Noise models and estimation methods

[cmaumet]

This is a proposition built with @nicholst to represent the noise models (following suggestion in #170).

We propose to characterise the noise variance (diagonal elements) and the noise dependance (off-diagonal elements):

Noise Variance

• is
  • homogeneous if all variances are identical (nidm:noiseVarianceHomogeneous = true) or;
  • heterogeneous otherwise (nidm:noiseVarianceHomogeneous = false).
  • Heterogeneous variance can be further specified (e.g. by group, by time, FSL FLAME, arbitrary...) using a separate attribute
• is defined spatially to be either:
  • local (nidm:varianceSpatialModel = nidm:SpatiallyLocal) or;
  • regularised (nidm:varianceSpatialModel = nidm:SpatiallyRegularised) or;
  • global (nidm:varianceSpatialModel = nidm:SpatiallyGlobal).

Noise Dependence

• is either
  • Independent (nidm:noiseDependence = nidm:IndependentNoise)
  • Compound Symmetry (nidm:noiseDependence = nidm:CompoundSymmetry)
  • Serially Correlated (nidm:noiseDependence = nidm:SeriallyCorrelatedNoise)
    • SeriallyCorrelated noise can be ApproxAR1, ARMA11, TaperedACF
  • Arbitrarily Correlated (nidm:noiseDependence = nidm:AbitrarilyCorrelatedNoise)
• is defined spatially to be either:
  • local (nidm:DependenceSpatialModel = nidm:SpatiallyLocal) or;
  • regularised (nidm:DependenceSpatialModel = nidm:SpatiallyRegularised) or;
  • global (nidm:DependenceSpatialModel = nidm:SpatiallyGlobal).

[cmaumet]

For example:

• in FSL 1st level we have: Spatially local homogeneous variance + Spatially regularised serially correlated (Tapered ACF) noise
• in SPM 1st level we have: Spatially local homogeneous variance + Spatially global serially correlated (ApproxAR1) noise
• in AFNI 1st level we have: Spatially local homogeneous variance + Spatially local serially correlated (ARMAII) noise

[nicholst]

Thanks @cmaumet!

Minor typo nidm:SpatiallyLocall -> nidm:SpatiallyLocal.
ARMAII -> ARMA11 (arma-one-one)

Instead of nidm:VarianceSpatialDefinition somehow nidm:VarianceSpatialAssumption or, maybe better yet nidm:VarianceSpatialModel

I'd also add to Noise Dependence nidm:CompoundSymmetry.

[cmaumet]

Thank you @nicholst, this is updated as suggested (directly in my initial comment).

[nicholst]

I just noticed Noise Dependence -> Homogeneous (nidm:noiseDependence = nidm:HomogeneousNoise). I remember this one... What is this?

Also, it is useful to arrange the lists in order of increasing complexity; for Noise Dependence a better order would be:

• Independent (nidm:noiseDependence = nidm:IndependentNoise)
• Compound Symmetry (nidm:noiseDependence = nidm:CompoundSymmetry)
• Serially Correlated (nidm:noiseDependence = nidm:SeriallyCorrelatedNoise)
• Arbitrarily Correlated (nidm:noiseDependence = nidm:AbitrarilyCorrelatedNoise)

(CS and SC could be flipped; left out 'Homogeneous' as I wasn't sure about it).

[nicholst]

Following discussion today with @cmaumet, we might as well add the actual distributional assumption

Noise Distribution

• Gaussian ... Examples... everything fit with the GLM (the default)
• Nonparametric ... Examples... when using SnPM, randomise, or any rank-based method
• Nonparametric-Symmetric ... Examples, any 2nd level fMRI analysis on contrast data
• Poisson ... Point-valued data (theoretically, no upper-bound on number of points observed)... Examples... coordinate based meta-analysis
• Binomial ... Count data out of a fixed maximum; Examples... lesion count data (based on binary lesion masks in standard space)

Note, that nonparametric inference methods assume exchangeability, and that nidm:noiseVarianceHomogeneous = true and nidm:noiseDependence = nidm:CompoundSymmetry implies exchangeability. So, I don't think we want an distinct term.

Also note, that all of these descriptors are about the noise, as in the epsilon in
Y = X beta + epsilon
not about the data.

[cmaumet]

Noise models and estimation methods are now implemented as follows:

Noise Model: Creation of a new entity of type NoiseModel with attributes:

• nidm:hasNoiseDistribution (possible values are child of NoiseDistribution):
  
• nidm:noiseVarianceHomogeneous (possible value: true/fasle),
• nidm:hasNoiseDependence (possible values are child of NoiseDependence):
  
• nidm:varianceSpatialModel (possible values are child of SpatialModel)
• nidm:dependenceSpatialModel (possible values are child of SpatialModel):
  

A NoiseModel entity is used by a ModelParametersEstimation activity.

Estimation methods: Creation of a new attribute withEstimationMethod in activities of type ModelParametersEstimation (possible values are child of EstimationMethod):

[nicholst]

Terms from STATO:

Binomial Distribution: http://purl.obolibrary.org/obo/STATO_0000276
Gaussian Distribution: http://purl.obolibrary.org/obo/STATO_0000227
Poisson Distribution: http://purl.obolibrary.org/obo/STATO_0000051

The global/local things are probably too imaging specific, but will post something over on STATO on the dependence terms.

[cmaumet]

Thank you @nicholst: Binomial, Gaussian and Poisson distributions are now linked to the STATO terms using a sameAs relationship.

[cmaumet]

We discussed this in NIDASH call on September 22nd (Minutes).

We identified the following steps forward:

• Propose a definition for the newly created terms: noise distribution (cf. Definition of "noise distribution" terms #191), dependence (cf. Defintion of "noise dependence" terms -> "error dependence" #193), variance (cf Definition of "noiseVarianceHomogeneous" -> "errorVarianceHomogeneous" #192) and estimation methods: @nicholst
• Update GLS term to GeneralizedLeastSquares (US spelling): @cmaumet

[cmaumet]

SPM - 1st level	SPM - 2nd level
nidm:hasNoiseDistribution = GaussianDistribution
nidm:noiseVarianceHomogeneous = true nidm:varianceSpatialModel = nidm:SpatiallyLocalModel
nidm:hasNoiseDependence =    nidm:SeriallyCorrelatedNoise nidm:dependenceSpatialModel=   nidm:SpatiallyGlobalModel	nidm:hasNoiseDependence=   nidm:IndependentNoise

FSL - 1st level	FSL - 2nd level
nidm:hasNoiseDistribution = GaussianDistribution
nidm:noiseVarianceHomogeneous = true nidm:varianceSpatialModel =    nidm:SpatiallyLocalModel	nidm:noiseVarianceHomogeneous = false nidm:varianceSpatialModel =    nidm:SpatiallyLocalModel
nidm:hasNoiseDependence =    nidm:SeriallyCorrelatedNoise nidm:dependenceSpatialModel=   nidm:SpatiallyRegularizedModel	nidm:hasNoiseDependence=   nidm:IndependentNoise

AFNI - 1st level	AFNI - 2nd level
nidm:hasNoiseDistribution = GaussianDistribution
nidm:noiseVarianceHomogeneous = true nidm:varianceSpatialModel =    nidm:SpatiallyLocalModel	nidm:noiseVarianceHomogeneous = true or false nidm:varianceSpatialModel =    nidm:SpatiallyLocalModel
nidm:hasNoiseDependence =    nidm:SeriallyCorrelatedNoise nidm:dependenceSpatialModel=   nidm:SpatiallyLocalModel	nidm:hasNoiseDependence=   nidm:IndependentNoise

[nicholst]

Independant -> Independent

One wrinkle: nidm:hasNoiseDependence = nidm:IndependantNoise indicates that there is no dependence, and hence nidm:dependenceSpatialModel isn't really defined. i.e. there are no parameters, and so clarifying that the (non-existent) parameters are nidm:SpatiallyGlobalModel seems odd.

What should we do? Is there "n/a" value, or just not specify it?

[nicholst]

Randomise & SnPM

First-level
n/a

Randomise & SnPM 2nd level - fMRI and difference data (sign-flipping)
nidm:hasNoiseDistribution = NonparametricSymmetric
nidm:noiseVarianceHomogeneous = false nidm:varianceSpatialModel = nidm:SpatiallyLocalModel
nidm:hasNoiseDependence = nidm:IndependentNoise

Randomise & SnPM 2nd level - Positive data
nidm:hasNoiseDistribution = Nonparametric
nidm:noiseVarianceHomogeneous = true nidm:varianceSpatialModel = nidm:SpatiallyLocalModel
nidm:hasNoiseDependence = nidm:ExchangeableNoise nidm:dependenceSpatialModel = nidm:SpatiallyLocalModel

Note, it may be surprising, but sign flipping makes no assumption of equal variance. See Winkler et al. (2014) for details.

1. Winkler AM, Ridgway GR, Webster MA, Smith SM, Nichols TE. Permutation inference for the general linear model. Neuroimage. 2014;92C:381–397.

[cmaumet]

Thank you @nicholst, this is great! I have updated the typo and removed the nidm:dependanceSpatialModel attribute whenever the noise is independent as suggested.

[cmaumet]

Do you think we could merge this pull request and start discussing the definitions in a new thread?