General

This is two lists of words, with explanations, as they are used throuhout this webpage.

This page is at an early stage, and far from complete.

The detailed list

Stage 1 (level 1, top level)

The observation likelihood and the link function.

Also: Level 1, top level (of the hierarchical model).

Stage 2

The linear predictor and the random effects. And the formula. Usually more than one parameter per observation. Notation \(\eta_i, f_i, u_i\).

Also: Level 2 (of the hierarchical model), predictor.

Stage 3

The hyper-parameters. Usually 1-10.

Also: Level 3.

Domain

Also: Spatial domain, study region, study area, or total area. The domain is where (in space) you allow fitting and predictions. This is where you intend to plot the spatial field.

Domain can also be used for “region” of values of other variables, e.g. time domain.

Objectivity and Truth

When modeling, we want to be somewhat objective, and we want to get the “truth” in some fashion. However, these words are not so useful for discourse, and we would rather use

  • Transparency: How well the assumptions (subjective or objective) are presented and clarified
  • Ability to generalize: How well the conclusions generalize to other situations

Bayesian inference

This word can mean several things. we would rather use

  • Bayesian modeling: Fully specified probabilistic (prior) models
  • Bayesian computation: Efficient computation and representation of the posterior
  • Assumption-Conclusion inference: Connecting different prior models to posterior conclusions

Prior

When talking about the prior, it can be

  • Priors for hyper-parameters
  • Priors for the random effects (e.g. spatial covariance structure)
  • Assumptions on distributions (e.g. the likelihood, or Gaussianity assumptions)

The simple list

Hyper-parameter: A parameter controlling other parameters. The parameters controlling the structure in a random effect, e.g. range and sigma in a spatial effect. The parameter(s) in the observation likelihood.

Parameter(s): In theory, any parameter in the model, i.e. any random variable except \(Y\). In practice, used to denote the large set of Gaussian variables in a random effect, or in the

Family: Same as likelihood, see likelihood.

Observation likelihood: Same as likelihood, see likelihood.

Likelihood: The distributions for the observations given the model for the predictor (formula).

Predictor: Symbol \(\eta\). The model, represented by the formula. This is assumed to be Gaussian when the hyper-parameters are fixed/known. This is where you believe the effects in the model to be additive, that they add up to the total underlying true distribution/intensity.

Linear predictor: Same as predictor, see predictor. There is no assumption that the predictor is a linear regression, it can be any additive model.

Latent variable: Same as predictor, see predictor.