Approximating multivariate posterior distribution functions from Monte Carlo samples for sequential Bayesian inference
An important feature of Bayesian statistics is the opportunity to do
sequential inference: the posterior distribution obtained after seeing a
dataset can be used as prior for a second inference. However, when Monte Carlo
sampling methods are used for inference, we only have a set of samples from the
posterior distribution. To do sequential inference, we then either have to
evaluate the second posterior at only these locations and reweight the samples
accordingly, or we can estimate a functional description of the posterior
probability distribution from the samples and use that as prior for the second
inference. Here, we investigated to what extent we can obtain an accurate joint
posterior from two datasets if the inference is done sequentially rather than
jointly, under the condition that each inference step is done using Monte Carlo
sampling. To test this, we evaluated the accuracy of kernel density estimates,
Gaussian mixtures, vine copulas and Gaussian processes in approximating
posterior distributions, and then tested whether these approximations can be
used in sequential inference. In low dimensionality, Gaussian processes are
more accurate, whereas in higher dimensionality Gaussian mixtures or vine
copulas perform better. In our test cases, posterior approximations are
preferable over direct sample reweighting, although joint inference is still
preferable over sequential inference. Since the performance is case-specific,
we provide an R package mvdens with a unified interface for the density
approximation methods
Information and Covariance Matrices for Multivariate Burr III and Logistic distributions
Main result of this paper is to derive the exact analytical expressions of
information and covariance matrices for multivariate Burr III and logistic
distributions. These distributions arise as tractable parametric models in
price and income distributions, reliability, economics, populations growth and
survival data. We showed that all the calculations can be obtained from one
main moment multi dimensional integral whose expression is obtained through
some particular change of variables. Indeed, we consider that this calculus
technique for improper integral has its own importance in applied probability
calculus.Comment: submitted to Communications in Statistic
A new specification of generalized linear models for categorical data
Regression models for categorical data are specified in heterogeneous ways.
We propose to unify the specification of such models. This allows us to define
the family of reference models for nominal data. We introduce the notion of
reversible models for ordinal data that distinguishes adjacent and cumulative
models from sequential ones. The combination of the proposed specification with
the definition of reference and reversible models and various invariance
properties leads to a new view of regression models for categorical data.Comment: 31 pages, 13 figure
Asymptotically distribution-free goodness-of-fit testing for tail copulas
Let be an i.i.d. sample from a bivariate
distribution function that lies in the max-domain of attraction of an extreme
value distribution. The asymptotic joint distribution of the standardized
component-wise maxima and is then
characterized by the marginal extreme value indices and the tail copula . We
propose a procedure for constructing asymptotically distribution-free
goodness-of-fit tests for the tail copula . The procedure is based on a
transformation of a suitable empirical process derived from a semi-parametric
estimator of . The transformed empirical process converges weakly to a
standard Wiener process, paving the way for a multitude of asymptotically
distribution-free goodness-of-fit tests. We also extend our results to the
-variate () case. In a simulation study we show that the limit theorems
provide good approximations for finite samples and that tests based on the
transformed empirical process have high power.Comment: Published at http://dx.doi.org/10.1214/14-AOS1304 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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