7,273 research outputs found
Bayesian semiparametric multi-state models
Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example is Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian (using Markov chain Monte Carlo simulation techniques) or empirically Bayesian (based on a mixed model representation). A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual specific variation has to be accounted for using covariate information and frailty terms
On the Prior and Posterior Distributions Used in Graphical Modelling
Graphical model learning and inference are often performed using Bayesian
techniques. In particular, learning is usually performed in two separate steps.
First, the graph structure is learned from the data; then the parameters of the
model are estimated conditional on that graph structure. While the probability
distributions involved in this second step have been studied in depth, the ones
used in the first step have not been explored in as much detail.
In this paper, we will study the prior and posterior distributions defined
over the space of the graph structures for the purpose of learning the
structure of a graphical model. In particular, we will provide a
characterisation of the behaviour of those distributions as a function of the
possible edges of the graph. We will then use the properties resulting from
this characterisation to define measures of structural variability for both
Bayesian and Markov networks, and we will point out some of their possible
applications.Comment: 28 pages, 6 figure
Incorporating the Basic Elements of a First-degree Fuzzy Logic and Certain Elments of Temporal Logic for Dynamic Management Applications
The approximate reasoning is perceived as a derivation of new formulas with the corresponding temporal attributes, within a fuzzy theory defined by the fuzzy set of special axioms. For dynamic management applications, the reasoning is evolutionary because of unexpected events which may change the state of the expert system. In this kind of situations it is necessary to elaborate certain mechanisms in order to maintain the coherence of the obtained conclusions, to figure out their degree of reliability and the time domain for which these are true. These last aspects stand as possible further directions of development at a basic logic level. The purpose of this paper is to characterise an extended fuzzy logic system with modal operators, attained by incorporating the basic elements of a first-degree fuzzy logic and certain elements of temporal logic.Dynamic Management Applications, Fuzzy Reasoning, Formalization, Time Restrictions, Modal Operators, Real-Time Expert Decision System (RTEDS)
Bayesian Semiparametric Multi-State Models
Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example are Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian using Markov chain Monte Carlo simulation techniques or empirically Bayesian based on a mixed model representation. A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and Non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual-specific variation has to be accounted for using covariate information and frailty terms
Bayesian Semiparametric Multi-State Models
Multi-state models provide a unified framework for the description of the evolution of discrete phenomena in continuous time. One particular example are Markov processes which can be characterised by a set of time-constant transition intensities between the states. In this paper, we will extend such parametric approaches to semiparametric models with flexible transition intensities based on Bayesian versions of penalised splines. The transition intensities will be modelled as smooth functions of time and can further be related to parametric as well as nonparametric covariate effects. Covariates with time-varying effects and frailty terms can be included in addition. Inference will be conducted either fully Bayesian using Markov chain Monte Carlo simulation techniques or empirically Bayesian based on a mixed model representation. A counting process representation of semiparametric multi-state models provides the likelihood formula and also forms the basis for model validation via martingale residual processes. As an application, we will consider human sleep data with a discrete set of sleep states such as REM and Non-REM phases. In this case, simple parametric approaches are inappropriate since the dynamics underlying human sleep are strongly varying throughout the night and individual-specific variation has to be accounted for using covariate information and frailty terms
Likelihood-based inference for max-stable processes
The last decade has seen max-stable processes emerge as a common tool for the
statistical modeling of spatial extremes. However, their application is
complicated due to the unavailability of the multivariate density function, and
so likelihood-based methods remain far from providing a complete and flexible
framework for inference. In this article we develop inferentially practical,
likelihood-based methods for fitting max-stable processes derived from a
composite-likelihood approach. The procedure is sufficiently reliable and
versatile to permit the simultaneous modeling of marginal and dependence
parameters in the spatial context at a moderate computational cost. The utility
of this methodology is examined via simulation, and illustrated by the analysis
of U.S. precipitation extremes
Bayesian computational methods
In this chapter, we will first present the most standard computational
challenges met in Bayesian Statistics, focussing primarily on mixture
estimation and on model choice issues, and then relate these problems with
computational solutions. Of course, this chapter is only a terse introduction
to the problems and solutions related to Bayesian computations. For more
complete references, see Robert and Casella (2004, 2009), or Marin and Robert
(2007), among others. We also restrain from providing an introduction to
Bayesian Statistics per se and for comprehensive coverage, address the reader
to Robert (2007), (again) among others.Comment: This is a revised version of a chapter written for the Handbook of
Computational Statistics, edited by J. Gentle, W. Hardle and Y. Mori in 2003,
in preparation for the second editio
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