Effective dimension for weighted ANOVA and anchored spaces

Effective dimension, an indicator of the difficulty of high dimensional integration, describes whether a function can be well approximated by low dimensional terms or a sum of low dimensional terms. This talk considers weighted ANOVA and anchored spaces of functions. The main focus is to study how the variance is related to the norms and why this connection is useful in the context of effective dimension, using  relations between the corresponding multivariate decompositions and the embedding between these two spaces.