Probability distributions

Constructors for the probability distributions supported by EpiNow2 as dist_spec objects.

Usage

LogNormal(meanlog, sdlog, mean, sd, ...)

Gamma(shape, rate, scale, mean, sd, ...)

Normal(mean, sd, ...)

Exp(rate, mean, ...)

Weibull(shape, scale, mean, sd, ...)

NonParametric(pmf, ...)

Fixed(value, ...)

Dirichlet(alpha, prior, concentration, ...)

Arguments

meanlog, sdlog

mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively.

mean, sd

mean and standard deviation of the distribution

...

arguments to define the limits of the distribution that will be passed to bound_dist()

shape, scale

shape and scale parameters. Must be positive, scale strictly.

rate

an alternative way to specify the scale.

pmf

Probability mass of the given distribution; this is passed as either a zero-indexed numeric vector (i.e. the fist entry represents the probability mass of zero) or a dist_spec (e.g. generated by Dirichlet()). If a numeric vector is not summing to one it will be normalised to sum to one internally.

value

Value of the fixed (delta) distribution

alpha

A positive numeric vector of concentration parameters.

prior

Either a numeric PMF vector (zero-indexed, i.e. the first entry represents probability mass at zero) or a dist_spec object. If a dist_spec object is provided it will be discretised and the PMF extracted. If numeric, it will be normalised to sum to one internally.

concentration

A positive scalar controlling how tightly the Dirichlet prior concentrates around the supplied PMF. The Dirichlet alpha vector is computed as alpha_i = concentration * p_i where p_i is the prior PMF. Guidance on values:

concentration = 1: weak prior, each alpha equals the PMF value (near-uniform for roughly equal PMF entries)
concentration = 5-20: moderate flexibility around the reference shape
concentration = 50+: strong anchoring to the reference PMF

Value

A dist_spec representing a distribution of the given specification.

Details

Probability distributions are ubiquitous in EpiNow2, usually representing epidemiological delays (e.g., the generation time for delays between becoming infecting and infecting others; or reporting delays)

They are generated using functions that have a name corresponding to the probability distribution that is being used. They generated dist_spec objects that are then passed to the models underlying EpiNow2. All parameters can be given either as fixed values (a numeric value) or as uncertain values (a dist_sepc). If given as uncertain values, currently only normally distributed parameters (generated using Normal()) are supported.

Each distribution has a representation in terms of "natural" parameters (the ones used in stan) but can sometimes also be specified using other parameters such as the mean or standard deviation of the distribution. If not given as natural parameters then these will be calculated from the given parameters. If they have uncertainty, this will be done by random sampling from the given uncertainty and converting resulting parameters to their natural representation.

Currently available distributions are lognormal, gamma, normal, fixed (delta), nonparametric, and estimated nonparametric. The nonparametric is a special case where the probability mass function is given directly as a numeric vector. The estimated nonparametric allows the PMF to be estimated during model fitting using a Dirichlet prior.

Examples

LogNormal(mean = 4, sd = 1)
#> - lognormal distribution:
#>   meanlog:
#>     1.4
#>   sdlog:
#>     0.25
LogNormal(mean = 4, sd = 1, max = 10)
#> - lognormal distribution (max: 10):
#>   meanlog:
#>     1.4
#>   sdlog:
#>     0.25
# If specifying uncertain parameters, use the natural parameters
LogNormal(meanlog = Normal(1.5, 0.5), sdlog = 0.25, max = 10)
#> - lognormal distribution (max: 10):
#>   meanlog:
#>     - normal distribution:
#>       mean:
#>         1.5
#>       sd:
#>         0.5
#>   sdlog:
#>     0.25
Gamma(mean = 4, sd = 1)
#> - gamma distribution:
#>   shape:
#>     16
#>   rate:
#>     4
Gamma(shape = 16, rate = 4)
#> - gamma distribution:
#>   shape:
#>     16
#>   rate:
#>     4
Gamma(shape = Normal(16, 2), rate = Normal(4, 1))
#> - gamma distribution:
#>   shape:
#>     - normal distribution:
#>       mean:
#>         16
#>       sd:
#>         2
#>   rate:
#>     - normal distribution:
#>       mean:
#>         4
#>       sd:
#>         1
Normal(mean = 4, sd = 1)
#> - normal distribution:
#>   mean:
#>     4
#>   sd:
#>     1
Normal(mean = 4, sd = 1, max = 10)
#> - normal distribution (max: 10):
#>   mean:
#>     4
#>   sd:
#>     1
Exp(rate = 1)
#> - exp distribution:
#>   rate:
#>     1
Exp(mean = 4)
#> - exp distribution:
#>   rate:
#>     0.25
Weibull(shape = 1, scale = 1)
#> - weibull distribution:
#>   shape:
#>     1
#>   scale:
#>     1
Weibull(shape = 1, scale = 1, max = 10)
#> - weibull distribution (max: 10):
#>   shape:
#>     1
#>   scale:
#>     1
Weibull(mean = 4, sd = 1)
#> - weibull distribution:
#>   shape:
#>     4.5
#>   scale:
#>     4.4
NonParametric(c(0.1, 0.3, 0.2, 0.4))
#> - nonparametric distribution
#>   PMF: [0.1 0.3 0.2 0.4]
NonParametric(c(0.1, 0.3, 0.2, 0.1, 0.1))
#> - nonparametric distribution
#>   PMF: [0.12 0.37 0.25 0.12 0.12]

# With a Dirichlet prior
NonParametric(pmf = Dirichlet(c(1, 1, 1, 1)))
#> - nonparametric distribution
#>   PMF: [0.25 0.25 0.25 0.25]
Fixed(value = 3)
#> - fixed value:
#>   3
Fixed(value = 3.5)
#> - fixed value:
#>   3.5
Dirichlet(c(1, 1, 1, 1))
#> - dirichlet distribution:
#>   alpha:
#>     1111
Dirichlet(prior = c(0.1, 0.3, 0.4, 0.2), concentration = 10)
#> - dirichlet distribution:
#>   alpha:
#>     1342

Usage

Arguments

Value

Details

See also

Examples