Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

Ando, Tomohiro

doi:10.1093/biomet/asm017

Cited by 212 publications

(193 citation statements)

References 24 publications

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“…Model comparison was conducted based on Bayesian predictive information criterion (BPIC) values (Ando, 2007), which relate the model's deviance to its complexity (see Table 1). SOA-independent binomial models provided, in general, a very good fit of participants' response patterns, indicated by Bayesian p values around the ideal value of 0.5 and R 2 values higher than 90 %.…”

Section: Modelmentioning

confidence: 99%

“…Note that RMSD is estimated larger and R 2 smaller, when using the full posterior predictive distribution rather than the maximum a posteriori (MAP) estimate as is often done. For model comparison, the Bayesian predictive information criterion (BPIC) (Ando, 2007) was assessed with model complexity pV measured as half the posterior variance of the model-level deviance (Gelman et al, 2004).…”

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confidence: 99%

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Integration of anatomical and external response mappings explains crossing effects in tactile localization: A probabilistic modeling approach

2015

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To act upon a tactile stimulus its original skinbased, anatomical spatial code has to be transformed into an external, posture-dependent reference frame, a process known as tactile remapping. When the limbs are crossed, anatomical and external location codes are in conflict, leading to a decline in tactile localization accuracy. It is unknown whether this impairment originates from the integration of the resulting external localization response with the original, anatomical one or from a failure of tactile remapping in crossed postures. We fitted probabilistic models based on these diverging accounts to the data from three tactile localization experiments. Hand crossing disturbed tactile left-right location choices in all experiments. Furthermore, the size of these crossing effects was modulated by stimulus configuration and task instructions. The best model accounted for these results by integration of the external response mapping with the original, anatomical one, while applying identical integration weights for uncrossed and crossed postures. Thus, the model explained the data without assuming failures of remapping. Moreover, performance differences across tasks were accounted for by non-individual parameter adjustments, indicating that individual participants' task adaptation results from one common functional mechanism. These results suggest that remapping is an automatic and accurate process, and that the observed localization impairments in touch result from a cognitively controlled integration process that combines anatomically and externally coded responses.

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Section: Modelmentioning

confidence: 99%

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confidence: 99%

Integration of anatomical and external response mappings explains crossing effects in tactile localization: A probabilistic modeling approach

2015

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“…The use of the prior (2.6) for B-spline function has been investigated by Ando (2004), Konishi et al (2004) and Lang and Brezger (2004).…”

Section: The Bayesian Estimation Via the Markov Chain Monte Carlo Methodsmentioning

confidence: 99%

“…Although the progress in MCMC simulation methods has made SV modeling popular, the assessment of the goodness of its extension is still ongoing. In this paper, to evaluate the goodness of the estimated models, we employ several Bayesian model selection criteria that include the Bayes factor (Kass and Raftery (1995), Kim et al (1998), Chib et al (2002)), the Bayesian predictive information criterion (Ando (2004(Ando ( , 2006c) and the deviance information criterion , Berg et al (2004)). To examine the goodness of the constructed model from various angles, three kinds of model selection criteria are used.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inference for Nonlinear and Non-Gaussian Stochastic Volatility Model with Leverage Effect

Ando

2006

JJSS

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Stochastic volatility (SV) models provide useful tools to describe the evolution of asset returns, which exhibit time-varying volatility. This paper extends a basic SV model to capture a leverage effect, a fat-tailed distribution of asset returns and a nonlinear relationship between the current volatility and the previous volatility process. The Bayesian approach with the Markov chain Monte Carlo method is employed to estimate model parameters. To assess the goodness of the estimated model, we calculated several Bayesian model selection criteria that include the Bayes factor, the Bayesian predictive information criterion and the deviance information criterion. The proposed method is tested on simulated data and then applied to daily returns on the Nikkei 225 index where several SV models are formally compared.

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“…For this study, we take the mean values of the parameters from the MCMC as an estimate of the maximum likelihood parameters, and then use conjugate-gradient optimization to improve this estimate to obtain our final maximum log likelihood. Other criteria, such as the Deviance Information Criterion (DIC) and Bayesian Predictive Information Criterion (BPIC) are directly computable from the MCMC chain, however the DIC has problems with overfitting the data and the BPIC is an unnecessarily complicated calculation for this simple problem (Ando 2007). At first impression, transdimensional MCMC would appear to be a good candidate for determining the maximum degree l of spherical harmonic analysis, and it has the advantage of determining model complexity in a single inversion, rather than requiring multiple inversions for different spaces of models as is the case for IC approaches.…”

Section: Model Space Selection Via the Aiccmentioning

confidence: 99%

A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference

Muir

Tkalčić

2015

Geophysical Journal International

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S U M M A R YThe problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.

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Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models

Cited by 212 publications

References 24 publications

Integration of anatomical and external response mappings explains crossing effects in tactile localization: A probabilistic modeling approach

Integration of anatomical and external response mappings explains crossing effects in tactile localization: A probabilistic modeling approach

Bayesian Inference for Nonlinear and Non-Gaussian Stochastic Volatility Model with Leverage Effect

A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference

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