I am currently working on Generalized Linear Mixed Models and need some help concerning the prediction of the random effects. More specifically, I don't understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I don't understand)

This is the representation in general. In a one way classification, $X$ would be the random effect, $Y$ the response group (vector) for the random effect.
Found in several papers and books of McCulloch et al.

I am currently working on generalized linear mixed models (GLMM) and need some help concerning the prediction of the random effects. More specifically, I don't understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I don't understand)

This is the representation in general. In a one way classification, $X$ would be the random effect, $Y$ the response group (vector) for the random effect.
Found in several papers and books of McCulloch et al.

I am currently working on Generalized Linear Mixed Models and need some help concerning the prediction of the random effects. More specifically, I don't understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I don't understand)

This is the representation in general. In a one way classification, X would be the random effect, Y the response group (vector) for the random effect.
Found in several papers and books of McCulloch et al.

I am currently working on Generalized Linear Mixed Models and need some help concerning the prediction of the random effects. More specifically, I don't understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I don't understand)

This is the representation in general. In a one way classification, $X$ would be the random effect, $Y$ the response group (vector) for the random effect.
Found in several papers and books of McCulloch et al.

I am currently working on Generalized Linear Mixed Models and need some help concerning the prediction of the random effects. More specifically, I dont understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I dont understand)

This is the representation in general. In a one way classification, X would be the random effect, Y the response group (vector) for the random effect. found in several papers and books of McCulloch et al.

I am currently working on Generalized Linear Mixed Models and need some help concerning the prediction of the random effects. More specifically, I don't understand the given representation of the conditional expectation of the random effect, i.e. $$ \mathbb{E}[X | Y] = \int f_{X|Y} (x|y)\: dx = \int \frac{f_{Y|X}(y|x)f_{X}(x)}{\int f_{Y|X}(y|x)f_{X}(x)dx} dx$$(the second equation being the one I don't understand)

This is the representation in general. In a one way classification, X would be the random effect, Y the response group (vector) for the random effect. 
Found in several papers and books of McCulloch et al.