Bayesian Model Selection Methods Research Articles

Advancing Bayesian Inference: Fitting Type I Half-logistic Nadarajah-Haghighi Distribution and its Comparison with Related Distributions for Censored Survival Data

In recent years, the field of Bayesian modeling of generalized distributions has garnered substantial attention. This surge in interest can be attributed to the remarkable strides made in computational capabilities and the enhanced accessibility of sophisticated software tools. This study aims to apply Bayesian inference methods to the Type I Half-logistic Nadarajah- Haghighi model and compares it with the Exponential model and the Type I Half-logistic Exponential model. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language STAN. To incorporate censored mechanisms within the STAN framework, customized codes are developed. The models are then compared using fully Bayesian model selection methods.. KEYWORDS :Censored data, Nadarajah-Haghighi distribution, Type I half-logistic family, LOOIC, WAIC, STAN.

Probing the delay time of supermassive black hole binary mergers with gravitational waves

ABSTRACT Merging supermassive black hole binaries are expected as a consequence of galaxy mergers, yet the detailed evolution path and underlying merging mechanisms of these binaries are still subject to large theoretical uncertainties. In this work, we propose to combine the (future) gravitational wave measurements of supermassive black hole binary merger events with the galaxy merger rate distributions from galaxy surveys/cosmological simulations, to infer the delay time of binary mergers, as a function of binary mass. The delay time encodes key information about binary evolution, which can be used to test the predictions of various evolution models. With a Mock data set of supermassive black hole binary merger events, we discuss how to infer the distribution of delay time with hierarchical Bayesian inference and test evolution models with the Bayesian model selection method. The astrophysical model uncertainties are also considered in the hierarchical Bayesian inference and Bayesian model selection.

Bayesian evidence and model selection approach for time-dependent dark energy

ABSTRACT We use parametrized post-Friedmann (PPF) description for dark energy and apply ellipsoidal nested sampling to perform the Bayesian model selection method on different time-dependent dark energy models using a combination of Planck and data based on distance measurements, namely baryon acoustic oscillations and supernovae luminosity distance. Models with two and three free parameters described in terms of linear scale factor a, or scaled in units of e-folding ln a are considered. Our results show that parametrizing dark energy in terms of ln a provides better constraints on the free parameters than polynomial expressions. In general, two free-parameter models are adequate to describe the dynamics of the dark energy compared to their three free-parameter generalizations. According to the Bayesian evidence, determining the strength of support for cosmological constant Λ over polynomial dark energy models remains inconclusive. Furthermore, considering the R statistic as the tension metric shows that one of the polynomial models gives rise to a tension between Planck and distance measurements data sets. The preference for the logarithmic equation of state over Λ is inconclusive, and the strength of support for $\rm \Lambda$ CDM over the oscillating model is moderate.

Plate‐Locking, Uncertainty Estimation and Spatial Correlations Revealed With a Bayesian Model Selection Method: Application to the Central Chile Subduction Zone

AbstractInversions of geodetic data are regularly used to estimate interseismic locking in subduction zones. However, the ill‐posed nature of these problems motivates us to include prior information, physically consistent with processes of the subduction seismic cycle. To deal with model instabilities, we present an inversion method to estimate both plate‐locking and model uncertainties by inverting Global Navigation Satellite System derived velocities based on a Bayesian model selection scheme. Our method allows us to impose positivity constraints via a multivariate folded‐normal distribution, with a specified covariance matrix. Model spatial correlations are explored and ranked to find models that best explain the observed data and for a better understanding of locking models. This approach searches for hyperparameters of the prior joint multivariate probability density function (PDF) of model parameters that minimize the Akaike Bayesian Information Criterion (ABIC). To validate our approach, we invert synthetic displacements from analytic models, yielding satisfactory results. We then apply the method to estimate the plate‐locking in Central Chile (28°–39°S) and its relation to the coseismic slip distribution of earthquakes with magnitudes Mw > 8.0, on the subduction zone since 2010. We also search among different prior PDFs for a single ductile‐fragile limit depth. Our results confirms a spatial correlation between locked asperities and the 2010 Mw 8.8 Maule and 2015 Mw 8.3 Illapel earthquake rupture zones. The robustness of our locking model shows potential to improve future seismic and tsunami hazard estimations.

Bayesian analysis of spatial dynamic panel data model with convex combinations of different spatial weight matrices: A reparameterized approach

This paper brings forward a novel Bayesian estimation and model selection method for spatial dynamic panel data model with convex combinations of different spatial weight matrices. We reparameterize the model as a high order spatial panel model, and recover the importance weights by a computationally tractable Markov Chain Monte Carlo (MCMC) sampler. We also propose a nested model selection procedure to test which spillover channel exerts significant influence and whether one channel dominates the others. Simulation suggests that the reparameterized approach works well both for parameter estimation and model selection.

Active Knowledge Extraction from Cyclic Voltammetry

Cyclic Voltammetry (CV) is an electro-chemical characterization technique used in an initial material screening for desired properties and to extract information about electro-chemical reactions. In some applications, to extract kinetic information of the associated reactions (e.g., rate constants and turn over frequencies), CV curve should have a specific shape (for example an S-shape). However, often the characterization settings to obtain such curve are not known a priori. In this paper, an active search framework is defined to accelerate identification of characterization settings that enable knowledge extraction from CV experiments. Towards this goal, a representation of CV responses is used in combination with Bayesian Model Selection (BMS) method to efficiently label the response to be either S-shape or not S-shape. Using an active search with BMS oracle, we report a linear target identification in a six-dimensional search space (comprised of thermodynamic, mass transfer, and solution variables as dimensions). Our framework has the potential to be a powerful virtual screening technique for molecular catalysts, bi-functional fuel cell catalysts, and other energy conversion and storage systems.

Rapid identification of strongly lensed gravitational-wave events with machine learning

A small fraction of the gravitational-wave (GW) signals that will be detected by second and third generation detectors are expected to be strongly lensed by galaxies and clusters, producing multiple observable copies. While optimal Bayesian model selection methods are developed to identify lensed signals, processing tens of thousands (billions) of possible pairs of events detected with second (third) generation detectors is both computationally intensive and time consuming. To mitigate this problem, we propose to use machine learning to rapidly rule out a vast majority of candidate lensed pairs. As a proof of principle, we simulate non-spinning binary black hole events added to Gaussian noise, and train the machine on their time-frequency maps (Q-transforms) and localisation skymaps (using Bayestar), both of which can be generated in seconds. We show that the trained machine is able to accurately identify lensed pairs with efficiencies comparable to existing Bayesian methods.

Do polygenic scores of cerebral small vessel disease MRI markers predict white matter lesions?

AbstractBackgroundEvidence of cerebral small vessel disease (CSVD) is commonly found in those with a diagnosis of Alzheimer’s disease (AD) and is associated with T2‐weighted MRI‐visible white matter hyperintensities (WMHs). Here we investigate whether macrostructural and microstructural polygenic risk scores (PRS) predict WMH volumes.MethodWe used Genome Wide Association Studies (GWAS), based on UK Biobank (UKB) MRI markers of WMH, Fractional Anisotropy (FA) and Mean Diffusivity (MD) from (Persyn et al., 2020, https://doi.org/10.1038/s41467‐020‐15932‐3) to compute PRS for n=730 participants (following strict quality control) from the AD Neuroimaging Initiative (ADNI) using PRSice. We calculated WMH volumes for ADNI subjects using a Bayesian Model Selection method BaMoS (Sudre et al., https://doi.org/10.1109/TMI.2015.2419072). Linear regression models (with confounds for age, gender, education, APOE4 status, total intracranial volume and five principal components of population structure) were used to test for association (including multiple testing correction) between WMH, FA and MD PRS (based on p‐value thresholds at p=1.0e‐05 and p=0.5) and WMH volumes in each of three diagnostic groups: Healthy Controls (HC; n=218), Mild Cognitive Impairment (MCI; n=390) and AD (n=122).ResultWMH and FA PRS did not predict WMH volume in the ADNIGO and ADNI2 cohort (Table 1) despite high correlation between BaMoS‐derived and BIANCA‐derived WMH volumes (r=0.84 on 19,070 UKB subjects). However, MD PRS at the p=0.5 threshold in the MCI group was positively correlated with WMH volume (Table 1) with t=3.4 (FDR‐corrected P=0.0008; Figure 1).ConclusionDespite a high heritability of WMH (h2=0.76; Sachdev et al.. 2016, https://doi.org/10.1161/STROKEAHA.116.012532), unexpectedly, WMH PRS did not predict WMH volume in ADNI in any of the diagnostic groups. The correlation between total WMH estimated with both tools was very high and thus is unlikely the source of this lack of association,however, this may be due to different inclusion criteria for ADNI. The statistically significant relationship in the ADNI MCI group between MD PRS and WMH volume may reflect the early white matter tract damage that is visible before AD manifests and these structural insults become overwhelming. This is reflected in many of the other PRS‐WMH corelations in the MCI group which are borderline statistical significance.

What do data‐driven Alzheimer’s disease subtypes tell us about white matter pathology and clinical progression?

AbstractBackgroundThe progression of Alzheimer’s Disease (AD) is heterogeneous with different brain regions manifesting pathology at different times during the disease. Differential sequences of grey matter (GM) volume changes, defining imaging‐based subtypes, may represent alternative disease origins, pathways or severity. Additionally, volumes of white matter hyperintensities (WMH), which increase with age, are associated with AD. In this study we used a machine learning method to estimate three types of AD trajectories and assessed their WMH load and longitudinal prognosis.MethodSubtype and Stage Inference (SuStaIn; Young et al., https://doi.org/10.1038/s41467‐018‐05892‐0) was used to estimate data‐driven disease progresion subtypes from cross‐sectional GM volumes in 795 subjects (from ADNI1/GO/2 with baseline 3T MRI scans processed with FreeSurfer 5.1 passing data quality control). Following additional quality control WMH volumes for 575 of these ADNI subjects were calculated using a Bayesian Model Selection method BaMoS (Sudre et al., https://doi.org/10.1109/TMI.2015.2419072) from three diagnostic groups: Healthy Controls (HC; n=181), Mild Cognitive Impairment (MCI; n=310) and Alzheimer’s Disease (AD; n=85). The association between SuStaIn subtypes and WMH and diagnostic conversion rates were evaluated using multiple pairwise comparisons and survival analysis, respectively.ResultSuStaIn identified three subtypes with distinct atrophy patterns: typical (atrophy begins in hippocampus and amygdala), cortical (atrophy starts in the temporal lobe, followed by cingulate and insula) and subcortical (atrophy begins in pallidum, putamen and caudate) (Figure 1). Participants with the subcortical subtype exhibited a significantly slower rate of clinical progression to MCI or AD (Figure 2, Table 1). Furthemore, subjects with the subcortical subtype showed lower median WMH (Figure 3a), a pattern observed across the diagnostic groups (Figure 3b).ConclusionParticipants classified as the subcortical subtype were least likely to have white matter structural changes associated with neurodegeneration and displayed the slowest rate of clinical conversion. While late hippocampal involvement in the subcortical subtype may explain less severe clinical symptoms and slower disease progression, the reason for lower WMH associated with this subtype trajectory is unknown. Further studies are needed to investigate the link between WMH and AD atrophy subtypes.

Bayesian model selection in additive partial linear models via locally adaptive splines

We provide a flexible framework for selecting among a class of additive partial linear models that allows both linear and nonlinear additive components. In practice, it is challenging to determine which additive components should be excluded from the model while simultaneously determining whether nonzero additive components should be represented as linear or non-linear components in the final model. In this paper, we propose a Bayesian model selection method that is facilitated by a carefully specified class of models, including the choice of a prior distribution and the nonparametric model used for the nonlinear additive components. We employ a series of latent variables that determine the effect of each variable among the three possibilities (no effect, linear effect, and nonlinear effect) and that simultaneously determine the knots of each spline for a suitable penalization of smooth functions. The use of a pseudo-prior distribution along with a collapsing scheme enables us to deploy well-behaved Markov chain Monte Carlo samplers, both for model selection and for fitting the preferred model. Our method and algorithm are deployed on a suite of numerical studies and are applied to a nutritional epidemiology study. The numerical results show that the proposed methodology outperforms previously available methods in terms of effective sample sizes of the Markov chain samplers and the overall misclassification rates.

A Comparison of Common IRT Model-selection Methods with Mixed-Format Tests

ABSTRACT To date, only frequentist model-selection methods have been studied with mixed-format data in the context of IRT model-selection, and it is unknown how popular Bayesian model-selection methods such as DIC, WAIC, and LOO perform. In this study, we present the results of a comprehensive simulation study that compared the performances of eight model-selection methods with mixed-format data to select the correct combination of IRT models. Findings of the simulation study indicate that DIC, WAIC, and LOO had excellent statistical power to choose the correct IRT model combination. They performed comparably with LRT and slightly preferably than AIC, and considerably better than BIC, AICc, and SABIC. In addition, the performances of the three Bayesian methods were more stable than those of AIC and LRT regardless of the sample size and ability distribution. The eight model-selection methods were applied to a real dataset for demonstration purpose.

The Limits of Marginality

The “marginality principle” for linear regression models states that when a higher order term is included, its constituent terms must also be included. The target article relies on this principle for the fixed-effects part of linear mixed models of ANOVA designs and considers the implication that if extended to combined fixed-and-random-effects models, model selection tests specific to some fixed-effects ANOVA terms are not possible. We review the basis for this principle for fixed-effects models and delineate its limits. We then consider its extension to combined fixed-and-random-effects models. We conclude that we have been unable to find in the literature, including the target article, and have ourselves been unable to construct any satisfactory argument against the use of incomplete ANOVA models. The only basis we could find requires one to assume that it is not possible to test point-null hypotheses, something we disagree with, and which we believe is incompatible with the Bayesian model-selection methods that are the basis of the target article.

Scrutinizing various phenomenological interactions in the context of holographic Ricci dark energy models

In this paper, we examine two types of interacting holographic dark energy model using Pantheon supernova data, BAO BOSS DR12, CMB Planck 2015, fgas (gas mass fraction) and SZ/Xray (Sunyaev–Zeldovich effect and X-ray emission) data from galaxy clusters (GC). In particular, we considered the Holographic Ricci dark energy and Extended holographic Ricci dark energy models. During this analysis, we considered seven types of phenomenological interaction terms (three linear and four non-linear) Q_1=3Hbleft( rho _{D}+rho _mright) , Q_2=3Hbrho _{D}, Q_3=3Hbrho _{m}, Q_4=3Hbleft( rho _{D}+frac{rho _{D}^2}{rho _{D}+rho _m}right) , Q_5=3Hbleft( rho _{m}+frac{rho _{m}^2}{rho _{D}+rho _m}right) , Q_6=3Hbleft( rho _{D}+rho _{m}+frac{rho _{D}^2}{rho _{D}+rho _m}right) , Q_7=3HbBig (rho _{D}+rho _{m}+frac{rho _{m}^2}{rho _{D}+rho _m}Big ) respectively. To find the best model we apply Bayesian Inference (BI) and use the Lambda CDM as the referring model for comparison. Using the Bayesian Evidence model selection method we note that the Q_3 and Q_5 interaction terms are favored by observational data among the other ones. The obtained results also demonstrated that the evidence from the Bayesian inference method against the considered types of holographic Ricci dark energy model is strong since the Lambda CDM is considered as the reference model and also the Lambda CDM is preferred over the models. We also observed that the values of the deceleration parameter and the transition redshift for all models are compatible with the latest observational data and Planck 2015. In addition, we studied the jerk parameter for all models. Using our modified CAMB code, we observed that the interacting models suppress the CMB spectrum at low multipoles and enhances the acoustic peaks.

Did Oldham Discover the Core After All? Handling Imprecise Historical Data with Hierarchical Bayesian Model Selection Methods

Abstract Historical seismic data are essential to fill in the gaps in geophysical knowledge caused by the low rate of significant seismic events. Handling historical data in the context of geophysical inverse problems requires special care, due to the large errors in the data collection process. Using Oldham’s data for the discovery of Earth’s core as a case study, we illustrate how a hierarchical Bayesian model selection methodology using leave-one-out cross validation can robustly and efficiently answer quantitative questions using even poor-quality geophysical data. We find that there is statistically significant evidence for the existence of the core using only the P-wave data that Oldham effectively discarded in his discussion.

P06 Genetics of juvenile idiopathic arthritis: the identification of a novel risk locus and clinical subgroup analysis

Poster presentation Tuesday 8 October Background Juvenile idiopathic arthritis (JIA) is a clinically heterogeneous group of childhood onset inflammatory joint diseases with strong evidence to support a genetic contribution to susceptibility. JIA is divided into seven clinical subgroups based on observed patterns of clinical symptoms using the International League of Associations for Rheumatology (ILAR) classification system. The genetic overlap between these groups is not completely understood and this lack of knowledge typically leads to the different ILAR groups being analysed as discrete entities and reducing the overall power of genetic association studies. The aim of this study was to conduct a large case-control association study on susceptibility to JIA to identify novel susceptibility loci and to investigate differences in these associations between the different ILAR groups. Methods JIA participants were genotyped on the Illumina Infinium CoreExome or OmniExpress arrays at the University of Manchester. UK population control genotype data was obtained from the Understanding Society Longitudinal Study. Quality control of data was performed conforming to conventional standards based on call rate, cryptic relatedness and ancestry outliers. Imputation was performed using the Haplotype Reference Consortium panel on the Michigan Imputation Server followed by exclusion of SNPs with low imputation accuracy (r2 < 0.5) and low minor allele frequency (< 1%). Association testing of all SNPs was performed with an additive model incorporating imputation uncertainty using SNPTEST. A subset of SNPs independently associated with all JIA (p-value < 5x10-6) were tested to evaluate if they were specific to a particular ILAR group or shared across multiple ILAR groups using Bayesian multinomial regression and model selection methods implemented in the Trinculo software package. Results Following quality control, the dataset consisted of > 7.4 million SNPs for 3,305 JIA cases and 9,196 controls. Association testing in a combined dataset of all ILAR groups identified seven SNPs associated at genome-wide significance (5x10-8); six of these have previously been reported for JIA while one is a novel association. The novel association (rs497523, p-value = 7.12x10-9, OR 0.85, 95% CI 0.8:0.9) maps to chromosome 16p11 and is located within intron one of the CCDC101 gene. In a subset of 44 independently associated SNPs we found no strong evidence to support association of any SNP to a specific ILAR group with the majority of the SNPs showing evidence for sharing across multiple groups. Conclusion In a large case control association study for susceptibility to JIA, we identified a novel association to a SNP in the intron of CCDC101. This gene is involved in transcriptional regulation through histone acetyltransferase. The results support a general model of sharing of loci across multiple ILAR groups. The combined analysis of data across subgroups, informed by model sharing, will maximise power to identify novel associations. Conflicts of Interest The authors declare no conflicts of interest.

Bayesian Model Selection in Fisheries Management and Ecology

AbstractResearchers often test ecological hypotheses relating to a myriad of questions ranging from assemblage structure, population dynamics, demography, abundance, growth rate, and more using mathematical models that explain trends in data. To aid in the evaluation process when faced with competing hypotheses, we employ statistical methods to evaluate the validity of these multiple hypotheses with the goal of deriving the most robust conclusions possible. In fisheries management and ecology, frequentist methodologies have largely dominated this approach. However, in recent years, researchers have increasingly used Bayesian inference methods to estimate model parameters. Our aim with this perspective is to provide the practicing fisheries ecologist with an accessible introduction to Bayesian model selection. Here we discuss Bayesian inference methods for model selection in the context of fisheries management and ecology with empirical examples to guide researchers in the use of these methods. In this perspective we discuss three methods for selecting among competing models. For comparing two models we discuss Bayes factor and for more complex models we discuss Watanabe–Akaike information criterion and leave-one-out cross-validation. We also describe what kinds of information to report when conducting Bayesian inference. We conclude this review with a discussion of final thoughts about these model selection techniques.

Establishment of structure-property linkages using a Bayesian model selection method: Application to a dual-phase metallic composite system

We investigate the viability of establishing low-cost surrogate structure-property (S–P) linkages by introducing a Bayesian model selection method to extend the Materials Knowledge Systems (MKS) homogenization framework, which employs the n-point spatial correlation function, principal component analysis, and regression techniques. In particular, we place emphasis not only on choosing the important structural features but also on interpreting their implications for the property under consideration. First, the yield strengths of synthetic microstructures with various morphological characteristics are estimated by physics-based crystal plasticity simulation. Then, the dimension-reduced microstructural features are revealed by a combination of 2-point spatial correlations and principal component analysis. The Bayesian model selection method is further applied to establish a microstructure-to-yield-strength surrogate model. Finally, the model is validated with an independent dataset and its constituent features are interpreted with a morphology reconstruction based on a Monte Carlo algorithm. The method is found to be capable of interpreting the key microstructural features as well as modeling the mechanical response of a dual-phase metallic composite in consideration of the diverse microstructural factors.

Bayesian Model Selection Methods for Multilevel IRT Models: A Comparison of Five DIC‐Based Indices

AbstractModel selection is important in any statistical analysis, and the primary goal is to find the preferred (or most parsimonious) model, based on certain criteria, from a set of candidate models given data. Several recent publications have employed the deviance information criterion (DIC) to do model selection among different forms of multilevel item response theory models (MLIRT). The majority of the practitioners use WinBUGS for implementing MCMC algorithms for MLIRT models, and the default version of DIC provided by WinBUGS focused on the measurement‐level parameters only. The results herein show that this version of DIC is inappropriate. This study introduces five variants of DIC as a model selection index for MLIRT models with dichotomous outcomes. Considering a multilevel IRT model with three levels, five forms of DIC are formed: first‐level conditional DIC computed from the measurement model only, which is the index given by many software packages such as WinBUGS; second‐level marginalized DIC and second‐level joint DIC computed from the second‐level model; and top‐level marginalized DIC and top‐level joint DIC computed from the entire model. We evaluate the performance of the five model selection indices via simulation studies. The manipulated factors include the number of groups, the number of second‐level covariates, the number of top‐level covariates, and the types of measurement models (one‐parameter vs. two‐parameter). Considering the computational viability and interpretability, the second‐level joint DIC is recommended for MLIRT models under our simulated conditions.

Estimating probability density functions using a combined maximum entropy moments and Bayesian method. Theory and numerical examples

Estimating the probability density function (pdf) from a limited sample of data is a challenging data analysis problem. Furthermore, determining which pdf best describes the available data involves an extra layer of complexity to the analysis, which if ignored, can have considerable consequences.We propose a combined maximum entropy (MaxEnt) moments and Bayesian model selection method to address this problem. The MaxEnt moments component is used to formulate a set of possible pdf models, each constrained by a different set of moments and parameterised by a set of Lagrangian multipliers. The Bayesian model selection component makes an inference about the most probable model, from the set of MaxEnt moment models. The structure of the prior pdf for the Lagrangian multipliers is determined from an expansion of the free energy functional for each MaxEnt model, and corresponding hyperparameters are calculated empirically.Numerical experiments were used to test the proposed method on samples taken from Gaussian and (more complex) non-Gaussian distributions, over a range of sample sizes. The results clearly demonstrate that the method can discriminate between simple and complex MaxEnt models for sample sizes approximately greater than 60. Our results demonstrate that MaxEnt and Bayesian methods are complementary. More critically, Bayesian inference is necessary when a set of competing MaxEnt models can be derived for a single dataset from a range of assumptions.

Establishment of Structure-Property Linkages Using a Bayesian Model Selection Method: Application to A Dual-Phase Metallic Composite System

Abstract We investigate the viability of establishing low-cost surrogate structure-property (S–P) linkages by introducing a Bayesian model selection method to extend the Materials Knowledge Systems (MKS) homogenization framework, which employs the n-point spatial correlation function, principal component analysis, and regression techniques. In particular, we place emphasis not only on choosing the important structural features but also on interpreting their implications for the property under consideration. First, the yield strengths of synthetic microstructures with various morphological characteristics are estimated by physics-based crystal plasticity simulation. Then, the dimension-reduced microstructural features are revealed by a combination of 2-point spatial correlations and principal component analysis. The Bayesian model selection method is further applied to establish a microstructure-to-yield-strength surrogate model. Finally, the model is validated with an independent dataset and its constituent features are interpreted with a morphology reconstruction based on a Monte Carlo algorithm. The method is found to be capable of interpreting the key microstructural features as well as modeling the mechanical response of a dual-phase metallic composite in consideration of the diverse microstructural factors.