Proportion of null proteins Sample Clauses

Proportion of null proteins. The strong zero assumption underlying the two-groups model states that: f1(z) = 0 ∀ z ∈ [−t∗, t∗] for some fixed t∗. Xxxxxxxx (2007)[118] and Efron [38, 39]), estimate p0 using the following simple construction. Let, f0 ∼ N (µ0, σ0) and H0(µ0, σ0) = t∗ ∫ −t∗ f0 = Φ t∗ − µ0 σ0 Φ −t∗ − µ0 − σ0 , and define the truncated normal distribution with density proportional to the normal distribution over [−t∗, t∗] and zero else where as, ft∗ (z) = f0(z) , z ∈ [−t∗, t∗] (3.14) 0 H0(µ0, σ0) Define, θt∗ ≡ t∗ ∫ −t∗ p0f0(z) = p0H0(µ0, σ0). (3.15) Then under the strong zero assumption, m0 ∼ Bin(m, θt∗ ) and the elements of z0 are i.i.d. with distribution given in (3.14), giving the likelihood Lt∗ (m, z0 | µ0, σ0, θt∗ ) = m m0 0 m θt∗ (1 − θt∗ ) m−m0 Y z∈z0 ft∗ (z). (3.16) 0 Maximizing Lt∗ yields, θˆt∗ = m0 . Then by definition (3.15), m pˆ = θˆt∗