This section lists a few VBA stand-alone functions that were designed to solve specific issues arising in the context of model-based statistical data analysis. This list is not exhaustive, and we encourage VBA users to look for (and/or contribute) other related functions within VBA’s core routines.

Want to derive a sampling approximation to the states’ trajectory density?

Check the function get_MCMC_predictiveDensity.m (and its variant get_MCMC_predictiveDensity_fb.m when states evolve according to some state-dependant feedback). The outputs of this procedure are time-dependant histograms, which can be eyeballed using the function plotDensity.m. Note: the function VBA_getLaplace.m does the same thing, but under a parametric (Laplace) approximation.

Want to check whether any variable is numerically weird?

Numerical variables can be “weird”, e.g. be complex-valued, be infinite or contain NaNs. The function VBA_isweird.m will return 1 if this is the case. Note: this function works on N-D arrays, structures, cell arrays or any combination of these.

Want to sample from an arbitrary 1D probability distribution?

Have a look at VBA_random('Arbirary', p, values)

Alternatively, the function VBA_random.m can be used to sample from gaussian, gamma, dirichlet, or multinomial densities…

Want to estimate impulse responses to a sequence of inputs?

Let \(x(t)\) be the response of a system to a sequence of inputs \(u(t)\), which can be described as a convolution operation, i.e.:

\[x(t) = x_0 + \sum_{\tau} h\left(\tau\right) u\left(t-\tau\right) + \epsilon\]

where \(h\left(\tau\right)\) is an unknown impulse response function, \(\tau\) is the convolution lag and \(\epsilon\) are model residuals.

The function VBA_conv2glm.m allows you to transform a sequence of inputs into a design matrix that, when fitted using a GLM, provides an estimate of the finite impulse response function…

The function VBA_VolterraKernels.m can be used to estimate the Volterra kernels of both observed data and systems’ states, given the posterior and out output VBA structures. This function exemplifies the use of VBA_conv2glm.m…

Want to get the square-root of a matrix?

Have a look at VBA_sqrtm.m :)

Want to get errorbars on estimated model residuals?

Let \(m\) be a simple generative model of the form: \(y=g(\phi)+\epsilon\), where \(y\) are observed data, \(g\) is the observation function, \(\phi\) are unknown model parameters and \(\epsilon\) are model residuals. When inverting the model (i.e. deriving the posterior density \(p\left(\theta\mid y\right)\)), VBA provides point estimates of model residuals, but does not provide the full posterior density \(p\left(\epsilon\mid y\right)\). This can be retrieved using the function VBA_getNoise.m.

Deriving all n-draws from a k-urn (with replacement)

Have a look at VBA_getNtuples.m :)

This is problem of combinatorics, which arises, e.g., in the context of between-condition model comparison. This is because here, one wants to evaluate the model evidences of all possible pairings (n-tuples, where \(n\) is the number of conditions) of condition-specific models (where there are \(k\) models)…

Want to extract the states’ variances from VBA’s posterior structure?

Have a look at VBA_getVar.m :)

Deriving the Kullback-Leibler divergence for Normal or Gamma densities

Have a look at VBA_KL.m :)

Want to evaluate the log-evidence of the null model?

Have a look at VBA_LMEH0.m :)

The ‘null model’ here is such that the data is entirely random. It may or may not directly correspond to a given ‘null assumption’ (\(H_0\)) used in classical testing procedures.

Want to orthogonalize a matrix?

Have a look at VBA_orth.m :)

Want to derive the posterior probability \(P\left(\phi=0\mid y\right)\)?

Have a look at VBA_PP0.m :)

Note: this function works for both evolution and observation parameters…

The function VBA_PPM.m can be used to derive \(P\left(\phi\geq a\mid y\right)\) or \(P\left(a\leq\phi\leq b\mid y\right)\). It also can be used to eyeball the corresponding posterior density…

Deriving a simple cross-validation measure of model generalizability

Have a look at VBA_PRESS.m :)

The predicted residual error sum of squares (PRESS) statistic is a form of cross-validation used in regression analysis to provide a summary measure of the fit of a model to a sample of observations that were not themselves used to estimate the model. It is calculated as the sums of squares of the prediction residuals for those observations.

Want to derive Savage-Dickey ratios?

Have a look at VBA_SavageDickey.m :)

Savage-Dickey ratios can be used to compute the free energy and posterior moments of a reduced model, given the prior and posterior densities of a full model. The key added-value of this scheme is that one does not need to perform the corresponding model inversion! This is particularly useful when comparing models within large model spaces.

Tools for classical contrast testing.

VBA includes a function (GLM_contrast.m) that enables classical (i.e. frequentist) statistical testing in the context of a GLM. Below is a set of related useful functions:

  • Contrast_MEbins.m: derives the contrast matrix for an F-test of group mean differences (useful when the number of groups or conditions is bigger than 2).
  • FtoR2.m: converts an F-statistic into a coefficient of determination (R2).
  • findCI.m: finds confidence intervals for given t or F statistics.
  • GLM_tolerance.m: computes regression tolerance of a given design matrix.
  • lev_GLM.m: computes the log-evidence of a GLM (frequentist limit).
  • PRESS_GLM.m: evaluates the PRESS-R2 cross-validation metric for a GLM.
  • removeOutliers.m: detects outliers based upon robust moment-matched Gaussian distribution.
  • testPower.m: returns the statistical power of a test, given the expected effect size and the corresponding degrees-of-freedom.
  • GLM_2pieces.m: fits a piece-wise linear model.

Want to extract a subplot into a single matlab figure?

VBA makes intensive use of “subplots”, i.e. multiple graphis within the same matlab window. These may, at times, be difficult to eyeball. Running the function VBA_getSubplots.m effectively attaches a “context menu” to every axis of the current matlab session. In turn, right-clicking on any axis enables one to extract the subplot into a single matlab figure. This can then be used to copy-paste the graphics, e.g., into powerpoint. Note: closing the figure will automatically replace the axis at its original location.

back to top