model{
  
Omega[1,1] <- 1
Omega[1,2] <- 0
Omega[2,1] <- 0
Omega[2,2] <- 1

pi <- 3.141592653589

# priors on process uncertainty
iSigma[1:2,1:2] ~ dwish(Omega[,], 2)  
Sigma[1:2,1:2] <- inverse(iSigma[,])

## mean turn angle: theta[1] (transient), theta[2] (ARS)
tmp[1] ~ dbeta(10, 10)
tmp[2] ~ dbeta(10, 10)
theta[1] <- (2 * tmp[1] - 1) * pi
theta[2] <- tmp[2] * pi * 2
## move persistence: gamma[1] (transient), gamma[2] (ARS)
## dev multiplier ensures gamma[1] > gamma[2], prevents state label switching
gamma[1] ~ dbeta(5, 1)
dev ~ dbeta(1, 1)
gamma[2] <- gamma[1] * dev
## behavioural state switching probabilities: alpha ``matrix''
alpha[1] ~ dbeta(1, 1)
alpha[2] ~ dbeta(1, 1)
## probabilities of initial behavioural state (transient or ARS)
lambda[1] ~ dbeta(1, 1)
lambda[2] <- 1 - lambda[1]

for(k in 1:N){
logpsi[k] ~ dunif(-10, 10)  #prior on scaling parameter for t-dist. error variances
psi[k] <- exp(logpsi[k])

b[Xidx[k]] ~ dcat(lambda[])  # assign behav. mode for first obs

for(i in 1:2){
x[Xidx[k],i] ~ dnorm(0, 0.0001)	
}

# assume simple random walk to estimate 2nd regular position
x[(Xidx[k]+1),1:2] ~ dmnorm(x[Xidx[k],], iSigma[,])

# transition equation
for(t in (Xidx[k]+1):(Xidx[k+1]-2)){
phi[t,1] <- alpha[b[t-1]]
phi[t,2] <- 1 - alpha[b[t-1]]
b[t] ~ dcat(phi[t,])

x.mn[t,1] <- x[t,1] + (cos(theta[b[t]]) * (x[t,1] - x[t-1,1]) - sin(theta[b[t]]) * (x[t,2] - x[t-1,2])) * gamma[b[t]]
x.mn[t,2] <- x[t,2] + (sin(theta[b[t]]) * (x[t,1] - x[t-1,1]) + cos(theta[b[t]]) * (x[t,2] - x[t-1,2])) * gamma[b[t]]

# predict next location (with error)		
x[t+1,1:2] ~ dmnorm(x.mn[t,], iSigma[,])	
}

zeta[k,1] <- alpha[b[Xidx[k+1]-2]]
zeta[k,2] <- 1 - zeta[k,1]
b[Xidx[k+1]-1] ~ dcat(zeta[k,])

# robust measurement equation
for(t in (Xidx[k]+1):(Xidx[k+1]-1)){  # loops over regular time intervals (t)
for(i in idx[t]:(idx[t+1]-1)){  # loops over observed locations within interval t
for(q in 1:2){
itau2.psi[i,q] <- psi[k] * itau2[i,q]
y[i,q] ~ dt(x[t,q], itau2.psi[i,q], nu[i,q])
} #q
} #i
}	#t
} #k
}