Approximate Bayesian inference for hierarchical Gaussian Markov random field models

2007 ◽  
Vol 137 (10) ◽  
pp. 3177-3192 ◽  
Author(s):  
HÅvard Rue ◽  
Sara Martino
Keyword(s):  
Bayesian Inference ◽  
Random Field ◽  
Markov Random Field ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Approximate Bayesian ◽  
Approximate Bayesian Inference

Risks of Classification of the Gaussian Markov Random Field Observations

2018 ◽  
Vol 35 (3) ◽  
pp. 422-436 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lina Dreižienė
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Field Observations ◽  
Gaussian Markov Random Field ◽  
Markov Random

scholarly journals Mobile Robotic Sensors for Environmental Monitoring using Gaussian Markov Random Field

Robotica ◽  
2020 ◽  
pp. 1-23
Author(s):  
Linh Nguyen ◽  
Sarath Kodagoda ◽  
Ravindra Ranasinghe ◽  
Gamini Dissanayake
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Adaptive Sampling ◽  
Published Data ◽  
Data Sets ◽  
Independence Property ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Sampling Optimization ◽  
Robotic Sensors

SUMMARY This paper addresses the issue of monitoring spatial environmental phenomena of interest utilizing information collected by a network of mobile, wireless, and noisy sensors that can take discrete measurements as they navigate through the environment. It is proposed to employ Gaussian Markov random field (GMRF) represented on an irregular discrete lattice by using the stochastic partial differential equations method to model the physical spatial field. It then derives a GMRF-based approach to effectively predict the field at unmeasured locations, given available observations, in both centralized and distributed manners. Furthermore, a novel but efficient optimality criterion is then proposed to design centralized and distributed adaptive sampling strategies for the mobile robotic sensors to find the most informative sampling paths in taking future measurements. By taking advantage of conditional independence property in the GMRF, the adaptive sampling optimization problem is proven to be resolved in a deterministic time. The effectiveness of the proposed approach is compared and demonstrated using pre-published data sets with appealing results.

Multiresolution texture analysis of bone radiographs using Gaussian Markov random-field models

1994 ◽  
Author(s):  
Jagath K. Samarabandu ◽  
Raj S. Acharya ◽  
E. Hausmann ◽  
K. A. Allen
Keyword(s):  
Random Field ◽  
Texture Analysis ◽  
Markov Random Field ◽  
Gaussian Markov Random Field ◽  
Markov Random

scholarly journals Bayesian inference of networks across multiple sample groups and data types

Biostatistics ◽  
2018 ◽  
Vol 21 (3) ◽  
pp. 561-576 ◽  
Author(s):  
Elin Shaddox ◽  
Christine B Peterson ◽  
Francesco C Stingo ◽  
Nicola A Hanania ◽  
Charmion Cruickshank-Quinn ◽  
...  
Keyword(s):  
Chronic Obstructive Pulmonary Disease ◽  
Bayesian Inference ◽  
Random Field ◽  
Markov Random Field ◽  
Chronic Obstructive ◽  
Data Types ◽  
Obstructive Pulmonary Disease ◽  
Markov Random ◽  
Network Similarity ◽  
Multiple Sample

Summary In this article, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to differing disease stage or subtype, is profiled across multiple platforms, such as metabolomics, proteomics, or transcriptomics data. Our proposed Bayesian hierarchical model first links the network structures within each platform using a Markov random field prior to relate edge selection across sample groups, and then links the network similarity parameters across platforms. This enables joint estimation in a flexible manner, as we make no assumptions on the directionality of influence across the data types or the extent of network similarity across the sample groups and platforms. In addition, our model formulation allows the number of variables and number of subjects to differ across the data types, and only requires that we have data for the same set of groups. We illustrate the proposed approach through both simulation studies and an application to gene expression levels and metabolite abundances on subjects with varying severity levels of chronic obstructive pulmonary disease. Bayesian inference; Chronic obstructive pulmonary disease (COPD); Data integration; Gaussian graphical model; Markov random field prior; Spike and slab prior.

scholarly journals Penalized complexity priors for degrees of freedom in Bayesian P-splines

2016 ◽  
Vol 16 (6) ◽  
pp. 429-453 ◽  
Author(s):  
Massimo Ventrucci ◽  
Håvard Rue
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Smooth Function ◽  
Degrees Of Freedom ◽  
Penalized Splines ◽  
Prior Elicitation ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Gaussian Data

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

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