Furthermore, even conceding that the trial judge at the outset applied an erroneous "probability of doubt" standard in deciding that plaintiffs failed to meet their burden of establishing a cause of action, the trial judge faced a conundrum that must be adequately explained.
Therefore, to compare the performance in terms of both the detection probability and the false alarm probability, we define an erroneous decision probability P e as follows: begin{array}rcl@ P_{e}=P_{text{OFF}}P_{f}+P_{text{ON}}(1~-~P_{d}) end{array} (37).
This gives us a total erroneous
We combine quality values from identical k-mers in the reads: for a multiset of k-mers X that agree on the jth nucleotide, it is erroneous with probability Π x ∈ X q x[ j].
We defined a SNP site of an individual as erroneous with a probability of P err, and typed the site as either homozygous or heterozygous with equal probabilities.
Therefore, all the subsequent decisions in the frame will be erroneous with high probability.
Under this assumption, if the true base is A, an observation of M could result either from a correct call of A (probability 1 − ε) or an erroneous call of C (probability ε/3) and therefore has probability 1 − 2 ε/3, and similarly if the true base is C.
If we now use the defined condition as a rejection of the general null hypothesis of no linkage disequilibrium, then the described probability is the probability of erroneous rejection of the general null hypothesis based on the simultaneous combination of separate test results.
Otherwise, we compute the probability that the base call r i (which matches v i ) is erroneous, by calculating Binomial probabilities for the three alternative bases x: (1) Pr X ≥ x = ∑ j = k n i n t k p j 1 − p n i − j where k = the observed read count for base x at position i.
The probability is equal to the probability of erroneous decoding at.
