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As the quality of the lot deteriorates with p increasing, the probability of getting a high-quality sample P(x ≤ c) diminishes, or inversely, the probability of getting a low-quality sample 1 − P(x ≤ c) increases.
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If we hypothesize that the posterior can be expressed as a set of samples p ( x t - 1 ∣ Z t - 1 ) ≈ 1 N s ∑ i = 1 N s δ ( x t - 1 - x t - 1 ( i ) ), (5).
Let N (H/V) be the number of occurrences of a given ratio H/V within M samples; p(x) = N(H/V)/M is the estimate of the probability of occurrence of a certain value x of H/V (the actual p(x) would be with the limit of M to infinity).
If we use a rejection sampling scheme to obtain samples from p(x) by first sampling from p0 x), we can ask how many samples we will need on average from p0 to obtain one sample from p. In this scheme, we produce a sample x∼p0 x) and then decide whether to accept or reject the sample based on the criterion u ≤ e αU ( x ) e αT, (10).
Where, M indicates the number of FSFs in the background; k indicates the number of FSFs in the sample; N is the total number of FSFs of the two sets; n represents the total number of FSFs in sample; and P(X = k) is the probability that implies a chance that a random variable X has k FSFs for a given taxonomic group [ 29].
In the pseudo-Gibbs sampling process, missing values at the k th SNP were sampled from p (X ^ mi s k | X obs, X ^ mi s − k ) based on a classification and regression tree model (CART) (Breiman et al. 1984).
For any pair of mutations j, k and sample p, let Pr [ X p j ≥ X p k ] denote the posterior probability that X p j ≥ X p k.
P x samples (P1, P2, P3 etc) are samples in which to measure DNA damage-induced DNA strand breaks, and R x samples (R1, R2, R3 etc) are samples where cells are post-incubated to allow repair.
The maximum likelihood solution of unknown parameter α is regarded as the estimated value, and then, we sample the bimodal PDF p(x).
For each unit of i in the sample, we observe a p x 1 vector of pretreatment covariates, X i ; the treatment received, T i ; and the value of the outcome variable associated with treatment, Y i.
Sampling an action from p ( x ) = Σ θ p p ( x | θ ) is much cheaper than sampling an action from equation (18) because of the reversed causal order in θ and x, which implies that β/α→ 0 in equation (ii) instead of β/α→∞ as in equation (17).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com