Search results for " random field"
showing 10 items of 41 documents
An autoregressive approach to spatio-temporal disease mapping
2007
Disease mapping has been a very active research field during recent years. Nevertheless, time trends in risks have been ignored in most of these studies, yet they can provide information with a very high epidemiological value. Lately, several spatio-temporal models have been proposed, either based on a parametric description of time trends, on independent risk estimates for every period, or on the definition of the joint covariance matrix for all the periods as a Kronecker product of matrices. The following paper offers an autoregressive approach to spatio-temporal disease mapping by fusing ideas from autoregressive time series in order to link information in time and by spatial modelling t…
On the convenience of heteroscedasticity in highly multivariate disease mapping
2019
Highly multivariate disease mapping has recently been proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential since it integrates the information of many diseases into a single model yielding richer and more accurate risk maps. In this paper we show how some of the proposals already put forward in this area display some particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. In this paper we propose two new models to deal with the variance-adaptiv…
Modelling residuals dependence in dynamic life tables: A geostatistical approach
2008
The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on R × R. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded in…
Spectral adaptation of hyperspectral flight lines using VHR contextual information
2014
Abstract: Due to technological constraints, hyperspectral earth observation imagery are often a mosaic of overlapping flight lines collected in different passes over the area of interest. This causes variations in aqcuisition conditions such that the reflected spectrum can vary significantly between these flight lines. Partly, this problem is solved by atmospherical correction, but residual spectral differences often remain. A probabilistic domain adaptation framework based on graph matching using Hidden Markov Random Fields was recently proposed for transforming hyperspectral data from one image to better correspond to the other. This paper investigates the use of scale and angle invariant…
Weeds sampling for map reconstruction: a Markov random field approach
2012
In the past 15 years, there has been a growing interest for the study of the spatial repartition of weeds in crops, mainly because this is a prerequisite to herbicides use reduction. There has been a large variety of statistical methods developped for this problem ([5], [7], [10]). However, one common point of all of these methods is that they are based on in situ collection of data about weeds spatial repartition. A crucial problem is then to choose where, in the eld, data should be collected. Since exhaustive sampling of a eld is too costly, a lot of attention has been paid to the development of spatial sampling methods ([12], [4], [6] [9]). Classical spatial stochastic model of weeds cou…
Échantillonnage adaptatif optimal dans les champs de Markov, application à l’échantillonnage d’une espèce adventice
2012
This work is divided into two parts: (i) the theoretical study of the problem of adaptive sampling in Markov Random Fields (MRF) and (ii) the modeling of the problem of weed sampling in a crop field and the design of adaptive sampling strategies for this problem. For the first point, we first modeled the problem of finding an optimal sampling strategy as a finite horizon Markov Decision Process (MDP). Then, we proposed a generic algorithm for computing an approximate solution to any finite horizon MDP with known model. This algorithm, called Least-Squared Dynamic Programming (LSDP), combines the concepts of dynamic programming and reinforcement learning. It was then adapted to compute adapt…
Hidden Markov Random Field model and BFGS algorithm for Brain Image Segmentation
2016
Brain MR images segmentation has attracted a particular focus in medical imaging. The automatic image analysis and interpretation became a necessity. Segmentation is one of the key operations to provide a crucial decision support to physicians. Its goal is to simplify the representation of an image into items meaningful and easier to analyze. Hidden Markov Random Fields (HMRF) provide an elegant way to model the segmentation problem. This model leads to the minimization problem of a function. BFGS (Broyden-Fletcher-Goldfarb-Shanno algorithm) is one of the most powerful methods to solve unconstrained optimization problem. This paper presents how we combine HMRF and BFGS to achieve a good seg…
Optimization of Linearized Belief Propagation for Distributed Detection
2020
In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a pr…
Modeling and Mitigating Errors in Belief Propagation for Distributed Detection
2021
We study the behavior of the belief-propagation (BP) algorithm affected by erroneous data exchange in a wireless sensor network (WSN). The WSN conducts a distributed multidimensional hypothesis test over binary random variables. The joint statistical behavior of the sensor observations is modeled by a Markov random field whose parameters are used to build the BP messages exchanged between the sensing nodes. Through linearization of the BP message-update rule, we analyze the behavior of the resulting erroneous decision variables and derive closed-form relationships that describe the impact of stochastic errors on the performance of the BP algorithm. We then develop a decentralized distribute…
Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes
2018
We propose a new fitting method to estimate the set of second-order parameters for the class of homogeneous spatio-temporal log-Gaussian Cox point processes. With simulations, we show that the proposed minimum contrast procedure, based on the spatio-temporal pair correlation function, provides reliable estimates and we compare the results with the current available methods. Moreover, the proposed method can be used in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. We describe earthquake sequences comparing several Cox model specifications.