User:Dfleury1/sandbox
From Wikipedia, the free encyclopedia
In functional magnetic resonance imaging (fMRI) data processing, second-level Bayesian inference refers to the application of Bayes factors (BFs) as indicators for second-level analysis/group analysis in examining regional brain activity. Bayesian inference has emerged as a competing alternative to p-values and frequentist explorations of type I and type II errors, primarily due to how Bayes Factors enable experimenters to measure statistical evidence given prior parameters and evidence rather than assuming a fixed pre-set of parameters. Due to the notoriety of high false positive activations during fMRI post-processing, leading techniques including Bonferroni correction and False Discovery Rates (FDRs) have been implemented to minimize type I errors.[1] However, recent reports suggest that these frequentist toolkits may be too liberal or harsh in controlling for type I errors, proposing random field theory (RFT) familywise error correction (FWE)-applied voxel-wise thresholding as an appropriate balance. Nevertheless, follow-up discussions suggest that even popular methods including RFT do not attain sufficient significance levels, instead inflating false positive rates.
![Statistical parametric map with voxel activations on an fMRI scan.](http://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Statistical_parametric_maps_of_BPND_of_11C-%28R%29-PK11195_in_CFS.ME_patients_and_healthy_controls.gif/320px-Statistical_parametric_maps_of_BPND_of_11C-%28R%29-PK11195_in_CFS.ME_patients_and_healthy_controls.gif)
Since Bayesian inference does not presume parameter values, or effect sizes, as precisely equal to a definite value, type I/II error interpretations no longer have utility. Instead, by applying Bayes factors, the effect size can be expressed as uncertainty in terms of a probability distribution based on a prior distribution, incoming data, and its updated posterior distribution on parameters. Ultimately, a Bayesian framework is free from presumptions about effects that are certainly zero or null hypotheses, rendering it less vulnerable to inflated false positive rates. In contrast to a P-value, which quantifies the probability that one will observe values of a test statistic that are as more or less extreme than observed results, a Bayesian framework permits researchers to express a posterior uncertainty of voxel activity hypotheses. The capacity for Bayes Factors as a tool to accept hypotheses, including null, based on a ratio of posterior probabilities between (null hypothesis) and
allows scientists to more readily make a decision on how to accept the null of the alternative[2][3].