# JAGS Model Code

The following three tables describe the distributions, functions and operators used in JAGS model code on this site. For additional information on the JAGS dialect of the BUGS language see the JAGS User Manual.

### JAGS Distributions

Distribution Description
dbern(p) Bernoulli where p is the probability
dbin(p, n) Binomial where p is the probability and n the number of trials
dcat(pi) Categorical where pi is a vector of (possibly unnormalized) probabilities
ddirch(alpha) Dirichlet where alpha is a vector of positive concentration parameters
dgamma(a, b) Gamma where a is the shape and b the rate
dlnorm(mu, sd^-2) Log-normal where mu is the log mean and sd the log standard deviation
dmnorm(mu, Omega) Multivariate normal where mu is a k-dimensional vector of the means and Omega is a k x k positive definite matrix
dnorm(mu, sd^-2) Normal where mu is the mean and sd the standard deviation
dpois(lambda) Poisson where lambda is the mean (and the variance)
dunif(a, b) Uniform where a is the lower limit and b the upper limit
dwish(R, k) Wishart where R is a p x p positive definite matrix and k >= p

### JAGS Functions

Function Description
equals(x, y) Test for equality of x and y
exp(x) Exponential of x
ifelse(x, a, b) If x then a else b
inprod(x,y) Inner product of x and y
inverse(x) Matrix inverse were x is a symmetric positive deﬁnite matrix
length(x) Length of vector x
log(x) Natural logarithm of x
logit(x) Log-odds of x
max(x,y) Maximum of x and y
min(x,y) Minimum of x and y
phi(x) Standard normal cumulative distribution function for x
pnorm(x, mu, sd^-2) Cumulative distribution function for x with a normal distribution with a mean of mu and standard deviation of sd
round(x) Round to integer away from 0
step(x) Test for x >= 0
sum(a) Sum of elements of a
T(x,y) Truncate distribution so that values lie between x and y

### JAGS Operators

Operator Description
<- Deterministic relationship
~ Stochastic relationship
1:n Vector of integers from 1 to n
a[1:n] Subset of first n values in a
for (i in 1:n) {...} Repeat for 1 to n times incrementing i each time
x^y Power where x is raised to the power of y