A search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks is presented. Events with hadronic jets and one or two oppositely charged leptons are selected from a data sample corresponding to an integrated luminosity of 19.5 fb$^{-1}$ collected by the CMS experiment at the LHC in pp collisions at a centre-of-mass energy of 8 TeV. In order to separate the signal from the larger $\mathrm{t \bar{t}}$+jets background, this analysis uses a matrix element method that assigns a probability density value to each reconstructed event under signal or background hypotheses. The ratio between the two values is used in a maximum likelihood fit to extract the signal yield. The results are presented in terms of the measured signal strength modifier, $\mu$, relative to the standard model prediction for a Higgs boson mass of 125 GeV. The observed (expected) exclusion limit at a 95% confidence level is $\mu$ lower than 4.2 (3.3), corresponding to a best fit value $\hat{\mu}=1.2^{+1.6}_{-1.5}$.

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