Bayesian Model Comparison Methods Research Articles

Comparing stochastic volatility specifications for large Bayesian VARs

Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochastic volatility specification for their particular application. We develop Bayesian model comparison methods–based on marginal likelihood estimators that combine conditional Monte Carlo and adaptive importance sampling–to choose among a variety of stochastic volatility specifications. The proposed methods can also be used to select an appropriate shrinkage prior on the VAR coefficients, which is a critical component for avoiding over-fitting in high-dimensional settings. Using US quarterly data of different dimensions, we find that both the Cholesky stochastic volatility and factor stochastic volatility outperform the common stochastic volatility specification. Their superior performance, however, can mostly be attributed to the more flexible priors that accommodate cross-variable shrinkage.

Grouping affective psychoses in early intervention: Justification for specific treatment guidelines

The concept of affective psychosis regroups psychotic disorders with mood syndrome. Previous studies provided evidence to support a dichotomy between affective and non-affective psychoses although questions remain regarding the utility and validity of such a category to develop clinical guidelines.The aim of this study is to explore similarities and differences within affective psychoses to question whether strategies would apply to all the diagnoses falling under this umbrella term.Using Bayesian model comparison methods, we explored the homogeneity of the characteristics of first-episode affective patients (N = 77) treated in a specialized 3-year early intervention in psychosis programme.Our analysis revealed affective psychoses display many similarities regarding socio-demographic variables, the course of positive and manic symptoms over three years, and outcome at discharge. Our results did not support the heterogeneous model. However, despite no significant differences in the course of symptoms with the major depressive disorder group, the schizoaffective disorder group displayed a more severe clinical picture at the beginning of the programme and a poorer functional outcome than the two other groups.Absence of clear boundaries and the several similarities within affective psychoses suggest they can usefully be grouped to define treatment strategies that are easily legible by clinicians.

Dynamic Causal Modeling of the Prefrontal/Amygdala Network During Processing of Emotional Faces.

Introduction: The importance of the amygdala/medial orbitofrontal cortex (OFC) network during processing of emotional stimuli, emotional faces in particular, is well established. This premise is supported by converging evidence from animal models, human neuroanatomical results, and neuroimaging studies. However, there is missing evidence from human brain connectivity studies that the OFC and no other prefrontal brain areas such as the dorsolateral prefrontal cortex (DLPFC) or ventrolateral prefrontal cortex (VLPFC) are responsible for amygdala regulation in the functional context of emotional face stimuli. Methods: Dynamic causal modeling of ultrahigh-field functional magnetic resonance imaging data acquired at 7 Tesla in 38 healthy subjects and a well-established paradigm for emotional face processing were used to assess the central role of the OFC to provide empirical validation for the assumed network architecture. Results: Using Bayesian model selection, it is demonstrated that indeed the OFC, and not the VLPFC and the DLPFC, downregulates amygdala activation during the emotion discrimination task. In addition, Bayesian model averaging group results were rigorously tested using bootstrapping, further corroborating these findings and providing an estimator for robustness and optimal sample sizes. Discussion: While it is true that VLPFC and DLPFC are relevant for the processing of emotional faces and are connected to the OFC, the OFC appears to be a central hub for the prefrontal/amygdala interaction. Impact statement Using dynamic causal modeling (DCM), abnormal effective connectivity in the orbitofrontal cortex (OFC)/amygdala network has been repeatedly observed in the pathophysiology of psychiatric disorders. However, it has to be considered that these findings are all based on the a priori assumption of the OFC being the central area for prefrontal control regulating amygdala activation. This is particularly important, as DCM results conditionally depend on the underlying model space used for model selection. Using Bayesian model comparison methods, it is shown that the OFC (and not the dorsolateral prefrontal cortex or ventrolateral prefrontal cortex) engages in amygdala downregulation in the context emotional face processing.

A complete search for redshift z ≳ 6.5 quasars in the VIKING survey

ABSTRACT We present the results of a new, deeper, and complete search for high-redshift 6.5 < z < 9.3 quasars over 977 deg2 of the VISTA Kilo-Degree Infrared Galaxy (VIKING) survey. This exploits a new list-driven data set providing photometry in all bands Z, Y, J, H, Ks, for all sources detected by VIKING in J. We use the Bayesian model comparison (BMC) selection method of Mortlock et al., producing a ranked list of just 21 candidates. The sources ranked 1, 2, 3, and 5 are the four known z > 6.5 quasars in this field. Additional observations of the other 17 candidates, primarily DESI Legacy Survey photometry and ESO FORS2 spectroscopy, confirm that none is a quasar. This is the first complete sample from the VIKING survey, and we provide the computed selection function. We include a detailed comparison of the BMC method against two other selection methods: colour cuts and minimum-χ2 SED fitting. We find that: (i) BMC produces eight times fewer false positives than colour cuts, while also reaching 0.3 mag deeper, (ii) the minimum-χ2 SED-fitting method is extremely efficient but reaches 0.7 mag less deep than the BMC method, and selects only one of the four known quasars. We show that BMC candidates, rejected because their photometric SEDs have high χ2 values, include bright examples of galaxies with very strong [O iii] λλ4959,5007 emission in the Y band, identified in fainter surveys by Matsuoka et al. This is a potential contaminant population in Euclid searches for faint z > 7 quasars, not previously accounted for, and that requires better characterization.

Bayesian discrimination of the panchromatic spectral energy distribution modelings of galaxies

AbstractFitting the multi-wavelength spectral energy distributions (SEDs) of galaxies is a widely used technique to extract information about the physical properties of galaxies. However, a major difficulty lies in the numerous uncertainties regarding almost all ingredients of the SED modeling of galaxies. The Bayesian methods provide a consistent conceptual basis for dealing with the problem of inference with many uncertainties. While the Bayesian parameter estimation method have become quite popular in the field of SED fitting of galaxies, the Bayesian model comparison method, which is based on the same Bayes’ rule, is still not widely used in this field. With the application of Bayesian model comparison method in a series of papers, we show that the results obtained with Bayesian model comparison are understandable in the context of stellar/galaxy physics. These results indicate that Bayesian model comparison is a reliable and very powerful method for the SED fitting of galaxies.

From action to abstraction: The sensorimotor grounding of metaphor in Parkinson's disease

Embodied cognition theories propose that the semantic representations engaged in during language comprehension are partly supported by perceptual and motor systems, via simulation. Activation in modality-specific regions of cortex is associated with the comprehension of literal language that describes the analogous modalities, but studies addressing the grounding of non-literal or figurative language, such as metaphors, have yielded mixed results. Differences in the psycholinguistic characteristics of sentence stimuli across studies have likely contributed to this lack of consensus. Furthermore, previous studies have been largely correlational, whilst patient studies are a critical way of determining if intact sensorimotor function is necessary to understand language drawing on sensorimotor information. We designed a battery of metaphorical and literal sentence stimuli using action and sound words, with an unprecedented level of control over critical psycholinguistic variables, to test hypotheses about the grounding of metaphorical language. In this Registered Report, we assessed the comprehension of these sentences in 41 patients with Parkinson's disease, who were predicted to be disproportionately affected by the action sentences relative to the sound sentences, and compared their performance to that of 39 healthy age-matched controls who were predicted to show no difference in performance due to sensory modality. Using preregistered Bayesian model comparison methods, we found that PD patients' comprehension of literal action sentences was not impaired, while there was some evidence for a slowing of responses to action metaphors. Follow up exploratory analyses suggest that this response time modality effect was driven by one type of metaphor (predicate) and was absent in another (nominal), despite the fact that the action semantics were similar in both syntactic forms. These results suggest that the conditions under which PD patients demonstrate hypothesized embodiment effects are limited. We offer a critical assessment of the PD action language literature and discuss implications for the embodiment debate. In addition, we suggest how future studies could leverage Bayesian statistical methods to provide more convincing evidence for or against embodied cognition effects.

A Comprehensive Bayesian Discrimination of the Simple Stellar Population Model, Star Formation History, and Dust Attenuation Law in the Spectral Energy Distribution Modeling of Galaxies

Abstract When modeling and interpreting the spectral energy distributions (SEDs) of galaxies, the simple stellar population (SSP) model, star formation history (SFH), and dust attenuation law (DAL) are three of the most important components. However, each of them carries significant uncertainties that have seriously limited our ability to reliably recover the physical properties of galaxies from the analysis of their SEDs. In this paper, we present a Bayesian framework to deal with these uncertain components simultaneously. Based on the Bayesian evidence, a quantitative implement of the principle of Occam’s razor, the method allows a more objective and quantitative discrimination among the different assumptions about these uncertain components. With a Ks -selected sample of 5467 low-redshift (mostly with z ≲ 1) galaxies in the COSMOS/UltraVISTA field and classified into passively evolving galaxies (PEGs) and star-forming galaxies (SFGs) with the UVJ diagram, we present a Bayesian discrimination of a set of 16 SSP models from five research groups (BC03 and CB07, M05, GALEV, Yunnan-II, BPASS V2.0), five forms of SFH (Burst, Constant, Exp-dec, Exp-inc, Delayed-τ), and four kinds of DAL (Calzetti law, MW, LMC, SMC). We show that the results obtained with the method are either obvious or understandable in the context of stellar/galaxy physics. We conclude that the Bayesian model comparison method, especially that for a sample of galaxies, is very useful for discriminating the different assumptions in the SED modeling of galaxies. The new version of the BayeSED code, which is used in this work, is publicly available at https://bitbucket.org/hanyk/bayesed/.

Understanding the US natural gas market: A Markov switching VAR approach

Over the past three decades, the US natural gas market has witnessed significant changes. Utilizing a standard Bayesian model comparison method, this paper formally determines four regimes existing in the market. It then employs a Markov switching vector autoregressive model to investigate the regime-dependent responses of the market to its fundamental shocks. The results reveal that the US natural gas market tends to be much more sensitive to shocks occurring in regimes existing after the Decontrol Act 1989 than the other regimes. The paper also finds that shocks to the natural gas demand and price have negligible effects on natural gas production while the price of natural gas is mainly driven by specific demand shocks. Augmenting the model by incorporating the price of crude oil, the results show that the impacts of oil price shocks on natural gas prices are relatively small and regime-dependent.

Comparing hybrid time-varying parameter VARs

Empirical questions such as whether the Phillips curve or the Okun’s law is stable can often be framed as a model comparison—e.g., comparing a vector autoregression (VAR) in which the coefficients in one equation are constant versus one that has time-varying parameters. We develop Bayesian model comparison methods to compare a class of time-varying parameter VARs we call hybrid TVP-VARs—VARs with time-varying parameters in some equations but constant coefficients in others. Using US data, we find evidence that the VAR coefficients in some, but not all, equations are time varying. Our finding highlights the empirical relevance of these hybrid TVP-VARs.

Understanding the US Natural Gas Market: A Markov Switching VAR Approach

Over the past three decades, the US natural gas market has witnessed significant changes. Utilizing a standard Bayesian model comparison method, this paper formally determines four regimes existing in the market. It then employs a Markov switching vector autoregressive model to investigate the regime-dependent responses of the market to its fundamental shocks. The results reveal that the US natural gas market tends to be much more sensitive to shocks occurring in regimes existing after the Decontrol Act 1989 than the other regimes. The paper also finds that shocks to the natural gas demand and price have negligible effects on natural gas production while the price of natural gas is mainly driven by specific demand shocks. Augmenting the model by incorporating the price of crude oil, the results show that the impacts of oil price shocks on natural gas prices are relatively small and regime-dependent.

Comparing Hybrid Time-Varying Parameter VARs

Empirical questions such as whether the Phillips curve or the Okun’s law is stable can often be framed as a model comparison—e.g., comparing a vector autoregression (VAR) in which the coefficients in one equation are constant versus one that has time-varying parameters. We develop Bayesian model comparison methods to compare a class of time-varying parameter VARs we call hybrid TVP-VARs—VARs with time-varying parameters in some equations but constant coefficients in others. Using US data, we find evidence that the VAR coefficients in some, but not all, equations are time varying. Our finding highlights the empirical relevance of these hybrid TVP-VARs.

Bayesian model comparison and characterization of bivariate distribution for shear strength parameters of soil

This paper develops a Bayesian approach for model comparison and characterization of the bivariate distribution of c′ and ϕ′ using limited site-specific data. The copula approach is presented to model the bivariate distribution of c′ and ϕ′. The Bayesian model comparison method is developed to select the most probable bivariate distribution model of c′ and ϕ′. The most probable model is used to characterize the joint probability density function (PDF) of c′ and ϕ′ under the Bayesian framework. The developed approach is illustrated and validated using real data of c′ and ϕ′ for clays from the core wall of Xiaolangdi rockfill dam in China.

Statistical Modelling of a Terrorist Network

Summary The paper investigates the group structure in a terrorist network through the latent class model and a Bayesian model comparison method for the number of latent classes. The analysis of the terrorist network is sensitive to the model specification. Under one model it clearly identifies a group containing the leaders and organizers, and the group structure suggests a hierarchy of leaders, trainers and ‘foot soldiers’ who carry out the attacks.

Bayesian inference and model comparison for metallic fatigue data

In this work, we present a statistical treatment of stress-life (S-N) data drawn from a collection of records of fatigue experiments that were performed on 75S-T6 aluminum alloys. Our main objective is to predict the fatigue life of materials by providing a systematic approach to model calibration, model selection and model ranking with reference to S-N data. To this purpose, we consider fatigue-limit models and random fatigue-limit models that are specially designed to allow the treatment of the run-outs (right-censored data). We first fit the models to the data by maximum likelihood methods and estimate the quantiles of the life distribution of the alloy specimen. To assess the robustness of the estimation of the quantile functions, we obtain bootstrap confidence bands by stratified resampling with respect to the cycle ratio. We then compare and rank the models by classical measures of fit based on information criteria. We also consider a Bayesian approach that provides, under the prior distribution of the model parameters selected by the user, their simulation-based posterior distributions. We implement and apply Bayesian model comparison methods, such as Bayes factor ranking and predictive information criteria based on cross-validation techniques under various a priori scenarios.

Statistical modelling of the group structure of social networks

This research evaluates the identification of group structure in social networks through the latent class model and a new Bayesian model comparison method for the number of latent classes. The approach is applied to a well-known network of women in Natchez Mississippi. The latent class analysis reproduces the group structure of the women identified by the original sociologists.

Bayesian model comparison: Log scores and

Abstract We investigate Bayesian approaches to answering the frequently-arising model-specification question (Q:) Is model M j better than M j ′ ? We contrast two Bayesian model-comparison methods–log scores and D I C –on their ability to correctly discriminate between fixed-effects Poisson (FEP) and random-effects Poisson (REP) sampling models.

Using Bayesian posterior model probabilities to identify omitted variables in spatial regression models

AbstractLeSage and Pace (2009) consider the impact of omitted variables in the face of spatial dependence in the disturbance process of a linear regression relationship and show that this can lead to a spatial Durbin model. Monte Carlo experiments and Bayesian model comparison methods are used to distinguish between spatial error and Durbin model specifications that arise with varying levels of correlation between included and omitted variables. The Monte Carlo results suggest use of the common factor relationship developed in Burridge (1981) as a way to test for the presence of omitted variables bias influencing specific explanatory variables.

Using Bayesian Posterior Model Probabilities to Identify Omitted Variables in Spatial Regression Models

LeSage and Pace (2009) consider the impact of omitted variables in the face of spatial dependence in the disturbance process of a linear regression relationship. Remarkably, they show that this can lead to a spatial regression model specification containing a spatial lag of the dependent and explanatory variables, providing an econometric as opposed to economic theory motivation for use of spatial regression models in applied work. Another implication of this econometric situation is the presence of global spatial spillovers. Global spillovers reflect a situation where changes in a characteristic of one observation/region (potentially) impacts outcomes in all other observations/regions. Specifically, global spillovers impact the neighbors, neighbors to the neighbors, neighbors to the neighbors to the neighbors, and so on, with decreasing influence as we move to higher-order/more distant neighbors.We explore the econometric role played by omitted variables under alternative scenarios that give rise to both spatial regression specifications involving either local or global spatial spillovers. Local spillovers are those that impact only immediately neighboring observations, but not higher-order neighbors (e.g., neighbors to neighbors and so on). In addition to theoretical consideration of the alternative scenarios that practitioners might use to identify an appropriate local versus global spatial spillover specification, we explore performance of Bayesian model comparison methods in distinguishing between local and global spillover specifications that arise with varying levels of correlation between included an omitted variables.

Evaluation of generalized linear models for soil liquefaction probability prediction

A soil deposit subjected to seismic loading can be viewed as a binary system: it will either liquefy or not liquefy. Generalized linear models are versatile tools for predicting the response of a binary system and hence potentially applicable to liquefaction prediction. In this study, the applicability of four generalized linear models (i.e., logistic, probit, log–log, and c-log–log) for liquefaction potential evaluation is assessed and compared. Eight liquefaction models based on the four generalized linear models and two sets of explanatory variables are evaluated. These models are first calibrated with past liquefaction performance data. A weighted-likelihood function method is used to consider the sampling bias in the calibration database. The predicted liquefaction probabilities from various models are then compared. When liquefaction probability is small, the predicted liquefaction probability is sensitive to the regression models used. The effect of sampling bias is more marked in the high cyclic stress ratio region. The eight models are finally ranked using a Bayesian model comparison method. For the generalized linear models examined, the logistic and c-log–log regression models are most supported by the past performance data. On the other hand, the probit and c-log–log regression models are much less applicable to liquefaction prediction.

A Bayesian Approach to Identifying and Interpreting Regional Convergence Clubs in Europe

This study suggests a two-step approach to identifying and interpreting regional convergence clubs in Europe. The first step involves identifying the number and composition of clubs using a space-time panel data model for annual income growth rates in conjunction with Bayesian model comparison methods. A second step uses a Bayesian space-time panel data model to assess how changes in the initial endowments of variables (that explain growth) impact regional income levels over time. These dynamic trajectories of changes in regional income levels over time allow us to draw inferences regarding the timing and magnitude of regional income responses to changes in the initial conditions for the clubs that have been identified in the first step. This is in contrast to conventional practice that involves setting the number of clubs ex ante, selecting the composition of the potential convergence clubs according to some a priori criterion (such as initial per capita income thresholds for example), and using cross-sectional growth regressions for estimation and interpretation purposes. (authors' abstract)