Update param-transform.md

_wiki/param-transform.md

@@ -25,6 +25,11 @@ One may use the [exponential](https://en.wikipedia.org/wiki/Exponential_function
 > Note that Bayesian inference is **not invariant through changes in model parameterization**. For example, let us consider the mapping $$x \rightarrow x^3$$. This mapping does not insert any hard constraint, in the sense that the mapped parameter $$x^3$$ is allowed to vary without finite bounds. Nevertheless, Bayesian inference on a model that uses parameter $$x$$ does not yield the same result as inference on the same model, but this time using the mapped parameter $$x^3$$. This is because passing through the $$x \rightarrow x^3$$ mapping can be seen as setting a non-Gaussian prior on $$x^3$$...
 
 
+## Constraining _sample moments_ of parameter subsets
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+It may happen that proper model parameterization requires to constrain the sample moments of some parameter subsets. For example, one may wish to make sure that observation parameters $$\Phi$$ have a zero sample mean (i.e. $$\overline{\phi}= 1/n \sum_i \phi_i =0$$) and aunitary sample variance (i.e. $$1/n\sum_i \left(\phi_i-\overline{\phi}\right)^2 =1$$. This is useful, e.g., in the context of [(re-parameterized) covariance component models]({{ site.baseurl }}/wiki/param-transform/). This kind of constraint can be easily enforced by zscoring the parameter vector $$\Phi$$ prior to entering the observation function.
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 # Setting non-Gaussian priors
 
 One may also want to impose a specific non-Gaussian prior to some parameters. For example, one may want to set [Beta](https://en.wikipedia.org/wiki/Beta_distribution) or [Gamma](https://en.wikipedia.org/wiki/Gamma_distribution) priors on model parameters. Although, superficially, VBA only deals with Gaussian priors, one can use parameter transformations to emulate non-Gaussian priors. This is exemplified below.