Bayes Linear Statistics

Goldstein, Michael; Wooff, David

doi:10.1002/9780470065662

Cited by 162 publications

(115 citation statements)

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“…Applying Gaussian error propagation to the MRE is actually not feasible if all dependencies and uncertainties have to be considered. The proposed method is based on Bayesian Probability Theory (BPT) [7] which provides a framework for scientific reasoning from uncertain data. BPT allows one to combine any sort of data or information [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Application of the Bayesian analysis to the modified Rutherford equation for NTM stabilization

Urso

Fischer

Isayama

et al. 2010

Plasma Phys. Control. Fusion

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Abstract. The determination of the free parameters present in the modified Rutherford equation (MRE), which is routinely used for studying the physics of Neoclassical Tearing Mode (NTM) stabilisation, is addressed by making use of the Bayesian probability theory. The evaluation of the free coefficients is particularly sensitive to the assumptions used in the modelled equation, to the correlation of various physical parameters, and to the uncertainties of the experimental measurements. A probabilistic method was applied for the consistent evaluation of the coefficients and their uncertainties using a large database of discharges and by considering the correlations and the uncertainties of the multiple physical quantities present in the MRE. The estimated values and uncertainties of the coefficients are related to the precise determination of the minimum amount of ECCD power necessary to stabilise NTMs in ITER.

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Section: Introductionmentioning

confidence: 99%

Application of the Bayesian analysis to the modified Rutherford equation for NTM stabilization

Urso

Fischer

Isayama

et al. 2010

Plasma Phys. Control. Fusion

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“…History matching can be viewed as a useful precursor to a fully Bayesian analysis that is often in itself sufficient for model checking and model development. Here we use it within a Bayes Linear framework, a simpler, more tractable version of Bayesian statistics, where only expectations, variances and covariances need to be specified (Goldstein 1999;Goldstein & Wooff 2007). However, if one is committed to a full Bayesian MCMC approach, performing an a priori history match can dramatically improve the subsequent efficiency of the MCMC by first removing the vast regions of input parameter space that would have extremely low posterior probability.…”

Section: Bayesian Emulation Methodologymentioning

confidence: 99%

“…Here instead we prefer to use the more tractable Bayes Linear approach, a version of Bayesian statistics that requires only expectations, variances and covariances for the prior specification, and which uses only efficient matrix calculations, and no MCMC (Goldstein & Wooff 2007). Therefore if we are prepared to specify E(β i j ), Var(β i j ), σ 2 u i , σ 2 v i and θ i , we can obtain the corresponding Bayes Linear priors for f i (x) namely E( f i (x)), Var( f i (x)) and Cov( f i (x), f i (x )) using equations (15) and (16).…”

Section: Emulator Constructionmentioning

confidence: 99%

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Rodrigues

Vernon

Bower

2016

Mon. Not. R. Astron. Soc.

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We explore the parameter space of the semi-analytic galaxy formation model GALFORM, studying the constraints imposed by measurements of the galaxy stellar mass function (GSMF) and its evolution. We use the Bayesian Emulator method to quickly eliminate vast implausible volumes of the parameter space and zoom in on the most interesting regions, allowing us to identify a set of models that match the observational data within model uncertainties. We find that the GSMF strongly constrains parameters related to quiescent star formation in discs, stellar and AGN feedback and threshold for disc instabilities, but weakly restricts other parameters. Constraining the model using local data alone does not usually select models that match the evolution of the GSMF well. Nevertheless, we show that a small subset of models provides acceptable match to GSMF data out to redshift 1.5. We explore the physical significance of the parameters of these models, in particular exploring whether the model provides a better description if the mass loading of the galactic winds generated by starbursts (β 0,burst ) and quiescent disks (β 0,disc ) is different. Performing a principal component analysis of the plausible volume of the parameter space, we write a set of relations between parameters obeyed by plausible models with respect to GSMF evolution. We find that while β 0,disc is strongly constrained by GSMF evolution data, constraints on β 0,burst are weak. Although it is possible to find plausible models for which β 0,burst = β 0,disc , most plausible models have β 0,burst > β 0,disc , implying -for these -larger SN feedback efficiency at higher redshifts.

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“…Research in forensic mathematics and statistical analysis have been explored by several researchers [11], [12]. In these kinds of cases, it is natural to construct the Bayes' linear graphical model by writing each random quantity in the model as a node on the diagram.…”

Section: Methodsmentioning

confidence: 99%

“…Data visualization can assist with at least three significant needs, where firstly it can assist with analytical reasoning, secondly in communication, and lastly it will assist in learning of how to convert the data to suit certain cases [11].…”

Section: Problem Statementmentioning

confidence: 99%

Improved Algorithms for Data Visualization in Forensic DNA Analysis

Noor¹,

Harun²,

Ghazali³

2014

LNSE

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Abstract-DNA profiles from forensic evidence have contributed significantly in criminal investigations. DNA profiles can be developed using several techniques including Short Tandem Repeat (STR) analysis. The algorithm for data visualization in forensic DNA analysis will be employed into a series of formulas by using a mathematical model that will be represented by a graphical model. By applying visualization, it can increase the value of using linear planning charts which, when combined with images pertaining to the distribution of resource usage in time and space, permits additional insights on the quality of a schedule to be glean.

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Bayes Linear Statistics

Cited by 162 publications

References 0 publications

Application of the Bayesian analysis to the modified Rutherford equation for NTM stabilization

Application of the Bayesian analysis to the modified Rutherford equation for NTM stabilization

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Improved Algorithms for Data Visualization in Forensic DNA Analysis

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