In practice, H0H0 is represented with the mathematical model λhypλhyp, which characterizes the hypothesized species SS in the audio feature space. Likewise λhyp‾ represents the alternative Abiraterone acetate H1H1. Thus the likelihood ratio (8) can be rewritten asequation(9)p(X λhyp)p(X λhyp‾).Furthermore, the logarithm of (9) gives representation of the log-likelihood ratio as:equation(10)Λ(X)=logp(X λhyp)-logp(X λhyp‾).The model λhypλhyp for H0H0 is well defined and can be estimated using the training dataset for the target bird species SS. However the model λhyp‾ for H1H1 is not well specified as it has to represent all possible alternatives to the hypothesized target species.
Given a collection of audio recordings from a large number of species that are representative of the community of sound-emitting species observed in the habitat, a single model λUBM∼λhyp‾ is build to represent the alternative hypothesis. It is also possible to use multiple background models tailored to specific sets of species or habitats, but the use of a single background model has advantages in terms of computational efficiency.