Model for fitting longitudinal traits subject to threshold response applied to genetic evaluation for heat tolerance

A semi-parametric non-linear longitudinal hierarchical model is presented. The model assumes that individual variation exists both in the degree of the linear change of performance (slope) beyond a particular threshold of the independent variable scale and in the magnitude of the threshold itself; these individual variations are attributed to genetic and environmental components. During implementation via a Bayesian MCMC approach, threshold levels were sampled using a Metropolis step because their fully conditional posterior distributions do not have a closed form. The model was tested by simulation following designs similar to previous studies on genetics of heat stress. Posterior means of parameters of interest, under all simulation scenarios, were close to their true values with the latter always being included in the uncertain regions, indicating an absence of bias. The proposed models provide flexible tools for studying genotype by environmental interaction as well as for fitting other longitudinal traits subject to abrupt changes in the performance at particular points on the independent variable scale

Inferring the dynamics of rising radical right-wing party support using Gaussian processes

The use of classical regression techniques in social science can prevent the discovery of complex, nonlinear mechanisms, and often relies too heavily on both the expertise and prior expectations of the data analyst. In this paper, we present a regression methodology that combines the interpretability of traditional, well used, statistical methods with the full predictability and flexibility of Bayesian statistics techniques. Our modelling approach allow us to find and explain the mechanisms behind the rise of Radical Right-wing Populist parties (RRPs), that we would have been unable to find using traditional methods. Using Swedish municipality level data (2002-2018) we find no evidence that the proportion of foreignborn residents is predictive of increases in RRP support. Instead, education levels and population density are the significant variables that impact the change in support for the RRP, in addition to spatial and temporal control variables. We argue that our methodology, which produces models with considerably better fit of the complexity and nonlinearities often found in social systems, provides a better tool for hypothesis testing and exploration of theories about RRPs and other social movements

Bayesian Classification and Regression Trees for Predicting Incidence of Cryptosporidiosis

Background Classification and regression tree (CART) models are tree-based exploratory data analysis methods which have been shown to be very useful in identifying and estimating complex hierarchical relationships in ecological and medical contexts. In this paper, a Bayesian CART model is described and applied to the problem of modelling the cryptosporidiosis infection in Queensland, Australia. Methodology/Principal Findings We compared the results of a Bayesian CART model with those obtained using a Bayesian spatial conditional autoregressive (CAR) model. Overall, the analyses indicated that the nature and magnitude of the effect estimates were similar for the two methods in this study, but the CART model more easily accommodated higher order interaction effects. Conclusions/Significance A Bayesian CART model for identification and estimation of the spatial distribution of disease risk is useful in monitoring and assessment of infectious diseases prevention and control

The quest for the solar g modes

Solar gravity modes (or g modes) -- oscillations of the solar interior for which buoyancy acts as the restoring force -- have the potential to provide unprecedented inference on the structure and dynamics of the solar core, inference that is not possible with the well observed acoustic modes (or p modes). The high amplitude of the g-mode eigenfunctions in the core and the evanesence of the modes in the convection zone make the modes particularly sensitive to the physical and dynamical conditions in the core. Owing to the existence of the convection zone, the g modes have very low amplitudes at photospheric levels, which makes the modes extremely hard to detect. In this paper, we review the current state of play regarding attempts to detect g modes. We review the theory of g modes, including theoretical estimation of the g-mode frequencies, amplitudes and damping rates. Then we go on to discuss the techniques that have been used to try to detect g modes. We review results in the literature, and finish by looking to the future, and the potential advances that can be made -- from both data and data-analysis perspectives -- to give unambiguous detections of individual g modes. The review ends by concluding that, at the time of writing, there is indeed a consensus amongst the authors that there is currently no undisputed detection of solar g modes.Comment: 71 pages, 18 figures, accepted by Astronomy and Astrophysics Revie

Classification with bayesian MARS

We present a new method for classification using a Bayesian version of the Multivariate Adaptive Regression Spline (MARS) model of J.H. Friedman (Annals of Statistics, 19, 1-141, 1991). Special attention is paid to the use of Markov chain Monte Carlo (MCMC) simulation to gain inference under the model. In particular we discuss three important developments in MCMC methodology. First, we describe the reversible jump MCMC algorithm of P.J. Green (Biometrika, 82, 711-732, 1995) which allows inference on a varying dimensional, possibly uncountable, model space. This allows us to consider MARS models of differing numbers and positions of splines. Secondly, we discuss marginalisation which is used to reduce the effective dimension of the parameter space under consideration. Thirdly, we describe the use of latent variables to improve the MCMC computation. Our methods are generic and can be applied to any basis function model including, wavelets, artificial neural nets and radial basis functions. We present examples to show that the Bayesian MARS classifier is competitive with other approaches on a number of benchmark data sets

Classification with bayesian MARS

We present a new method for classification using a Bayesian version of the Multivariate Adaptive Regression Spline (MARS) model of J.H. Friedman (Annals of Statistics, 19, 1-141, 1991). Special attention is paid to the use of Markov chain Monte Carlo (MCMC) simulation to gain inference under the model. In particular we discuss three important developments in MCMC methodology. First, we describe the reversible jump MCMC algorithm of P.J. Green (Biometrika, 82, 711-732, 1995) which allows inference on a varying dimensional, possibly uncountable, model space. This allows us to consider MARS models of differing numbers and positions of splines. Secondly, we discuss marginalisation which is used to reduce the effective dimension of the parameter space under consideration. Thirdly, we describe the use of latent variables to improve the MCMC computation. Our methods are generic and can be applied to any basis function model including, wavelets, artificial neural nets and radial basis functions. We present examples to show that the Bayesian MARS classifier is competitive with other approaches on a number of benchmark data sets

Accounting for model uncertainty in seemingly unrelated regressions

This article considers inference in a Bayesian seemingly unrelated regression (SUR) model where the set of regressors is assumed unknown a priori. That is, we allow for uncertainty in the covariate set by defining a prior distribution on the model space. The posterior inference is analytically intractable and we adopt computer-intensive simulation using variable dimension Markov chain Monte Carlo algorithms to approximate quantities of interest. Applications are given for vector autoregression (VAR) models of unknown order and multivariate spline models with unknown knot points

Bayesian partition modelling

This paper reviews recent ideas in Bayesian classification modelling via partitioning. These methods provide predictive estimates for class assignments using averages of a sample of models generated from the posterior distribution of the model parameters. We discuss modifications to the basic approach more suitable for problems when there are many predictor variables and/or a large training smple. © 2002 Elsevier Science B.V. All rights reserved

Bayesian prediction via partitioning

This article proposes a new Bayesian approach to prediction on continuous covariates. The Bayesian partition model constructs arbitrarily complex regression and classification surfaces by splitting the covariate space into an unknown number of disjoint regions. Within each region the data are assumed to be exchangeable and come from some simple distribution. Using conjugate priors, the marginal likelihoods of the models can be obtained analytically for any proposed partitioning of the space where the number and location of the regions is assumed unknown a priori. Markov chain Monte Carlo simulation techniques are used to obtain predictive distributions at the design points by averaging across posterior samples of partitions. © 2005 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America