17,848 research outputs found
Generalized structured additive regression based on Bayesian P-splines
Generalized additive models (GAM) for modelling nonlinear effects of continuous covariates are now well established tools for the applied statistician. In this paper we develop Bayesian GAM's and extensions to generalized structured additive regression based on one or two dimensional P-splines as the main building block. The approach extends previous work by Lang und Brezger (2003) for Gaussian responses. Inference relies on Markov chain Monte Carlo (MCMC) simulation techniques, and is either based on iteratively weighted least squares (IWLS) proposals or on latent utility representations of (multi)categorical regression models. Our approach covers the most common univariate response distributions, e.g. the Binomial, Poisson or Gamma distribution, as well as multicategorical responses. For the first time, we present Bayesian semiparametric inference for the widely used multinomial logit models. As we will demonstrate through two applications on the forest health status of trees and a space-time analysis of health insurance data, the approach allows realistic modelling of complex problems. We consider the enormous flexibility and extendability of our approach as a main advantage of Bayesian inference based on MCMC techniques compared to more traditional approaches. Software for the methodology presented in the paper is provided within the public domain package BayesX
Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model
Bayesian inference methods are applied within a Bayesian hierarchical
modelling framework to the problems of joint state and parameter estimation,
and of state forecasting. We explore and demonstrate the ideas in the context
of a simple nonlinear marine biogeochemical model. A novel approach is proposed
to the formulation of the stochastic process model, in which ecophysiological
properties of plankton communities are represented by autoregressive stochastic
processes. This approach captures the effects of changes in plankton
communities over time, and it allows the incorporation of literature metadata
on individual species into prior distributions for process model parameters.
The approach is applied to a case study at Ocean Station Papa, using Particle
Markov chain Monte Carlo computational techniques. The results suggest that, by
drawing on objective prior information, it is possible to extract useful
information about model state and a subset of parameters, and even to make
useful long-term forecasts, based on sparse and noisy observations
General Design Bayesian Generalized Linear Mixed Models
Linear mixed models are able to handle an extraordinary range of
complications in regression-type analyses. Their most common use is to account
for within-subject correlation in longitudinal data analysis. They are also the
standard vehicle for smoothing spatial count data. However, when treated in
full generality, mixed models can also handle spline-type smoothing and closely
approximate kriging. This allows for nonparametric regression models (e.g.,
additive models and varying coefficient models) to be handled within the mixed
model framework. The key is to allow the random effects design matrix to have
general structure; hence our label general design. For continuous response
data, particularly when Gaussianity of the response is reasonably assumed,
computation is now quite mature and supported by the R, SAS and S-PLUS
packages. Such is not the case for binary and count responses, where
generalized linear mixed models (GLMMs) are required, but are hindered by the
presence of intractable multivariate integrals. Software known to us supports
special cases of the GLMM (e.g., PROC NLMIXED in SAS or glmmML in R) or relies
on the sometimes crude Laplace-type approximation of integrals (e.g., the SAS
macro glimmix or glmmPQL in R). This paper describes the fitting of general
design generalized linear mixed models. A Bayesian approach is taken and Markov
chain Monte Carlo (MCMC) is used for estimation and inference. In this
generalized setting, MCMC requires sampling from nonstandard distributions. In
this article, we demonstrate that the MCMC package WinBUGS facilitates sound
fitting of general design Bayesian generalized linear mixed models in practice.Comment: Published at http://dx.doi.org/10.1214/088342306000000015 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Robust Linear Spectral Unmixing using Anomaly Detection
This paper presents a Bayesian algorithm for linear spectral unmixing of
hyperspectral images that accounts for anomalies present in the data. The model
proposed assumes that the pixel reflectances are linear mixtures of unknown
endmembers, corrupted by an additional nonlinear term modelling anomalies and
additive Gaussian noise. A Markov random field is used for anomaly detection
based on the spatial and spectral structures of the anomalies. This allows
outliers to be identified in particular regions and wavelengths of the data
cube. A Bayesian algorithm is proposed to estimate the parameters involved in
the model yielding a joint linear unmixing and anomaly detection algorithm.
Simulations conducted with synthetic and real hyperspectral images demonstrate
the accuracy of the proposed unmixing and outlier detection strategy for the
analysis of hyperspectral images
Bayesian State Space Modeling of Physical Processes in Industrial Hygiene
Exposure assessment models are deterministic models derived from
physical-chemical laws. In real workplace settings, chemical concentration
measurements can be noisy and indirectly measured. In addition, inference on
important parameters such as generation and ventilation rates are usually of
interest since they are difficult to obtain. In this paper we outline a
flexible Bayesian framework for parameter inference and exposure prediction. In
particular, we propose using Bayesian state space models by discretizing the
differential equation models and incorporating information from observed
measurements and expert prior knowledge. At each time point, a new measurement
is available that contains some noise, so using the physical model and the
available measurements, we try to obtain a more accurate state estimate, which
can be called filtering. We consider Monte Carlo sampling methods for parameter
estimation and inference under nonlinear and non-Gaussian assumptions. The
performance of the different methods is studied on computer-simulated and
controlled laboratory-generated data. We consider some commonly used exposure
models representing different physical hypotheses
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