Perspectives on Bayesian Methods and Big Data

Allenby, Greg M.; Bradlow, Eric T.; George, Edward I.; Liechty, John; McCulloch, Robert E.

doi:10.1007/s40547-014-0017-9

Cited by 19 publications

(11 citation statements)

References 26 publications

(25 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As pointed out in Section 1, the very same statistical estimation techniques are of eminent importance for a wide range of other functional neuroimaging data models. Moreover, together with the GLM, they also form a fundamental building block of model-based behavioral data analyses as recently proposed in the context of "computational psychiatry" (e.g., Montague et al, 2012;Schwartenbeck and Friston, 2016;Stephan et al, 2016a,b,c) and recent developments in the analysis of "big data" (e.g., Allenby et al, 2014;Ghahramani, 2015).…”

Section: Estimator Qualitymentioning

confidence: 99%

Variational Bayesian parameter estimation techniques for the general linear model

Starke¹,

Ostwald²

2016

Preprint

View full text Add to dashboard Cite

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modelling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation.

show abstract

Section: Estimator Qualitymentioning

confidence: 99%

Variational Bayesian parameter estimation techniques for the general linear model

Starke¹,

Ostwald²

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…But with emerging gene chips based on 28M+ different SNP markers based on sequencing technologies (Daetwyler et al 2014), it seems apparent that many more phenotypic records will be needed than are currently available for many livestock species, particularly in light of the fact that multicollinearity among adjacent markers will be typically extreme. Within a completely different context, Allenby et al (2014) wrote that focusing on statistical sufficiency or data compression will become increasingly important, drawing the analogy that inferences will be akin to finding a needle in a haystack that keeps getting increasingly bigger. Yang et al (2015) recognized that reliable inferences on hyperparameters could be rather formidable with extremely high marker densities, particularly as MCMC diagnostic performance (i.e., ESS) degrades substantially for the same number of MCMC cycles with a higher m/n while the computational cost of each MCMC cycle increases proportionally to m. They proposed that inferences on g, regardless of which WGP model is used, could be based on values of ϑ extrapolated from inferences based on lower marker density panels; nevertheless, further work is badly needed in this area.…”

Section: Increasing Marker Densitiesmentioning

confidence: 99%

“…Furthermore, MCMC does not allow a form of 'memory' when re-running or updating analyses based on the collection of more data. As Allenby et al (2014) attests, "real-time" posterior densities are very difficult to get with big data using MCMC in an era where just-in-time analysis updates are increasingly demanded (Liu et al 2014). This is particularly true in animal breeding where inferences on breeding values are continually updated (Wiggans et al 2015).…”

Section: Improving Mcmc Schemesmentioning

confidence: 99%

“…To address this concern, it has been suggested to run multiple shorter chain analyses and using meta-analytic methods to combine the results based on previous MCMC analyses (Allenby et al 2014). In the meantime, researchers continue to strive to improve computational efficiency of MCMC sampling schemes in animal breeding (Shariati and Sorensen 2008;Shariati et al 2009;Yang et al 2015).…”

Section: Improving Mcmc Schemesmentioning

confidence: 99%

“…Strategies based on expectation maximization (EM) have drawn increasing interest for WGP models in animal breeding (Kärkkäinen and Sillanpää 2012). In fact, EM has been characterized as a form of "big data Bayes" (Allenby et al 2014) whereby the primary focus is adapting computationally efficient strategies to compute joint posterior modes. Furthermore, EM is amenable to analysis updates whereby one can readily use solutions from a previous analysis as starting values for the current analysis.…”

Section: Approximate Analytical Approachesmentioning

confidence: 99%

See 2 more Smart Citations

Statistical and Computational Challenges in Whole Genome Prediction and Genome-Wide Association Analyses for Plant and Animal Breeding

Tempelman

2015

JABES

View full text Add to dashboard Cite

Whole genome prediction (WGP) modeling and genome-wide association (GWA) analyses are big data issues in agricultural quantitative genetics. Both areas require meaningful input from the statistical scholarly community in order to further improve the accuracy of prediction of genetic merit and inference on putative causal variants as well as improving the computational efficiency of existing methods and algorithms. These concerns have become increasingly critical as new sequencing technologies will only exacerbate current model dimensionality problems. We focus primarily on mixed model and hierarchical Bayesian analyses which have been most commonly pursued by animal and plant breeders for WGP thus far. We draw attention to our observation that many such previous analyses have not carefully inferred upon hyperparameters defined at the top levels of the Bayesian model hierarchy, but simply arbitrarily specify their values. We also reassess previous discussions on WGP model dimensionality, believing that useful data augmentation schemes utilized in various Markov Chain Monte Carlo (MCMC) schemes have led to a general misunderstanding that heavy-tailed or variable selection-based WGP models may be highly parameterized relative to more standard mixed model representations. Computational efficiency is addressed with respect to MCMC and competitive, albeit approximate, alternatives. Furthermore, GWA analyses are reassessed, encouraging a greater reliance on shrinkage-based inferences based on critically chosen priors, instead of potentially nonreproducible fixed effects P valuebased inference.

show abstract