We can similarly compute the "observed" and counterfactual probabilities of success of an individual with X 1 = 1 using predictions from PM 1 and PM 0 respectively.
RMSE is computed using the observed empirical crime proportions compared to the modeled proportion of crimes for each time period for each location.
The forecasting metrics defined as the correlation coefficient (r), Nash-Sutcliffe efficiency (ENS), Willmott's Index (WI), root-mean-square error (RMSE) and mean absolute error (MAE) computed between the observed and forecasted stream-flow data are employed to assess the ELM model's effectiveness.
[ 19] It compares the model-based (estimated) covariances with those computed from the observed data i.e. unconstrained covariance matrix.
To find its differential, compute v ¯ ⋅ v ¯ ′ ( W + J ) − v ¯ ⋅ v ¯ ′ ( W ) and keep the terms at the first order in J. Before computing the whole sum, observe that ( W + J ) k ⋅ C k, q ⋅ ( W + J ) ′ q − W k ⋅ C k, q ⋅ W ′ q = ∑ m = 0 k − 1 W m ⋅ J ⋅ W k − 1 − m ⋅ C k, q ⋅ W ′ q + ∑ m = 0 q − 1 W k ⋅ C k, q ⋅ W ′ m ⋅ J ′ ⋅ W ′ q − 1 − m + O ( ∥ J ∥ 2 ).
Computing the probability of observing a given heteroplasmy thus involves a sum, over all mtDNA states that correspond to that heteroplasmy, of the probability of that state.
More precisely, in addition to computing the probability of observing multiple non-reference base calls due to sequencing errors, CRISP compares the distribution of allele counts across multiple pools using contingency tables.
The general method for computing the probability of observing a particular mutational configuration, k ¯, which is defined as counts of mutations on t ¯ and can be interpreted as the likelihood, has been described in detail previously (Lohse et al. 2011, equation 1) and involves taking higher-order derivatives of the GF of genealogical branches.
