The nonlinear factor analysis model described in publication V has the following structure:

- The mapping from factors to observations is modelled by an MLP network with one hidden layer as described by (34).
- The factors can have Gaussian or mixtures-of-Gaussians models. This corresponds to a nonlinear extension of linear factor analysis or linear independent factor analysis, respectively. The factors are assumed to be independent.
- Hierarchical models are used for describing the prior information about the parameters. Gaussian distributions are used extensively.
- The variance parameters of the Gaussians are parameterised by the logarithm of the standard deviation. This yields a roughly Gaussian posterior probability for these parameters.