Search results for "Names"
showing 10 items of 6843 documents
Intrinsic credible regions: An objective Bayesian approach to interval estimation
2005
This paper definesintrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data.Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, theintrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general…
Generalization of Jeffreys Divergence-Based Priors for Bayesian Hypothesis Testing
2008
Summary We introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence-based (DB) priors. DB priors have simple forms and desirable properties like information (finite sample) consistency and are often similar to other existing proposals like intrinsic priors. Moreover, in normal linear model scenarios, they reproduce the Jeffreys–Zellner–Siow priors exactly. Most importantly, in challenging scenarios such as irregular models and mixture models, DB priors are well defined and very reasonable, whereas alternative proposals are not. We derive approximations to the DB priors as w…
Prior-based Bayesian information criterion
2019
We present a new approach to model selection and Bayes factor determination, based on Laplace expansions (as in BIC), which we call Prior-based Bayes Information Criterion (PBIC). In this approach, the Laplace expansion is only done with the likelihood function, and then a suitable prior distribution is chosen to allow exact computation of the (approximate) marginal likelihood arising from the Laplace approximation and the prior. The result is a closed-form expression similar to BIC, but now involves a term arising from the prior distribution (which BIC ignores) and also incorporates the idea that different parameters can have different effective sample sizes (whereas BIC only allows one ov…
Hitting straight lines by compound Poisson process paths
1990
In a recent article Mallows and Nair (1989,Ann. Inst. Statist. Math.,41, 1–8) determined the probability of intersectionP{X(t)=αt for somet≥0} between a compound Poisson process {X(t), t≥0} and a straight line through the origin. Using four different approaches (direct probabilistic, via differential equations and via Laplace transforms) we extend their results to obtain the probability of intersection between {X(t), t≥0} and arbitrary lines. Also, we display a relationship with the theory of Galton-Watson processes. Additional results concern the intersections with two (or more) parallel lines.
Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature
2010
By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. F…
Bayesian analysis of a disability model for lung cancer survival
2016
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…
Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model
2016
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…
Stability of a stochastic SIR system
2005
Abstract We propose a stochastic SIR model with or without distributed time delay and we study the stability of disease-free equilibrium. The numerical simulation of the stochastic SIR model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found.
MCMC methods to approximate conditional predictive distributions
2006
Sampling from conditional distributions is a problem often encountered in statistics when inferences are based on conditional distributions which are not of closed-form. Several Markov chain Monte Carlo (MCMC) algorithms to simulate from them are proposed. Potential problems are pointed out and some suitable modifications are suggested. Approximations based on conditioning sets are also explored. The issues are illustrated within a specific statistical tool for Bayesian model checking, and compared in an example. An example in frequentist conditional testing is also given.
Bayesian Mapping of Lichens Growing on Trees
2001
Suitability of trees as hosts for epiphytic lichens are studied in a forest stand of size 25 ha. Suitability is measured as occupation probabilites which are modelled using hierarchical Bayesian approach. These probabilities are useful for an ecologist. They give smoothed spatial distribution map of suitability for each of the species and can be used in detecting high- and low-probability areas. In addition, suitability is explained by tree-level covariates. Spatial dependence, which is due to unobserved spatially structured covariates, is modelled through an unobserved Markov random field. Markov chain Monte Carlo method has been applied in Bayesian computation. The extensive spatial data …