85,268 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 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
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
Mental calculation : its place in the development of numeracy
The current concerns about the standards of numeracy in primary schools, as these are manifest in different official reports (HMI, 1997; DfEE, 1998), have given a revised emphasis to mental calculation. While not completely discounting the wider aspects of mathematical achievement, the topics of space and shape, data handling and measurement are being de-emphasised (Brown et al, 2000) and mental calculation is being emphasised, with there being daily opportunities for children to develop efficient and flexible mental methods of calculating (QCA, 1999; Wilson, 1999). However, the term, mental calculation is not clearly defined (Harries and Spooner, 2000) and without conceptual clarity it may be very difficult for us to recognise, let alone understand, what pedagogical practices are needed to support the objective of increased emphasis on mental calculation. What follows is some consideration of what is meant by the term mental calculation and what this meaning implies for practice
The distribution function of a semiflexible polymer and random walks with constraints
In studying the end-to-end distribution function of a worm like
chain by using the propagator method we have established that the combinatorial
problem of counting the paths contributing to can be mapped onto the
problem of random walks with constraints, which is closely related to the
representation theory of the Temperley-Lieb algebra. By using this mapping we
derive an exact expression of the Fourier-Laplace transform of the distribution
function, , as a matrix element of an inverse of an infinite rank
matrix. Using this result we also derived a recursion relation permitting to
compute directly. We present the results of the computation of
and its moments. The moments of can be
calculated \emph{exactly} by calculating the (1,1) matrix element of -th
power of a truncated matrix of rank .Comment: 6 pages, 2 figures, added a referenc
Excess Floppy Modes and Multi-Branched Mechanisms in Metamaterials with Symmetries
Floppy modes --- deformations that cost zero energy --- are central to the
mechanics of a wide class of systems. For disordered systems, such as random
networks and particle packings, it is well-understood how the number of floppy
modes is controlled by the topology of the connections. Here we uncover that
symmetric geometries, present in e.g. mechanical metamaterials, can feature an
unlimited number of excess floppy modes that are absent in generic geometries,
and in addition can support floppy modes that are multi-branched. We study the
number of excess floppy modes by comparing generic and symmetric
geometries with identical topologies, and show that is extensive,
peaks at intermediate connection densities, and exhibits mean field scaling. We
then develop an approximate yet accurate cluster counting algorithm that
captures these findings. Finally, we leverage our insights to design
metamaterials with multiple folding mechanisms.Comment: Main text has 4 pages and 5 figures, and is further supported by
Supplementary Informatio
- …