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I was looking at the Luria–Delbrück experiment and its semi-log plot of experimental data along with Poisson and Luria-Delbrück models (referred to as P1 and P2 respectively from now on).

With P1(m) and P2(m) and n(m), the total number of trials that resulted in m mutants given in the semi-log plot, I was asked to calculate the log of the likelihood ratio, which means the following:

log( p(data|Lamarckian)/p(data|Darwinian) ) = log( p(data|Lamarckian) ) - log(p(data|Darwinian) )

Then, the book claims that $$\log(p(data|theory)) = \textrm{A}\Sigma_m n(m) \log(P_{theory}(m)) $$ for some constant A for normalization

So to calculate log( p(data|Lamarckian)/p(data|Darwinian) ), the book suggests that I just take the difference of P1 and P2 in the semi-log plot and multiply the difference by n(m), then sum over all m

which confuses me because if the above is true, then it seems to imply the following

$$\log(p(data|theory)) = \textrm{A}\Sigma_m n(m) \log(P_{theory}(m))= \textrm{A}\Sigma_m\log(P_{theory}(m)^{n(m)}) $$