plot_prior_COI: Plot prior on COI

Description Usage Arguments Details

Description

Produce plot of the prior on COI for given parameters. Options include the uniform distribution, and a modified form of Poisson and negative binomial distribution (see details).

Usage

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plot_prior_COI(COI_model = "poisson", COI_mean = 3,
  COI_dispersion = 2, COI_max = 20)

Arguments

COI_model

the type of prior on COI. Must be one of "uniform", "poisson", or "nb" (negative binomial)

COI_mean

the prior mean (before truncating at COI_max). Note that this parameter only applies under the "poisson" and "nb" models

COI_dispersion

the ratio of the variance to the mean of the prior on COI. Only applies under the negative binomial model. Must be >1

COI_max

the maximum COI allowed. Distributions are truncated at this value

Details

The prior on COI can be uniform, Poisson, or negative binomial. In the uniform case there is an equal chance of any given sample having a COI between 1 and COI_max (inclusive). In the Poisson and negative binomial cases it is important to note that the distribution is over (COI-1), rather than over COI. This is because both Poisson and negative binomial distributions allow for 0 values, which cannot be the case here because observed samples must contain at least 1 genotype. Poisson and negative binomial distributions are also truncated at COI_max.

The full probability mass distribution for the Poisson case with COI_mean = μ and COI_max = M can be written

Pr(COI = n) = z (μ-1)^(n-1) exp(-(μ-1)) / (n-1)!

where z is a normalising constant that ensures the distribution sums to unity, and is defined as:

1/z = ∑_{i=1}^M (μ-1)^(i-1) exp(-(μ-1)) / (i-1)!

The mean of this distribution will generally be very close to μ, and the variance will be close to μ-1 (strictly it will approach these values as M tends to infinity).

The full probability mass distribution for the negative binomial case with COI_mean = μ, COI_dispersion = v/μ and COI_max = M can be written

Pr(COI = n) = z Γ(n-1+N)/( Γ(N)(n-1)! ) p^N (1-p)^(n-1)

where N = (μ-1)^2/(v-μ+1), p = (μ-1)/v, and z is a normalising constant that ensures the distribution sums to unity, and is defined as:

1/z = ∑_{i=1}^M Γ(i-1+N)/( Γ(N)(i-1)! ) p^N (1-p)^(i-1)

The mean of this distribution will generally be very close to μ and the variance will be close to v (strictly it will approach these values as M tends to infinity).


bobverity/MALECOT documentation built on May 13, 2019, 4:01 a.m.