Search results for "Markov"
showing 10 items of 628 documents
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…
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…
Evaluating currency crises: the case of the European monetary system
2007
In this paper we examine the nature of currency crises. We ascertain whether the currency crises of the European Monetary System (EMS) were based either on fundamentals, or on self-fulfilling market expectations driven by extrinsic uncertainty. In particular, we extend previous work of Jeanne and Masson (J Int Econ 50:327–350, 2000) regarding the evaluation of currency crisis. We contribute to the existing literature proposing the use of Markov regime-switching with time-varying transition probability model. Our empirical results suggest that the currency crises of the EMS were not due only to market expectations driven by external uncertainty, or ‘sunspots’, but also to fundamental variabl…
A hierarchical Bayesian birth cohort analysis from incomplete registry data: evaluating the trends in the age of onset of insulin-dependent diabetes …
2005
Childhood diabetes is one of the major non-communicable diseases in children under 15 years of age. It requires a life-long insulin treatment and may lead to serious complications. Along with the worldwide increase in the incidence several countries have recently reported a decreasing trend in the age of onset of the disease. The aim of this study is to analyse long-term data on the incidence of the childhood diabetes in Finland from the birth cohorts perspective. The annual incidence data were available for the period 1965--1996 which translates into 1951--1996 birth cohorts. Hence the data consist of completely and partially observed cohorts. Bayesian modelling was employed in the analysi…
Pairwise Markov properties for regression graphs
2016
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of conditional distributions, named regressions in joint responses. The involved random variables may be discrete, continuous or of both types. Such a generating process specifies for each response a conditioning set that contains just its regressor variables, and it leads to at least one valid ordering of all nodes in the corresponding regression graph that has three types of edge: one for undirected dependences among context variables, another for undirect…
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 …
Statistics of return times for weighted maps of the interval
2000
For non markovian, piecewise monotonic maps of the interval associated to a potential, we prove that the law of the entrance time in a cylinder, when renormalized by the measure of the cylinder, converges to an exponential law for almost all cylinders. Thanks to this result, we prove that the fluctuations of Rn, first return time in a cylinder, are lognormal.
Componentwise adaptation for high dimensional MCMC
2005
We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.
Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter
2013
Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is…