Adjust Bayesian priors - Two Source Trophic Position

Adjust priors for two source trophic position model derived from Post 2002.

Usage

two_source_priors_params(
  a = NULL,
  b = NULL,
  c1 = NULL,
  c1_sigma = NULL,
  c2 = NULL,
  c2_sigma = NULL,
  n1 = NULL,
  n1_sigma = NULL,
  n2 = NULL,
  n2_sigma = NULL,
  dn = NULL,
  dn_sigma = NULL,
  tp_lb = NULL,
  tp_ub = NULL,
  sigma_lb = NULL,
  sigma_ub = NULL,
  bp = FALSE
)

Arguments

a

(\(\alpha\)) exponent of the random variable for beta distribution. Defaults to 1. See beta distribution for more information.

b

(\(\beta\)) shape parameter for beta distribution. Defaults to 1. See beta distribution for more information.

c1

mean (\(\mu\)) prior for the mean of the first \(\delta^{13}\)C baseline. Defaults to -21.

c1_sigma

variance (\(\sigma\))for the mean of the first \(\delta^{13}\)C baseline. Defaults to 1.

c2

mean (\(\mu\)) prior for or the mean of the second \(\delta^{13}\)C baseline. Defaults to -26.

c2_sigma

variance (\(\sigma\))for the mean of the first \(\delta^{13}\)C baseline. Defaults to 1.

n1

mean (\(\mu\)) prior for the mean of the first \(\delta^{15}\)N baseline. Defaults to 8.

n1_sigma

variance (\(\sigma\))for the mean of the first \(\delta^{15}\)N baseline. Defaults to 1.

n2

mean (\(\mu\)) prior for or the mean of the second \(\delta^{15}\)N baseline. Defaults to 9.5.

n2_sigma

variance (\(\sigma\)) for the mean of the second \(\delta^{15}\)N baseline. Defaults to 1.

dn

mean (\(\mu\)) prior value for \(\Delta\)N. Defaults to 3.4.

dn_sigma

variance (\(\sigma\)) for \(\delta^{15}\)N. Defaults to 0.5.

tp_lb

lower bound for priors for trophic position. Defaults to 2.

tp_ub

upper bound for priors for trophic position. Defaults to 10.

sigma_lb

lower bound for priors for \(\sigma\). Defaults to 0.

sigma_ub

upper bound for priors for \(\sigma\). Defaults to 10.

bp

logical value that controls whether informed priors are supplied to the model for both \(\delta^{15}\)N and \(\delta^{15}\)C baselines. Default is FALSE meaning the model will use uninformed priors, however, the supplied data.frame needs values for both \(\delta^{15}\)N and \(\delta^{15}\)C baseline (c1, c2, n1, and n2).

Value

stanvars object to be used with brms() call.

Details

We will use the following equations from Post 2002:

1. $$\delta^{13}C_c = \alpha * (\delta ^{13}C_1 - \delta ^{13}C_2) + \delta ^{13}C_2$$

2. $$\delta^{15}N = \Delta N \times (tp - \lambda_1) + n_1 \times \alpha + n_2 \times (1 - \alpha)$$

3. $$\delta^{15}N = \Delta N \times (tp - (\lambda_1 \times \alpha + \lambda_2 \times (1 - \alpha))) + n_1 \times \alpha + n_2 \times (1 - \alpha)$$

• The random exponent (\(\alpha\); a) and shape parameters (\(\beta\); b) for \(\alpha\). This prior assumes a beta distribution.

• The mean (c1; \(\mu\)) and variance (c1_sigma; \(\sigma\)) of the mean for the first \(\delta^{13}C\) for a given baseline. This prior assumes a normal distributions.

• The mean (c2;\(\mu\)) and variance (c2_sigma; \(\sigma\)) of the mean for the second \(\delta^{13}C\) for a given baseline. This prior assumes a normal distributions.

• The mean (n1; \(\mu\)) and variance (n1_sigma; \(\sigma\)) of the mean for the first \(\delta^{15}N\) for a given baseline. This prior assumes a normal distributions.

• The mean (n2;\(\mu\)) and variance (n2_sigma; \(\sigma\)) of the mean for the second \(\delta^{15}\)N for a given baseline. This prior assumes a normal distributions.

• The mean (dn; \(\mu\)) and variance (dn_sigma; \(\sigma\)) of \(\Delta\)N (i.e, trophic enrichment factor). This prior assumes a normal distributions.

• The lower (tp_lb) and upper (tp_ub) bounds for priors for trophic position. This prior assumes a uniform distributions.

• The lower (sigma_lb) and upper (sigma_ub) bounds for variance (\(\sigma\)). This prior assumes a uniform distributions.

See also

two_source_priors(), two_source_model(), and brms::brms()

Examples

two_source_priors_params()
#> $a
#> $a$name
#> [1] "a"
#> 
#> $a$sdata
#> [1] 1
#> 
#> $a$scode
#> [1] "real a;"
#> 
#> $a$block
#> [1] "data"
#> 
#> $a$position
#> [1] "start"
#> 
#> $a$pll_args
#> [1] "data real a"
#> 
#> 
#> $b
#> $b$name
#> [1] "b"
#> 
#> $b$sdata
#> [1] 1
#> 
#> $b$scode
#> [1] "real b;"
#> 
#> $b$block
#> [1] "data"
#> 
#> $b$position
#> [1] "start"
#> 
#> $b$pll_args
#> [1] "data real b"
#> 
#> 
#> $dn
#> $dn$name
#> [1] "dn"
#> 
#> $dn$sdata
#> [1] 3.4
#> 
#> $dn$scode
#> [1] "real dn;"
#> 
#> $dn$block
#> [1] "data"
#> 
#> $dn$position
#> [1] "start"
#> 
#> $dn$pll_args
#> [1] "data real dn"
#> 
#> 
#> $dn_sigma
#> $dn_sigma$name
#> [1] "dn_sigma"
#> 
#> $dn_sigma$sdata
#> [1] 0.5
#> 
#> $dn_sigma$scode
#> [1] "real dn_sigma;"
#> 
#> $dn_sigma$block
#> [1] "data"
#> 
#> $dn_sigma$position
#> [1] "start"
#> 
#> $dn_sigma$pll_args
#> [1] "data real dn_sigma"
#> 
#> 
#> $tp_lb
#> $tp_lb$name
#> [1] "tp_lb"
#> 
#> $tp_lb$sdata
#> [1] 2
#> 
#> $tp_lb$scode
#> [1] "real tp_lb;"
#> 
#> $tp_lb$block
#> [1] "data"
#> 
#> $tp_lb$position
#> [1] "start"
#> 
#> $tp_lb$pll_args
#> [1] "data real tp_lb"
#> 
#> 
#> $tp_ub
#> $tp_ub$name
#> [1] "tp_ub"
#> 
#> $tp_ub$sdata
#> [1] 10
#> 
#> $tp_ub$scode
#> [1] "real tp_ub;"
#> 
#> $tp_ub$block
#> [1] "data"
#> 
#> $tp_ub$position
#> [1] "start"
#> 
#> $tp_ub$pll_args
#> [1] "data real tp_ub"
#> 
#> 
#> $sigma_lb
#> $sigma_lb$name
#> [1] "sigma_lb"
#> 
#> $sigma_lb$sdata
#> [1] 0
#> 
#> $sigma_lb$scode
#> [1] "real sigma_lb;"
#> 
#> $sigma_lb$block
#> [1] "data"
#> 
#> $sigma_lb$position
#> [1] "start"
#> 
#> $sigma_lb$pll_args
#> [1] "data real sigma_lb"
#> 
#> 
#> $sigma_ub
#> $sigma_ub$name
#> [1] "sigma_ub"
#> 
#> $sigma_ub$sdata
#> [1] 10
#> 
#> $sigma_ub$scode
#> [1] "real sigma_ub;"
#> 
#> $sigma_ub$block
#> [1] "data"
#> 
#> $sigma_ub$position
#> [1] "start"
#> 
#> $sigma_ub$pll_args
#> [1] "data real sigma_ub"
#> 
#> 
#> attr(,"class")
#> [1] "stanvars"