Method for determining sequence alignment significance

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x, P(x|KN1,K,λ(j)N1,λ+), using the Island method wherein KN1,K is determined using N1,K islands, λ(j)N1,λ+ is determined using N1,λ islands and j≧3;
• c. comparing P(x|KN1,K,λ(j)N1,λ+) to Plh;
• d. if P(x|KN1,K,λ(j)N1,λ+)≦Pth, determining a second estimate of the p-value of said alignment score x, P(x|KN2,K,λ(j)N2,λ+) using the Island method wherein KN2,K is determined using N2,K≧9000 islands, λ(j)N2,λ+ is determined using N2,λ≧9000 islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e. comparing P(x|KN2,K,λ(j)N2,λ+) to Pth;
• and
• f. if P(x|KN2,K,λ(j)N2,λ+)≦Pth, determining said alignment score is statistically significant, otherwise, determining said alignment score is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x, P(x|KN1,K,λ(j)N2,λ+), using the Island method wherein KN1,K is determined using N1,K islands, λ(j)N1,λ+ is determined using N1,λ islands and j≧3;
• c. comparing P(x|KN1,K,λ(j)N1,λ+) to Pth
• d. if P(x|KN1,K,λ(j)N1,λ+)≦Pth, determining a second estimate of the p-value of said alignment score x, P(x|KN2,K,λ(j)N2,λ+), using the Island method wherein KN2,K is determined using N2,K islands, λ(j)N2,λ+ is determined using N2,λ islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e. repeating steps c) and d) until determining a final estimate of the p-value of said alignment score, P(x|KNfinal,K,λ(j)Nfinal,λ+), using the, Island method wherein KNfinal,K is determined using Nfinal,K≧9000 islands, λ(j)Nfinal,λ+ is determined using Nfinal,λ≧9000 islands and j≧3;
• f. comparing P(x|KNfinal,K,λ(j)Nfinal,λ+) to Pth;
• and
• g. if P(x|KNfinal,K,λ(j)Nfinal,λ+)≦Pth determining said alignment score x is statistically significant, otherwise determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x, P(x|KN1,λ(j)N1+), using the Island method wherein KN1 and λ(j)N1+ are each determined using N1 islands and j>3;
• C. comparing P(x|KN1,λ(j)N1+) to Pth;
• d. if P(x|KN1,λ(j)N1+)≦Pth, determining a second estimate of the p-value of said alignment score x, P(x|KN2,λ(j)N2+), using the Island method wherein KN2 and λ(j)N2+ are each determined using N2 islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e. repeating steps c) and d) until determining a final estimate of the p-value of said alignment score, P(x|KNfinal,λ(j)Nfinal), using the Island method wherein KNfinal and λ(j)Nfinal+ are each determined using Nfinal≧9000 islands and j≧3, otherwise;
• f. comparing P(x|KNfinal,λ(j)Nfinal+) to Pth;
• and
• g. if P(x|KNfinal,λ(j)Nfinal+)≦Pth, determining said alignment score x is statistically significant, otherwise determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x, P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+), using the Island method wherein K(λ(j)N1,λ+)N1,K− is determined using N1,K islands, λ(j)N1,λ is determined using N1,λ islands and j≧3;
• c. comparing P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+) to Pth;
• and
• d if P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+)>Pth, determining said alignment score x is statistically insignificant, otherwise, determining said alignment score may or may not be statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x, P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+), using the Island method wherein K(λ(j)N1,λ+)N1,K− is determined using N1,K islands, λ(j)N1,λ is determined using N1,λ islands and j≧3;
• C. comparing P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+) to Pth;
• d. if P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+)≦Pth, determining a second estimate of the p-value to said alignment score x, P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N2,λ+), using the Island method wherein K(λ(j)N2,λ+)N2,K− is determined using N2,K≧9000 islands, λ(j)N2,λ+ is determined using N2,λ≧9000 islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e. comparing P(x|K(λ(j)N2,λ)N2,K−,λ(j)N2,λ+) to Pth;
• and
• if P(x|K(λ(j)N2,λ)N2,K−,λ(j)N2,λ+)≦Pth, determining said alignment score x is statistically significant, otherwise determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x P(x|K(λ(j)N1,λ+)N1,K−, λ(j)N1,2+), using the Island method wherein K(λ(j)N1,λ+)N1,K− is determined using N1,K islands, λ(j)N1,λ+ is determined using N1,λ islands and j≧3;
• c. comparing P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+) to Pth;
• d) if P(x|K(λ(j)N1,λ+)N1,K−,λ(j)N1,λ+)≦Pth, determining a second estimate of the p-value to said alignment score x, P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N2,λ+) using the Island method wherein K(λ(j)N2,λ+)N2,K−, is determined using N2,K islands, λ(j)N2,λ+ is determined using N2,λ islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e) repeating steps c) and d) until determining a final estimate of the p-value of said alignment score x, P(x|K(λ(j)Nfinal,λ+)Nfinal,K−λ(j)Nfinal,λ+), using the Island method wherein K(λ(j)Nfinal,λ+)Nfinal,K−is determined using Nfinal,K≧9000 islands, λ(j)Nfinal,λ+ is determined using Nfinal,λ≧9000 islands and j≧3;
• f) comparing P(x|K(λ(j)Nfinal,λ+)Nfinal,K−λ(j)Nfinal,λ+) to Pth;
• and
• g) if P(x|K(λ(j)Nfinal,λ+)Nfinal,K−λ(j)Nfinal,λ+)≦Pth determining said alignment score x is statistically significant, otherwise determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x P(x|K(λ(j)N+)N1−,λ(j)N1+), using the Island method wherein K(λ(j)N1+)N1− and λ(j)N1+ are each determined using N1 islands and j≧3;
• c. comparing P(x|K(λ(j)N1+)N1−,λ(j)N1+) to Pth;
• d. if P(x|K(λ(j)N1+)N1−,λ(j)N1+)≦Pth, determining a second estimate of the p-value to said alignment score x. P(x|K(λ(j)N2+)N2−,λ(j)N2+) using the Island method wherein K(λ(j)N2+)N2− and λ(j)N2+ are each determined using N2 islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• e) repeating steps c) and d) until determining a final estimate of the p-value of said alignment score x, P(x|K(λ(j)Nfinal+)Nfinal−,λ(j)Nfinal+), using the Island method wherein K(λ(j)Nfinal+)Nfinal− and λ(j)Nfinal+ are each determined using Nfinal≧9000 islands and j≧3;
• f) comparing P(x|K(λ(j)Nfinal+)Nfinal−,λ(j)Nfinal+) to Pth;
• and
• g) if P(x|K(λ(j)Nfinal+)Nfinal−,λ(j)Nfinal+)≦Pth determining said alignment score x is statistically significant, otherwise determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x P(x|K(λ(j)N1,λ+)N1,K+λ(j)N1,λ−), using the Island method wherein K(λ(j)N1,λ+)N1,K+ is determined using N1,K islands, λ(j)N1,λ+ and λ(j)N1,λ+ are each determined using N1,λ islands and j≧3
• c. comparing P(x|K(λ(j)N1,λ+)N1,K+,λ(j)N1,λ−) to Pth;
• d. if P(x|K(λ(j)N1,λ+))N1,K+,λ(j)N1,λ−)>Pth, determining a second estimate of the p-value to said alignment score x, P(x|K(λ(j)N2,λ+)N2,K+,λ(j)N2,λ+), using the Island method wherein K(λ(j)N2,λ+)N2,K− is determined using N2,K=N1,K islands, λ(j)N2,λ+ is determined using N2,λ=N1,λ islands and j≧3, otherwise, determining said alignment score x is statistically significant;
• e. comparing P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N1,λ+) to Pth;
• f if P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N1,λ+)≦Pth, determining a third estimate of the p-value of said alignment score x, P(x|K(λ(j)N3,λ+)N3,K−,λ(j)N3,λ+) using the Island method wherein K(λ(j)N3,λ+)N3,K+ is determined using, N3,λ≧9,000 islands, λ(j)N3λ− and λ(j)N3,λ+ are each determined using N3,λ≧9,000 islands and j≦3, otherwise, determining said alignment score x is statistically insignificant;
• g. comparing P(x|K(λ(j)N3,λ+)N3,K+,λ(j)N3,λ−) to p and
• h. if P(x|K(λ(j)N3,λ+)N3,K+,λ(j)N3,λ−)≦Pth, determining said alignment score x is statistically significant, otherwise, determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x P(x|K(λ(j)N1,λ+)N1,K+,λ(j)N1,λ−), using the Island method wherein K(λ(j)N1,λ+)N1,K+ is determined using N1,K islands, λ(j)N1,λ− and λ(j)N1,λ+ are each determined using N1,λ islands and j≦3
• C. comparing P(x|K(λ(j)N1,λ+)N1,K+,λ(j)N1,λ−)
• d. if P(x|K(λ(j)N1,λ)N1,K,λ(j)N1,λ−)>Pth, determining a second estimate of the p-value of said alignment score x, P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N2,λ+, using the Island method wherein K(λ(j)N2,λ+)N2,K− is determined using N2,K×N1,K islands, λ(j)N2,λ+ is determined using N2,λ×N1,λ islands and j≧3, otherwise, determining said alignment score x is statistically significant;
• e. comparing P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N2λ+) to Pth;
• f. if P(x|K(λ(j)N2,λ+)N2,K−,λ(j)N2λ+)≦Pth,determining a third estimate of the p-value of said alignment score x, P(x|K(λ(j)N3,λ+)N3,K+,λ(j)N3,λ−), using the Island method wherein K(λ(j)N3,λ+)N3,K+ is determined using N3,K islands, λ(j)N3,λ+ and λ(j)N3,λ− are each determined using N3,λ islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• g. repeating steps c)-f) until determining a final estimate of the p-value of said alignment score x, P(x|K(λ(j)Nfinal,λ+)Nfinal,K+,λ(j)Nfinal,λ−), using the Island method wherein K(λ(j)Nfinal,λ+)Nfinal,K+ is determined using Nfinal,K≧9000 islands, λ(j)Nfinal,λ− and λ(j)Nfinal,λ+ are each determined using Nfinal,λ≧9000 islands and j≧3;
• h. comparing P(x|K(λ(j)Nfinal,λ+))Nfinal,K+,λ(j)Nfinal,λ−) to Pth;
• and
• i. if P(x|K(λ(j)Nfinal,λ+)Nfinal,K+,λ(j)Nfinal,λ−)≦Pth, determining said alignment score x is statistically significant, otherwise, determining said alignment score x is statistically insignificant.

A method for determining whether an alignment score x, determined from the alignment of a first sequence with a second sequence, is statistically significant or insignificant comprising the steps of:

• a. determining a threshold p-value, Pth;
• b. determining a first estimate of the p-value of said alignment score x P(x|K(λ(j)N1+)N1+,λ(j)N1−), using the Island method wherein K(λ(j)N1+)N1+,λ(j)N1+) and λ(j)N1− are each determined using N1 islands and j>3;
• c. comparing P(x|K(λ(j)N1+)N1+,λ(j)N1−) to Pth;
• d. if P(x|K(λ(j)N1+)N1+,λ(j)N1−)>Pth, determining a second estimate of the p-value of said alignment score x, P(x|K(λ(j)N2+)N2−,λ(j)N2+), using the Island method wherein K(λ(j)N2+)N2− and λ(j)N2+ are each determined using N2=N1, islands and j≧3, otherwise, determining said alignment score x is statistically significant;
• e. comparing P(x|K(λ(j)N2+)N2−,λ(j)N2+) to Pth if P(x|K(λ(j)N2+)N2−,λ(j)N2+)≦Pth, determining a third estimate of the p-value of said alignment score x, P(x|K(λ(j)N3+)N3+,λ(j)N3−), using the Island method wherein K(λ(j)N3+)N3+,λ(j)N3+ and λ(j)N3− are each determined using N3 islands and j≧3, otherwise, determining said alignment score x is statistically insignificant;
• g. repeating steps c)-f) until determining a final estimate of the p-value of said alignment score x, P(x|K(λ(j)Nfinal+)Nfinal+,λ(j)Nfinal−), using the Island method wherein K(λ(j)Nfinal+)Nfinal+,λ(j)Nfinal− and λ(j)Nfinal− are each determined using Nfinal≧9000 islands and j≧3;
• h. comparing P(x|K(λ(j)Nfinal+)Nfinal+,λ(j)Nfinal−) to Pth and
• i. if P(x|K(λ(j)Nfinal+)Nfinal+,λ(j)Nfinal−)≦Pth, determining said alignment score x is statistically significant, otherwise, determining said alignment score x is statistically insignificant.