7,520 research outputs found
OBJECTIVE BAYESIAN ANALYSIS OF A GENERALIZED LOGNORMAL DISTRIBUTION
The generalized lognormal distribution plays an important role in various aspects of life testing experiments. We examine Bayesian analysis of this distribution using objective priors (in the general sense of priors constructed using some formal rules) for the model parameters in this paper. Specifically, the derivation of explicit expressions for multiple types of the Jeffreys priors, the reference priors with different group ordering of the parameters, and the first-order matching priors. We investigate the important issue of proper posterior distributions. It is shown that only two of them lead to proper posterior distributions. Monte Carlo simulations are conducted to compare the performances of the Bayesian approaches under the various priors. Last, a real-world data case will be shown to illustrate the theoretical analysis
Bayesian Inference under Cluster Sampling with Probability Proportional to Size
Cluster sampling is common in survey practice, and the corresponding
inference has been predominantly design-based. We develop a Bayesian framework
for cluster sampling and account for the design effect in the outcome modeling.
We consider a two-stage cluster sampling design where the clusters are first
selected with probability proportional to cluster size, and then units are
randomly sampled inside selected clusters. Challenges arise when the sizes of
nonsampled cluster are unknown. We propose nonparametric and parametric
Bayesian approaches for predicting the unknown cluster sizes, with this
inference performed simultaneously with the model for survey outcome.
Simulation studies show that the integrated Bayesian approach outperforms
classical methods with efficiency gains. We use Stan for computing and apply
the proposal to the Fragile Families and Child Wellbeing study as an
illustration of complex survey inference in health surveys
Joint constraints on galaxy bias and through the N-pdf of the galaxy number density
We present a full description of the N-probability density function of the
galaxy number density fluctuations. This N-pdf is given in terms, on the one
hand, of the cold dark matter correlations and, on the other hand, of the
galaxy bias parameter. The method relies on the assumption commonly adopted
that the dark matter density fluctuations follow a local non-linear
transformation of the initial energy density perturbations. The N-pdf of the
galaxy number density fluctuations allows for an optimal estimation of the bias
parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if
there exists any a priori information on the bias parameter), and of those
parameters defining the dark matter correlations, in particular its amplitude
(). It also provides the proper framework to perform model selection
between two competitive hypotheses. The parameters estimation capabilities of
the N-pdf are proved by SDSS-like simulations (both ideal log-normal
simulations and mocks obtained from Las Damas simulations), showing that our
estimator is unbiased. We apply our formalism to the 7th release of the SDSS
main sample (for a volume-limited subset with absolute magnitudes ). We obtain and , for galaxy number density fluctuations in cells of a size of
Mpc. Different model selection criteria show that galaxy biasing is
clearly favoured.Comment: 25 pages, 9 figures, 2 tables. v2: Substantial revision, adding the
joint constraints with \sigma_8 and testing with Las Damas mocks. Matches
version accepted for publication in JCA
Bayes reliability measures of Lognormal and inverse Gaussian distributions under ML-II ε-contaminated class of prior distributions
In this paper we employ ML-II ε-contaminated class of priors to study the sensitivity of Bayes Reliability measures for an Inverse Gaussian (IG) distribution and Lognormal (LN) distribution to misspecification in the prior. The numerical illustrations suggest that reliability measures of both the distributions are not sensitive to moderate amount of misspecification in prior distributions belonging to the class of ML-II ε-contaminated.Bayes reliability, ML-II ε-contaminated prior
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