7 research outputs found
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression provides a general framework for complex
Gaussian and non-Gaussian regression models, with predictors comprising
arbitrary combinations of nonlinear functions and surfaces, spatial effects,
varying coefficients, random effects and further regression terms. The large
flexibility of structured additive regression makes function selection a
challenging and important task, aiming at (1) selecting the relevant
covariates, (2) choosing an appropriate and parsimonious representation of the
impact of covariates on the predictor and (3) determining the required
interactions. We propose a spike-and-slab prior structure for function
selection that allows to include or exclude single coefficients as well as
blocks of coefficients representing specific model terms. A novel
multiplicative parameter expansion is required to obtain good mixing and
convergence properties in a Markov chain Monte Carlo simulation approach and is
shown to induce desirable shrinkage properties. In simulation studies and with
(real) benchmark classification data, we investigate sensitivity to
hyperparameter settings and compare performance to competitors. The flexibility
and applicability of our approach are demonstrated in an additive piecewise
exponential model with time-varying effects for right-censored survival times
of intensive care patients with sepsis. Geoadditive and additive mixed logit
model applications are discussed in an extensive appendix
Hyper-g priors for generalised additive model selection
We propose an automatic Bayesian approach to the selection of covariates and penalised splines transformations thereof in generalised additive models. Specification of a hyper-g prior for the model parameters and a multiplicity-correction prior for the models themselves is crucial for this task. We introduce the methodology in the normal model and illustrate it with an application to diabetes data. Extension to non-normal exponential families is finally discussed
Bayesian fractional polynomials
This paper sets out to implement the Bayesian paradigm for fractional polynomial models under the assumption of normally distributed error terms. Fractional polynomials widen the class of ordinary polynomials and offer an additive and transportable modelling approach. The methodology is based on a Bayesian linear model with a quasi-default hyper-g prior and combines variable selection with parametric modelling of additive effects. A Markov chain Monte Carlo algorithm for the exploration of the model space is presented. This theoretically well-founded stochastic search constitutes a substantial improvement to ad hoc stepwise procedures for the fitting of fractional polynomial models. The method is applied to a data set on the relationship between ozone levels and meteorological parameters, previously analysed in the literature
Genome-wide DNA-(de)methylation is associated with Noninfectious Bud-failure exhibition in Almond (Prunus dulcis [Mill.] D.A.Webb)
Noninfectious bud-failure (BF) remains a major threat to almond production in California, particularly with the recent rapid expansion of acreage and as more intensive cultural practices and modern cultivars are adopted. BF has been shown to be inherited in both vegetative and sexual progeny, with exhibition related to the age and propagation history of scion clonal sources. These characteristics suggest an epigenetic influence, such as the loss of juvenility mediated by DNA-(de)methylation. Various degrees of BF have been reported among cultivars as well as within sources of clonal propagation of the same cultivar. Genome-wide methylation profiles for different clones within almond genotypes were developed to examine their association with BF levels and association with the chronological time from initial propagation. The degree of BF exhibition was found to be associated with DNA-(de)methylation and clonal age, which suggests that epigenetic changes associated with ageing may be involved in the differential exhibition of BF within and among almond clones. Research is needed to investigate the potential of DNA-(de)methylation status as a predictor for BF as well as for effective strategies to improve clonal selection against age related deterioration. This is the first report of an epigenetic-related disorder threatening a major tree crop