priors {Bernadette}

Prior distributions and options

Description

The functions described on this page are used to specify the prior-related arguments of the modeling functions in the Bernadette package.

The default priors used in the Bernadette modeling functions are intended to be weakly informative. For many applications the defaults will perform well, but prudent use of more informative priors is encouraged. Uniform prior distributions are possible (e.g. by setting stan_igbm's prior argument to NULL) but, unless the data is very strong, they are not recommended and are not non-informative, giving the same probability mass to implausible values as plausible ones.

Usage

normal(location = 0, scale = NULL)

student_t(df = 1, location = 0, scale = NULL)

cauchy(location = 0, scale = NULL)

gamma(shape = 2, rate = 1)

exponential(rate = 1)

Arguments

location

Prior location. In most cases, this is the prior mean, but for cauchy (which is equivalent to student_t with df=1), the mean does not exist and location is the prior median. The default value is 0.

scale

Prior scale. The default depends on the family (see Details).

df

Degrees of freedom.

shape

Prior shape for the gamma distribution. Defaults to 2.

rate

Prior rate for the exponential distribution. Defaults to 1. For the exponential distribution, the rate parameter is the reciprocal of the mean.

Details

The details depend on the family of the prior being used:

Student t family

Family members:

• normal(location, scale)

• student_t(df, location, scale)

• cauchy(location, scale)

As the degrees of freedom approaches infinity, the Student t distribution approaches the normal distribution and if the degrees of freedom are one, then the Student t distribution is the Cauchy distribution. If scale is not specified it will default to 2.5.

Value

A named list to be used internally by the Bernadette model fitting functions.

See Also

The vignette for the Bernadette package discusses the use of some of the supported prior distributions.

Examples

# Age-specific mortality/incidence count time series:
# Age-specific mortality/incidence count time series:
data(age_specific_mortality_counts)
data(age_specific_infection_counts)

# Import the age distribution for Greece in 2020:
age_distr <- age_distribution(country = "Greece", year = 2020)

# Lookup table:
lookup_table <- data.frame(Initial = age_distr$AgeGrp,
                          Mapping = c(rep("0-39",  8),
                                      rep("40-64", 5),
                                      rep("65+"  , 3)))

# Aggregate the age distribution table:
aggr_age <- aggregate_age_distribution(age_distr, lookup_table)

# Import the projected contact matrix for Greece:
conmat <- contact_matrix(country = "GRC")

# Aggregate the contact matrix:
aggr_cm <- aggregate_contact_matrix(conmat, lookup_table, aggr_age)

# Aggregate the IFR:
ifr_mapping <- c(rep("0-39", 8), rep("40-64", 5), rep("65+", 3))

aggr_age_ifr <- aggregate_ifr_react(age_distr, ifr_mapping, age_specific_infection_counts)

# Infection-to-death distribution:
ditd <- itd_distribution(ts_length  = nrow(age_specific_mortality_counts),
                         gamma_mean = 24.19231,
                         gamma_cv   = 0.3987261)

# Can assign priors to names:
N05      <- normal(0, 5)
Gamma22  <- gamma(2,2)
igbm_fit <- stan_igbm(y_data                      = age_specific_mortality_counts,
                      contact_matrix              = aggr_cm,
                      age_distribution_population = aggr_age,
                      age_specific_ifr            = aggr_age_ifr[[3]],
                      itd_distr                   = ditd,
                      likelihood_variance_type    = "quadratic",
                      prior_volatility            = N05,
                      prior_nb_dispersion         = Gamma22,
                      algorithm_inference         = "optimizing")