The argument that I'm dealing is very specific, I hope to make you understand the problem without going into detail.

I have this score function:

\begin{align} score = MargL^q + MargL^{\theta} \end{align}


\begin{align} MargL^{\theta} = \prod_{X \in X}{\prod_{u}{\prod_x{\frac{\Gamma(\alpha_{x|u})}{\Gamma(\alpha_{x|b}+M[x|u])}}}} \times \prod_{x' \not = x}{\frac{\Gamma(\alpha_{xx'|u}+M[x,x'|u])}{\Gamma(\alpha_{xx'|u})}} \end{align}

\begin{align} MargL^q = \prod_{X \in X}{\prod_{u}{\prod_x{ \frac{\Gamma(\alpha_{x|u}+M[x|u]+1)(\tau_{x|u})^{\alpha_{x|u}+1}}{\Gamma(\alpha_{x|u}+1)(\tau_{x|u}+T[x|u])^{\alpha_{x|u}+M[x|u]+1}} }}} \end{align}

I know that $\alpha_{x|u}$ and $\tau_{x|u}$ are costant for each $x$ and for each $u$.

I also know $\alpha_{x|u} = \sum_{x'} \alpha_{x x'|u}$

and $M[x|u] = \sum_{x'} M[x,x'|u]$

In the literature, I found a rule concerning $MargL^{\theta}$ which tells me that under certain conditions, its value can no longer grow. Referring to a simple mathematical model is not said nothing about $MargL^q$.

Looking $MargL^{\theta}$ and $MargL^q$ structur you can say that if $MargL^{\theta}$ can not grow even then $MargL^q$ can? or otherwise make assumptions about it?


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