Bayesian inference from count data using discrete uniform priors

Description

This package allows to infer population sizes using a binomial likelihood and least informative discrete uniform priors.

Author(s)

Federico Comoglio federico.comoglio@gmail.com

Maurizio Rinaldi

References

Comoglio F, Fracchia L, Rinaldi M (2013) Bayesian Inference from Count Data Using Discrete Uniform Priors. PLoS ONE 8(10): e74388

An S4 class to store measurements (count data, sampling fractions), prior support and posterior parameters

Description

An S4 class to store measurements (count data, sampling fractions), prior support and posterior parameters

Usage

## S4 method for signature 'Counts'
get_counts(object)

## S4 method for signature 'Counts'
get_fractions(object)

## S4 replacement method for signature 'Counts'
set_counts(object) <- value

## S4 replacement method for signature 'Counts'
set_fractions(object) <- value

## S4 method for signature 'Counts'
compute_posterior(
  object,
  n_start,
  n_end,
  replacement = FALSE,
  b = 1e-10,
  alg = "dup"
)

## S4 method for signature 'Counts'
get_posterior_param(object, low = 0.025, up = 0.975, ...)

## S4 method for signature 'Counts'
plot_posterior(object, low = 0.025, up = 0.975, xlab, step, ...)

Arguments

Value

counts vector from a Counts object

fractions vector from a Counts object

an object of class Counts

an object of class Counts

an object of class Counts

an object of class Counts

no return value, called for side effects

Methods (by generic)

• get_counts(Counts): Returns counts from a Counts object

• get_fractions(Counts): Returns fractions from a Counts object

• set_counts(Counts) <- value: Replaces counts of a Counts object with the provided values

• set_fractions(Counts) <- value: Replaces fractions of a Counts object with the provided values

• compute_posterior(Counts): Compute the posterior probability distribution of the population size

• get_posterior_param(Counts): Extract statistical parameters (e.g. credible intervals) from a posterior probability distribution

• plot_posterior(Counts): Plot posterior probability distribution and posterior parameters

Slots

counts

integer vector of counts (required)

fractions

numeric vector of sampling fractions (required)

n_start

start of prior support range. If omitted and total counts greater than zero, computed as 0.5 * mle, where mle is the maximum likelihood estimate of the population size

n_end

end of prior support range. If omitted and total counts greater than zero, computed as 2 * mle, where mle is the maximum likelihood estimate of the population size

f_product

product of (1-fractions)

mle

maximum likelihood estimate of the population size (ratio between total counts and total sampling fraction)

norm_constant

normalization constant

posterior

numeric vector of posterior probabilities over the prior support

map_p

maximum of posterior probability

map_index

index of prior support corresponding to the maximum a posteriori

map

maximum a posteriori of population size

q_low

lower bound of the credible interval

q_low_p

probability of the lower bound of the credible interval

q_low_index

index of the prior support corresponding to q_low

q_low_cum_p

cumulative posterior probability from n_start to q_low (left tail)

q_up

upper bound of the credible interval

q_up_p

probability of the upper bound of the credible interval

q_up_index

index of the prior support corresponding to q_high

q_up_cum_p

cumulative posterior probability from q_high to n_end (right tail)

gamma

logical, TRUE if posterior computed using a Gamma approximation

Note

The posterior slot contains either the PMF or a logical value used to compute posterior parameters with a Gamma approximation (see reference for details)

Lower and upper bounds of the credibile interval are computed at a default confidence level of 95

For more details on the normalization constant, see Corollary 1 in reference

Author(s)

Federico Comoglio

References

Comoglio F, Fracchia L and Rinaldi M (2013) Bayesian inference from count data using discrete uniform priors. PLoS ONE 8(10): e74388

See Also

compute_posterior, get_posterior_param

Examples

# constructor:
# create an object of class 'Counts'
new_counts(counts = c(30, 35), fractions = c(0.075, 0.1))

# same, using new
new("Counts", counts = c(30, 35), fractions = c(0.075, 0.1))

Compute ECDF (empirical cumulative distribution function)

Description

Compute ECDF (empirical cumulative distribution function)

Usage

compute_ecdf(posterior)

Arguments

Value

numeric vector with empirical cumulative distribution function (cumulative sum of posterior)

Compute normalization constant

Description

Compute normalization constant

Usage

compute_normalization_constant(counts, n_start, n_end, f_product)

Arguments

Value

normalization constant to compute posterior density

Compute the posterior probability distribution of the population size for an object of class Counts

Description

Compute the posterior probability distribution of the population size using a discrete uniform prior and a binomial likelihood ("dup" algorithm, Comoglio et al.). An approximation using a Gamma prior and a Poisson likelihood is used when applicable ("gamma" algorithm) method (see Clough et al. for details)

Usage

compute_posterior(
  object,
  n_start,
  n_end,
  replacement = FALSE,
  b = 1e-10,
  alg = "dup"
)

Arguments

Value

an object of class Counts

Author(s)

Federico Comoglio

References

Comoglio F, Fracchia L and Rinaldi M (2013) Bayesian inference from count data using discrete uniform priors. PLoS ONE 8(10): e74388

Clough HE et al. (2005) Quantifying Uncertainty Associated with Microbial Count Data: A Bayesian Approach. Biometrics 61: 610-616

Examples

counts <- new_counts(counts = c(20,30), fractions = c(0.075, 0.10))

# default parameters ("dup" algorithm, sampling without replacement, default prior support)
posterior <- compute_posterior(counts)

# custom prior support ("dup" algorithm)
posterior <- compute_posterior(counts, n_start = 0, n_end = 1e3)

# gamma prior ("gamma" algorithm)
posterior <- compute_posterior(counts, alg = "gamma")

# sampling with replacement
posterior <- compute_posterior(counts, replacement = TRUE)

Compute posterior probability with replacement

Description

Compute posterior probability with replacement

Usage

compute_posterior_with_replacement(n, counts, f_product, denominator)

Arguments

Value

posterior probability of n

See Also

compute_normalization_constant

Compute sum of terms (function F, Comoglio et al.)

Description

Compute sum of terms (function F, Comoglio et al.)

Usage

compute_sum(counts, n, f_product)

Arguments

Value

sum of terms in function F

Compute single term (function F, Comoglio et al.)

Description

Compute single term (function F, Comoglio et al.)

Usage

compute_term(counts, n, f_product, t)

Arguments

Value

single term of function F

Compute posterior probability using a Gamma-Poisson model (Clough et al.)

Description

Compute posterior probability using a Gamma-Poisson model (Clough et al.)

Usage

gamma_poisson_clough(object, n_start, n_end, a = 1, b = 1e-10)

Arguments

Value

vector of posterior probabilities

Note

if support range spans more than 100k values, the posterior is not computed

Get counts slot for an object of class Counts

Description

Get counts slot for an object of class Counts

Usage

get_counts(object)

Arguments

Value

counts vector from a Counts object

Get fractions slot for an object of class Counts

Description

Get fractions slot for an object of class Counts

Usage

get_fractions(object)

Arguments

Value

fractions vector from a Counts object

Compute posterior probability distribution parameters (e.g. credible intervals) for an object of class Counts

Description

This function computes posterior parameters and credible intervals at the given confidence level (default to 95%).

Usage

get_posterior_param(object, low = 0.025, up = 0.975, ...)

Arguments

Value

an object of class Counts

Author(s)

Federico Comoglio

References

Comoglio F, Fracchia L and Rinaldi M (2013) Bayesian inference from count data using discrete uniform priors. PLoS ONE 8(10): e74388

Clough HE et al. (2005) Quantifying Uncertainty Associated with Microbial Count Data: A Bayesian Approach. Biometrics 61: 610-616

Examples

counts <- new_counts(counts = c(20,30), fractions = c(0.075, 0.10))

# default parameters ("dup" algorithm, sampling without replacement, default prior support)
posterior <- compute_posterior(counts)

get_posterior_param(posterior)

Initialize Counts class

Description

Initialize Counts class

Usage

## S4 method for signature 'Counts'
initialize(.Object, counts, fractions)

Arguments

Constructor for Counts class

Description

Constructor for Counts class

Usage

new_counts(counts, fractions)

Arguments

Value

An object of the Counts class

Plot method for Counts class

Description

Plot method for Counts class

Usage

## S4 method for signature 'Counts'
plot(x, y, ...)

Arguments

Value

no return value, called for side effects

Plot posterior probability distribution and display posterior parameters for an object of class Counts

Description

Plot posterior probability distribution and display posterior parameters for an object of class Counts

Usage

plot_posterior(object, low = 0.025, up = 0.975, xlab, step, ...)

Arguments

Value

no return value, called for side effects

Author(s)

Federico Comoglio

References

Comoglio F, Fracchia L and Rinaldi M (2013) Bayesian inference from count data using discrete uniform priors. PLoS ONE 8(10): e74388

Examples

counts <- new_counts(counts = c(20,30), fractions = c(0.075, 0.10))

# default parameters ("dup" algorithm, sampling without replacement, default prior support)
posterior <- compute_posterior(counts)

# plot posterior
plot_posterior(posterior, type = 'l', lwd = 3, col = 'blue3')

Set counts slot for an object of class Counts

Description

Set counts slot for an object of class Counts

Usage

set_counts(object) <- value

Arguments

Value

an object of class Counts

Set fractions slot for an object of class Counts

Description

Set fractions slot for an object of class Counts

Usage

set_fractions(object) <- value

Arguments

Value

an object of class Counts

Print method for Counts class

Description

Print method for Counts class

Usage

## S4 method for signature 'Counts'
show(object)

Arguments

Value

no return value, called for side effects

Summary method for Counts class

Description

Summary method for Counts class

Usage

## S4 method for signature 'Counts'
summary(object, ...)

Arguments

Value

no return value, called for side effects