Bayesian evidence and model selection

Knuth, Kevin H.; Habeck, Michael; Malakar, N. K.; Mubeen, Asim M.; Placek, Ben

doi:10.1016/j.dsp.2015.06.012

Cited by 79 publications

(70 citation statements)

References 106 publications

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“…We defined P(U|intr) as the probability that the cluster is unbound and P(B|intr) as the probability that the cluster is bound given the observed intrinsic radial velocity distribution. The Bayesian evidence approach (e.g., Knuth et al 2015) considers the Bayes factor (the odds ratio) given by…”

Section: Stellar Dynamics Of L1688mentioning

confidence: 99%

TheGaia-ESO Survey: Dynamical analysis of the L1688 region in Ophiuchus

Rigliaco

Wilking

Meyer

et al. 2016

A&A

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The Gaia ESO Public Spectroscopic Survey (GES) is providing the astronomical community with high-precision measurements of many stellar parameters including radial velocities (RVs) of stars belonging to several young clusters and star-forming regions. One of the main goals of the young cluster observations is to study their dynamical evolution and provide insight into their future, revealing whether they will eventually disperse to populate the field rather than evolve into bound open clusters. In this paper we report the analysis of the dynamical state of L1688 in the ρ Ophiuchi molecular cloud using the dataset provided by the GES consortium. We performed the membership selection of the more than 300 objects observed. Using the presence of the lithium absorption and the location in the Hertzspung-Russell diagram, we identify 45 already known members and two new association members. We provide accurate RVs for all 47 confirmed members. A dynamical analysis, after accounting for unresolved binaries and errors, shows that the stellar surface population of L1688 has a velocity dispersion σ ∼ 1.14 ± 0.35 km s −1 that is consistent with being in virial equilibrium and is bound with a ∼80% probability. We also find a velocity gradient in the stellar surface population of ∼1.0 km s −1 pc −1 in the northwest-southeast direction, which is consistent with that found for the pre-stellar dense cores, and we discuss the possibility of sequential and triggered star formation in L1688.

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Section: Stellar Dynamics Of L1688mentioning

confidence: 99%

TheGaia-ESO Survey: Dynamical analysis of the L1688 region in Ophiuchus

Rigliaco

Wilking

Meyer

et al. 2016

A&A

View full text Add to dashboard Cite

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“…and e ∼ MN 0, σ 2 I , (8). Closer inspection of (44) shows us that the parameter space of β is constrained by the difference vector z.…”

Section: A Proper Ignorance Priormentioning

confidence: 99%

“…As to the second term in the right-hand of (66), the error vector e has known multivariate probability distribution (8). If we rewrite the elements in e as a function of its norm e and the angles where 0 < e < ∞, −π/2 < α i < π/2, for i = 1, 2, .…”

Section: A Proper Ignorance Priormentioning

confidence: 99%

“…where X 1 is an N × m 1 predictor matrix and X 2 an N × m 2 , with m 2 > m 1 , and where both e 1 and e 1 are multivariate normally distributed MN 0, σ 2 I , where I is the N × N identity matrix and σ is some known standard deviation, (8). Let the uniform prior of a regression coefficient be given as…”

Section: The Problem With Improper Priorsmentioning

confidence: 99%

“…So, if we assign equal prior probabilities to our likelihood models M i , then we may rank these models by way of their respective evidence values, where the model with the highest evidence value is the model which has the highest posterior probability of all the models that were taken into consideration [7,8].…”

Section: The Evidence and Bayesian Model Selectionmentioning

confidence: 99%

See 2 more Smart Citations

Deriving Proper Uniform Priors for Regression Coefficients, Parts I, II, and III

Erp

Linger

Gelder

2017

Entropy

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Abstract:It is a relatively well-known fact that in problems of Bayesian model selection, improper priors should, in general, be avoided. In this paper we will derive and discuss a collection of four proper uniform priors which lie on an ascending scale of informativeness. It will turn out that these priors lead us to evidences that are closely associated with the implied evidence of the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). All the discussed evidences are then used in two small Monte Carlo studies, wherein for different sample sizes and noise levels the evidences are used to select between competing C-spline regression models. Also, there is given, for illustrative purposes, an outline on how to construct simple trivariate C-spline regression models. In regards to the length of this paper, only one half of this paper consists of theory and derivations, the other half consists of graphs and outputs of the two Monte Carlo studies.

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A new process sensitivity index to identify important system processes under process model and parametric uncertainty

Dai

Walker

et al. 2017

Water Resources Research

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A hydrological model consists of multiple process level submodels, and each submodel represents a process key to the operation of the simulated system. Global sensitivity analysis methods have been widely used to identify important processes for system model development and improvement. The existing methods of global sensitivity analysis only consider parametric uncertainty, and are not capable of handling model uncertainty caused by multiple process models that arise from competing hypotheses about one or more processes. To address this problem, this study develops a new method to probe model output sensitivity to competing process models by integrating model averaging methods with variance‐based global sensitivity analysis. A process sensitivity index is derived as a single summary measure of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and their parameters. For demonstration, the new index is used to assign importance to the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that convert precipitation to recharge, and the geology process is simulated by two models of hydraulic conductivity. Each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.

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Bayesian evidence and model selection

Cited by 79 publications

References 106 publications

TheGaia-ESO Survey: Dynamical analysis of the L1688 region in Ophiuchus

TheGaia-ESO Survey: Dynamical analysis of the L1688 region in Ophiuchus

Deriving Proper Uniform Priors for Regression Coefficients, Parts I, II, and III

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

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