#include <Rcpp.h>
using namespace Rcpp;



// This file contains the following functions:

// linpredcompute - computing the linear predictor for covariates.
// quadform - computing quadratic forms phi %*% Q %*% theta.
// binomialbetaupdateMALA - update regression parameters in the binomial model using MALA
// binomialbetaupdateRW - update regression parameters in the binomial model using RW
// binomialcarupdate - update random effects in the binomial model
// binomialindepupdate - update the independent effects in the binomial model
// poissonbetaupdateMALA - update regression parameters in the poisson model using MALA
// poissonbetaupdateRW - update regression parameters in the poisson model using RW
// poissoncarupdate - update random effects in the poisson model
// poissonindepupdate - update the independent effects in the poisson model
// gaussiancarupdate - update random effects in the Gaussian model
// binomialmcarupdate - update random effects in the binomial MCAR model
// poissonmcarupdate - update random effects in the poisson MCAR model

// [[Rcpp::export]]
NumericVector linpredcompute(NumericMatrix X, const int nsites, const int p, 
                          NumericVector beta, NumericVector offset)
{
//Create new objects
// Compute the linear predictor
NumericVector linpred(nsites);
double temp; 


//  Compute the linear predictor via a double for loop
     for(int j = 0; j < nsites; j++)
     {
     temp = 0;
      
          for(int l = 0; l < p; l++) temp = temp + X(j,l) * beta[l];     
          
     linpred[j] = temp + offset[j];  
     }


// Return the result
return linpred;
}




// [[Rcpp::export]]
double quadform(NumericMatrix Wtriplet, NumericVector Wtripletsum, const int n_triplet, const int nsites, 
                    NumericVector phi, NumericVector theta, double rho)
{
// Compute a quadratic form for the random effects
// Create new objects 
double tau2_posteriorscale;
double tau2_quadform = 0, tau2_phisq = 0;
int row, col;
   
   
// Compute the off diagonal elements of the quadratic form
     for(int l = 0; l < n_triplet; l++)
     {
     row = Wtriplet(l,0) - 1;
     col = Wtriplet(l,1) - 1;
     tau2_quadform = tau2_quadform + phi[(Wtriplet(l,0) - 1)] * theta[(Wtriplet(l,1) - 1)] * Wtriplet(l,2); 
     }
 
 
 // Compute the diagonal elements of the quadratic form          
     for(int l = 0; l < nsites; l++)
     {
     tau2_phisq = tau2_phisq + phi[l] * theta[l] * (rho * Wtripletsum[l] + 1 - rho);    
     }
           
     
// Compute the quadratic form
tau2_posteriorscale = 0.5 * (tau2_phisq - rho * tau2_quadform);

 
// Return the simulated value
return tau2_posteriorscale;
}



// [[Rcpp::export]]
List binomialcarupdate(NumericMatrix Wtriplet, NumericMatrix Wbegfin, 
                       NumericVector Wtripletsum,const int nsites, NumericVector phi, double tau2, 
                       const NumericVector y, const NumericVector failures, NumericVector trials, const double phi_tune, 
                       double rho, NumericVector offset, NumericVector missind)
{
    // Update the spatially correlated random effects 
    //Create new objects
    int accept=0, rowstart=0, rowend=0;
    double acceptance, acceptance1, acceptance2,  sumphi, mala_old, mala_new;
    double oldpriorbit, newpriorbit, oldlikebit, newlikebit;
    double priorvardenom, priormean, priorvar;
    double propphi, pold, pnew, proposal_var;
    NumericVector phinew(nsites);
    
    
    //  Update each random effect in turn
    phinew = phi;

        for(int j = 0; j < nsites; j++)
        {
        // Calculate prior variance
        priorvardenom = rho * Wtripletsum[j] + 1 - rho;
        priorvar = tau2 / priorvardenom;
        
        // Calculate the prior mean
        rowstart = Wbegfin(j,0) - 1;
        rowend = Wbegfin(j,1);
        sumphi = 0;
        for(int l = rowstart; l < rowend; l++) sumphi += Wtriplet(l, 2) * phinew[(Wtriplet(l,1) - 1)];
        priormean = rho * sumphi / priorvardenom;  
        
        // Different updates depending on whether the y[j] is missing or not.
            if(missind[j]==1)
            {
            // propose a value
            proposal_var = priorvar * phi_tune;
            mala_old = phinew[j] + 0.5 * proposal_var * (y[j] - (trials[j] * exp(phinew[j] + offset[j])) / (1 + exp(phinew[j] + offset[j])) - (phinew[j] - priormean) /priorvar);
            propphi = rnorm(1, mala_old, sqrt(proposal_var))[0];
            
            // Accept or reject it
            // Full conditional ratio
            newpriorbit = (0.5/priorvar) * pow((propphi - priormean), 2); 
            oldpriorbit = (0.5/priorvar) * pow((phinew[j] - priormean), 2);
            pold = exp(offset[j] + phinew[j]) / (1 + exp(offset[j] + phinew[j]));
            pnew = exp(offset[j] + propphi) / (1 + exp(offset[j] + propphi));
            oldlikebit = missind[j] * (y[j] * log(pold) + failures[j] * log((1-pold)));
            newlikebit = missind[j] * (y[j] * log(pnew) + failures[j] * log((1-pnew)));
            acceptance1 = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit);

            // Proposal distribution ratio
            mala_new = propphi + 0.5 * proposal_var * (y[j] - (trials[j] * exp(propphi + offset[j])) / (1 + exp(propphi + offset[j])) - (propphi - priormean) /priorvar);
            acceptance2 = exp(-(0.5 / proposal_var) * (pow((phinew[j] - mala_new),2) - pow((propphi-mala_old),2)));
            acceptance = acceptance1 * acceptance2;
            
            // Acceptace or reject the proposal
            if(runif(1)[0] <= acceptance) 
            {
                phinew[j] = propphi;
                accept = accept + 1;
            }
            else
            { 
            }    
        }else
        {
            phinew[j] = rnorm(1, priormean, sqrt(priorvar))[0];    
        }
    }

// Return the results
List out(2);
out[0] = phinew;
out[1] = accept;
return out;
}



// [[Rcpp::export]]
List binomialbetaupdateMALA(NumericMatrix X, const int nsites, const int p, NumericVector beta, 
                            NumericVector offset, NumericVector y,  NumericVector failures,
                            NumericVector trials, NumericVector prior_meanbeta, 
                            NumericVector prior_varbeta, NumericVector missind, const int nblock,
                            double beta_tune, List block_list)
{
    // Compute the acceptance probability for beta
    //Create new objects
    int accept=0;
    double oldlikebit=0, newlikebit=0, likebit, priorbit=0;
    double acceptance;
    NumericVector lp_current(nsites), lp_proposal(nsites), p_current(nsites), p_proposal(nsites), mala_temp1(nsites);
    
    // Create two beta vectors
    NumericVector beta_old(p);
    NumericVector beta_new(p);
    for(int g=0; g<p; g++)
    {
        beta_old[g] = beta[g];
        beta_new[g] = beta[g];
    }
    
    // Update each block in turn
    for(int r=0; r<nblock; r++)
    {
        // Determine the block to update
        IntegerVector idx = block_list[r];
        int len = block_list[(nblock+r)];
        
        // Propose a value
        lp_current = linpredcompute(X, nsites, p, beta_old, offset);
        mala_temp1 = missind * (y -  trials * exp(lp_current) / (1 + exp(lp_current)));
        NumericVector mala_temp2(len), mala_old(len);
        for(int g=0; g<len; g++)
        {
            mala_temp2[g] = sum(X(_,idx[g]) * mala_temp1);
            mala_old[g] = beta_old[idx[g]] + 0.5 * pow(beta_tune,2) * (-(beta_old[idx[g]] - prior_meanbeta[idx[g]]) / prior_varbeta[idx[g]] + mala_temp2[g]); 
            beta_new[idx[g]] = rnorm(1, mala_old[g], beta_tune)[0];
        }
        
        // Compute the acceptance ratio - full conditionals  
        oldlikebit = 0;
        newlikebit=0;
        lp_proposal = linpredcompute(X, nsites, p, beta_new, offset);     
        for(int j = 0; j < nsites; j++)     
        {
            p_current[j] = exp(lp_current[j]) / (1 + exp(lp_current[j]));
            p_proposal[j] = exp(lp_proposal[j]) / (1 + exp(lp_proposal[j]));
            oldlikebit = oldlikebit + missind[j] * (y[j] * log(p_current[j]) + failures[j] * log((1-p_current[j])));
            newlikebit = newlikebit + missind[j] * (y[j] * log(p_proposal[j]) + failures[j] * log((1-p_proposal[j])));
        }
        likebit = newlikebit - oldlikebit;
        
        
        for(int g = 0; g < len; g++)     
        {
            priorbit = priorbit + 0.5 * pow((beta_old[idx[g]]-prior_meanbeta[idx[g]]),2) / prior_varbeta[idx[g]] - 0.5 * pow((beta_new[idx[g]]-prior_meanbeta[idx[g]]),2) / prior_varbeta[idx[g]];
        }
        
        // Compute the acceptance ratio - proposal distributions
        mala_temp1 = missind * (y -  trials * exp(lp_proposal) / (1 + exp(lp_proposal)));
        NumericVector mala_new(len);
        double prop_accept=0;
        for(int g=0; g<len; g++)
        {
            mala_temp2[g] = sum(X(_,idx[g]) * mala_temp1);
            mala_new[g] = beta_new[idx[g]] + 0.5 * pow(beta_tune,2) * (-(beta_new[idx[g]] - prior_meanbeta[idx[g]]) / prior_varbeta[idx[g]] + mala_temp2[g]); 
            prop_accept = prop_accept +   pow((beta_new[idx[g]] - mala_old[g]), 2) -  pow((beta_old[idx[g]] - mala_new[g]), 2); 
        }
        
        // Accept or reject hte proposal      
        acceptance = exp(0.5 * prop_accept / pow(beta_tune,2) + likebit + priorbit);
        if(runif(1)[0] <= acceptance) 
        {
            for(int g=0; g<len; g++)
            {
                beta_old[idx[g]] = beta_new[idx[g]];  
            }
            accept = accept + 1;
        }
        else
        { 
            for(int g=0; g<len; g++)
            {
                beta_new[idx[g]] = beta_old[idx[g]];  
            }   
        }
    }
    
    
    // Compute the acceptance probability and return the value
    //acceptance = exp(likebit + priorbit);
    List out(2);
    out[0] = beta_new;
    out[1] = accept;
    return out;    
}




// [[Rcpp::export]]
List binomialbetaupdateRW(NumericMatrix X, const int nsites, const int p, NumericVector beta, 
                            NumericVector offset, NumericVector y,  NumericVector failures,
                            NumericVector prior_meanbeta, NumericVector prior_varbeta, 
                            NumericVector missind, double beta_tune)
{
    // Compute the acceptance probability for beta
    //Create new objects
    double oldlikebit=0, newlikebit=0, likebit, priorbit=0;
    double acceptance;
    NumericVector lp_current(nsites), lp_proposal(nsites), p_current(nsites), p_proposal(nsites), mala_temp1(nsites);
    List out(2);
    
    // Create a beta new vector
        NumericVector beta_new(p);
        for(int g = 0; g < p; g++)
        {
        beta_new[g] = beta[g];
        }
    
    // Update the parameters in one go as p is less than 3
    // Propose a value
        for(int g = 0; g < p; g++)
        {
        beta_new[g] = rnorm(1, beta[g], beta_tune)[0];
        }
    
    // Compute the acceptance ratio - full conditionals   
    lp_current = linpredcompute(X, nsites, p, beta, offset);
    lp_proposal = linpredcompute(X, nsites, p, beta_new, offset);     
        for(int j = 0; j < nsites; j++)     
        {
        p_current[j] = exp(lp_current[j]) / (1 + exp(lp_current[j]));
        p_proposal[j] = exp(lp_proposal[j]) / (1 + exp(lp_proposal[j]));
        oldlikebit = oldlikebit + missind[j] * (y[j] * log(p_current[j]) + failures[j] * log((1-p_current[j])));
        newlikebit = newlikebit + missind[j] * (y[j] * log(p_proposal[j]) + failures[j] * log((1-p_proposal[j])));
        }
     likebit = newlikebit - oldlikebit;
    
        for(int g = 0; g < p; g++)     
        {
        priorbit = priorbit + 0.5 * pow((beta[g]-prior_meanbeta[g]),2) / prior_varbeta[g] - 0.5 * pow((beta_new[g]-prior_meanbeta[g]),2) / prior_varbeta[g];
        }
    
        
    // Accept or reject the proposal      
    acceptance = exp(likebit + priorbit);
        if(runif(1)[0] <= acceptance) 
        {
            out[0] = beta_new;
            out[1] = 1;
        }
        else
        { 
            out[0] = beta;
            out[1] = 0; 
        }
        
        
        // Compute the acceptance probability and return the value
        return out;    
}





// [[Rcpp::export]]
List binomialindepupdate(const int nsites, NumericVector theta, double sigma2, const NumericVector y, 
               const NumericVector failures, const NumericVector trials, const double theta_tune,  NumericVector offset, NumericVector missind)
{
// Update the independent random effects 
//Create new objects
int accept=0;
double acceptance, acceptance1, acceptance2, mala_old, mala_new;
double oldpriorbit, newpriorbit, oldlikebit, newlikebit;
double proptheta, pold, pnew;
NumericVector thetanew(nsites);
 
   
//  Update each random effect in turn
thetanew = theta;
    for(int j = 0; j < nsites; j++)
    {
    // Different updates depending on whether the y[j] is missing or not.
        if(missind[j]==1)
        {
        // propose a value
        mala_old = thetanew[j] + 0.5 * pow(theta_tune, 2) * (y[j] - (trials[j] * exp(thetanew[j] + offset[j])) / (1 + exp(thetanew[j] + offset[j])) - thetanew[j] / sigma2);
        proptheta = rnorm(1, mala_old, theta_tune)[0];
        
        // Accept or reject it
        // Full conditional ratio
        newpriorbit = (0.5/sigma2) * pow(proptheta, 2); 
        oldpriorbit = (0.5/sigma2) * pow(thetanew[j], 2);
        
        pold = exp(offset[j] + thetanew[j]) / (1 + exp(offset[j] + thetanew[j]));
        pnew = exp(offset[j] + proptheta) / (1 + exp(offset[j] + proptheta));
        oldlikebit = missind[j] * (y[j] * log(pold) + failures[j] * log((1-pold)));
        newlikebit = missind[j] * (y[j] * log(pnew) + failures[j] * log((1-pnew)));
        acceptance1 = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit);

        // Proposal distribution ratio
        mala_new = proptheta + 0.5 * pow(theta_tune, 2) * (y[j] - (trials[j] * exp(proptheta + offset[j])) / (1 + exp(proptheta + offset[j])) - proptheta / sigma2);
        acceptance2 = exp(-(0.5 / pow(theta_tune, 2)) * (pow((thetanew[j] - mala_new),2) - pow((proptheta-mala_old),2)));
        acceptance = acceptance1 * acceptance2;
        
        // Acceptace or reject the proposal
            if(runif(1)[0] <= acceptance) 
            {
            thetanew[j] = proptheta;
            accept = accept + 1;
            }
            else
            { 
            }    
        }else
        {
        thetanew[j] = rnorm(1, 0, theta_tune)[0];    
        }
    }

List out(2);
out[0] = thetanew;
out[1] = accept;
return out;
}



// [[Rcpp::export]]
List poissonindepupdate(const int nsites, NumericVector theta, double sigma2, const NumericVector y, 
               const double theta_tune,  NumericVector offset, NumericVector missind)
{
// Update the spatially correlated random effects 
//Create new objects
int accept=0;
double acceptance, acceptance1, acceptance2, mala_old, mala_new;
double oldpriorbit, newpriorbit, oldlikebit, newlikebit;
double proptheta, lpold, lpnew;
NumericVector thetanew(nsites);
 
   
//  Update each random effect in turn
thetanew = theta;
     for(int j = 0; j < nsites; j++)
     {
         // Different updates depending on whether the y[j] is missing or not.
         if(missind[j]==1)
         {
             // propose a value
             mala_old = thetanew[j] + 0.5 * pow(theta_tune, 2) * (y[j] - exp(thetanew[j] + offset[j]) - thetanew[j] / sigma2);
             proptheta = rnorm(1, mala_old, theta_tune)[0];
             
             // Accept or reject it
             // Full conditional ratio
             newpriorbit = (0.5/sigma2) * pow(proptheta, 2); 
             oldpriorbit = (0.5/sigma2) * pow(thetanew[j], 2);
             lpold = offset[j] + thetanew[j];
             lpnew = offset[j] + proptheta;
             oldlikebit = missind[j] * (y[j] * lpold - exp(lpold));
             newlikebit = missind[j] * (y[j] * lpnew - exp(lpnew));
             acceptance1 = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit);
             
             // Proposal distribution ratio
             mala_new = proptheta + 0.5 * pow(theta_tune, 2) * (y[j] - exp(proptheta + offset[j]) - proptheta / sigma2);
             acceptance2 = exp(-(0.5 / pow(theta_tune, 2)) * (pow((thetanew[j] - mala_new),2) - pow((proptheta-mala_old),2)));
             acceptance = acceptance1 * acceptance2;
             
             // Acceptace or reject the proposal
             if(runif(1)[0] <= acceptance) 
             {
                 thetanew[j] = proptheta;
                 accept = accept + 1;
             }
             else
             { 
             }    
         }else
         {
             thetanew[j] = rnorm(1, 0, theta_tune)[0];    
         }
    }


List out(2);
out[0] = thetanew;
out[1] = accept;
return out;
}


// [[Rcpp::export]]
List poissonbetaupdateMALA(NumericMatrix X, const int nsites, const int p, NumericVector beta, 
                       NumericVector offset, NumericVector y, NumericVector prior_meanbeta, 
                       NumericVector prior_varbeta, NumericVector missind, const int nblock,
                       double beta_tune, List block_list)
{
    // Compute the acceptance probability for beta
    //Create new objects
    int accept=0;
    double oldlikebit=0, newlikebit=0, likebit, priorbit=0;
    double acceptance;
    NumericVector lp_current(nsites), lp_proposal(nsites), mala_temp1(nsites);
    
    // Create two beta vectors
    NumericVector beta_old(p);
    NumericVector beta_new(p);
    for(int g=0; g<p; g++)
    {
        beta_old[g] = beta[g];
        beta_new[g] = beta[g];
    }
    
    // Update each block in turn
    for(int r=0; r<nblock; r++)
    {
        // Determine the block to update
        IntegerVector idx = block_list[r];
        int len = block_list[(nblock+r)];
        
        // Propose a value
        lp_current = linpredcompute(X, nsites, p, beta_old, offset);
        mala_temp1 = missind * (y - exp(lp_current));
        NumericVector mala_temp2(len), mala_old(len);
        for(int g=0; g<len; g++)
        {
            mala_temp2[g] = sum(X(_,idx[g]) * mala_temp1);
            mala_old[g] = beta_old[idx[g]] + 0.5 * pow(beta_tune,2) * (-(beta_old[idx[g]] - prior_meanbeta[idx[g]]) / prior_varbeta[idx[g]] + mala_temp2[g]); 
            beta_new[idx[g]] = rnorm(1, mala_old[g], beta_tune)[0];
        }
        
        // Compute the acceptance ratio - full conditionals 
        oldlikebit = 0;
        newlikebit=0;
        lp_proposal = linpredcompute(X, nsites, p, beta_new, offset);     
        for(int j = 0; j < nsites; j++)     
        {
            oldlikebit = oldlikebit + missind[j] * (y[j] * lp_current[j] - exp(lp_current[j]));
            newlikebit = newlikebit + missind[j] * (y[j] * lp_proposal[j] - exp(lp_proposal[j]));
        }
        likebit = newlikebit - oldlikebit;
        
        for(int g = 0; g < len; g++)     
        {
            priorbit = priorbit + 0.5 * pow((beta_old[idx[g]]-prior_meanbeta[idx[g]]),2) / prior_varbeta[idx[g]] - 0.5 * pow((beta_new[idx[g]]-prior_meanbeta[idx[g]]),2) / prior_varbeta[idx[g]];
        }
        
        // Compute the acceptance ratio - proposal distributions
        mala_temp1 = missind * (y - exp(lp_proposal));
        NumericVector mala_new(len);
        double prop_accept=0;
        for(int g=0; g<len; g++)
        {
            mala_temp2[g] = sum(X(_,idx[g]) * mala_temp1);
            mala_new[g] = beta_new[idx[g]] + 0.5 * pow(beta_tune,2) * (-(beta_new[idx[g]] - prior_meanbeta[idx[g]]) / prior_varbeta[idx[g]] + mala_temp2[g]); 
            prop_accept = prop_accept +   pow((beta_new[idx[g]] - mala_old[g]), 2) -  pow((beta_old[idx[g]] - mala_new[g]), 2); 
        }
        
        // Accept or reject hte proposal      
        acceptance = exp(0.5 * prop_accept / pow(beta_tune,2) + likebit + priorbit);
        if(runif(1)[0] <= acceptance) 
        {
            for(int g=0; g<len; g++)
            {
                beta_old[idx[g]] = beta_new[idx[g]];  
            }
            accept = accept + 1;
        }
        else
        { 
            for(int g=0; g<len; g++)
            {
                beta_new[idx[g]] = beta_old[idx[g]];  
            }   
        }
    }
    
    
    
    // Compute the acceptance probability and return the value
    //acceptance = exp(likebit + priorbit);
    List out(2);
    out[0] = beta_new;
    out[1] = accept;
    return out;    
}



// [[Rcpp::export]]
List poissonbetaupdateRW(NumericMatrix X, const int nsites, const int p, NumericVector beta, 
                           NumericVector offset, NumericVector y, NumericVector prior_meanbeta, 
                           NumericVector prior_varbeta, NumericVector missind, double beta_tune)
{
    // Compute the acceptance probability for beta
    //Create new objects
    double oldlikebit=0, newlikebit=0, likebit, priorbit=0;
    double acceptance;
    NumericVector lp_current(nsites), lp_proposal(nsites);
    List out(2);
    
    // Create a beta new vector
    NumericVector beta_new(p);
        for(int g = 0; g < p; g++)
        {
        beta_new[g] = beta[g];
        }
    
    
    // Update the parameters in one go as p is less than 3
    // Propose a value
        for(int g = 0; g < p; g++)
        {
        beta_new[g] = rnorm(1, beta[g], beta_tune)[0];
        }
        
    // Compute the acceptance ratio - full conditionals   
    lp_current = linpredcompute(X, nsites, p, beta, offset);
    lp_proposal = linpredcompute(X, nsites, p, beta_new, offset);     
        for(int j = 0; j < nsites; j++)     
        {
        oldlikebit = oldlikebit + missind[j] * (y[j] * lp_current[j] - exp(lp_current[j]));
        newlikebit = newlikebit + missind[j] * (y[j] * lp_proposal[j] - exp(lp_proposal[j]));
        }
    likebit = newlikebit - oldlikebit;
        
        for(int g = 0; g < p; g++)     
        {
        priorbit = priorbit + 0.5 * pow((beta[g]-prior_meanbeta[g]),2) / prior_varbeta[g] - 0.5 * pow((beta_new[g]-prior_meanbeta[g]),2) / prior_varbeta[g];
        }
        

    // Accept or reject the proposal      
    acceptance = exp(likebit + priorbit);
        if(runif(1)[0] <= acceptance) 
        {
        out[0] = beta_new;
        out[1] = 1;
        }
        else
        { 
        out[0] = beta;
        out[1] = 0; 
        }

    
    // Compute the acceptance probability and return the value
    return out;    
}




// [[Rcpp::export]]
List poissoncarupdate(NumericMatrix Wtriplet, NumericMatrix Wbegfin, 
                      NumericVector Wtripletsum, const int nsites, NumericVector phi, 
                      double tau2, const NumericVector y, const double phi_tune, 
                      double rho, NumericVector offset, NumericVector missind)
{
    // Update the spatially correlated random effects 
    //Create new objects
    int accept=0,rowstart=0, rowend=0;
    double acceptance, acceptance1, acceptance2, sumphi, proposal_var, mala_old, mala_new;
    double oldpriorbit, newpriorbit, oldlikebit, newlikebit;
    double priorvardenom, priormean, priorvar;
    double propphi, lpold, lpnew;
    NumericVector phinew(nsites);
    
    
    //  Update each random effect in turn
    phinew = phi;
    
    for(int j = 0; j < nsites; j++)
    {
        // Calculate prior variance
        priorvardenom = rho * Wtripletsum[j] + 1 - rho;
        priorvar = tau2 / priorvardenom;
        
        // Calculate the prior mean
        rowstart = Wbegfin(j,0) - 1;
        rowend = Wbegfin(j,1);
        sumphi = 0;
        for(int l = rowstart; l < rowend; l++) sumphi += Wtriplet(l, 2) * phinew[(Wtriplet(l,1) - 1)];
        priormean = rho * sumphi / priorvardenom; 
        
        // Different updates depending on whether the y[j] is missing or not.
        if(missind[j]==1)
        {
            // propose a value
            proposal_var = priorvar * phi_tune;
            mala_old = phinew[j] + 0.5 * proposal_var * (y[j] - exp(phinew[j] + offset[j]) - (phinew[j] - priormean) /priorvar);
            propphi = rnorm(1, mala_old, sqrt(proposal_var))[0];
            
            // Accept or reject it
            // Full conditional ratio
            newpriorbit = (0.5/priorvar) * pow((propphi - priormean), 2); 
            oldpriorbit = (0.5/priorvar) * pow((phinew[j] - priormean), 2);
            lpold = offset[j] + phinew[j];
            lpnew = offset[j] + propphi;
            oldlikebit = missind[j] * (y[j] * lpold - exp(lpold));
            newlikebit = missind[j] * (y[j] * lpnew - exp(lpnew));
            acceptance1 = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit);
            
            // Proposal distribution ratio
            mala_new = propphi + 0.5 * proposal_var * (y[j] - exp(propphi + offset[j]) - (propphi - priormean) /priorvar);
            acceptance2 = exp(-(0.5 / proposal_var) * (pow((phinew[j] - mala_new),2) - pow((propphi-mala_old),2)));
            acceptance = acceptance1 * acceptance2;
            
            // Acceptace or reject the proposal
            if(runif(1)[0] <= acceptance) 
            {
                phinew[j] = propphi;
                accept = accept + 1;
            }
            else
            { 
            }    
        }else
        {
        phinew[j] = rnorm(1, priormean, sqrt(priorvar))[0];    
        }
    }
    
    
    List out(2);
    out[0] = phinew;
    out[1] = accept;
    return out;
}





// [[Rcpp::export]]
NumericVector gaussiancarupdate(NumericMatrix Wtriplet, NumericMatrix Wbegfin, 
     NumericVector Wtripletsum, const int nsites, NumericVector phi, double tau2, 
     double rho, double nu2, NumericVector offset, NumericVector missind)
{
// Update the spatially correlated random effects 
//Create new objects
int rowstart=0, rowend=0;
double sumphi;
double fcprecision, fcsd, fcmean;
double priorvardenom, priormean, priorvar;
NumericVector phinew(nsites);


//  Update each random effect in turn
phinew = phi;
     for(int j = 0; j < nsites; j++)
     {
     // Calculate prior variance
     priorvardenom = rho * Wtripletsum[j] + 1 - rho;
     priorvar = tau2 / priorvardenom;
     
     // Calculate the prior mean
     rowstart = Wbegfin(j,0) - 1;
     rowend = Wbegfin(j,1);
     sumphi = 0;
          for(int l = rowstart; l < rowend; l++) sumphi += Wtriplet(l, 2) * phinew[(Wtriplet(l,1) - 1)];
     priormean = rho * sumphi / priorvardenom; 
      
      // propose a value  
      fcprecision = missind[j] * (1/nu2) + (1/priorvar);
      fcsd = pow((1/fcprecision),0.5);
      fcmean = (priormean / priorvar + missind[j] * offset[j]) / fcprecision;
      phinew[j] = rnorm(1, fcmean, fcsd)[0];      
      }


return phinew;
}



// [[Rcpp::export]]
List binomialmcarupdate(NumericMatrix Wtriplet, NumericMatrix Wbegfin, 
                        const int nsites,  const int nvar, NumericMatrix phi, 
                        NumericMatrix Y, NumericMatrix failures, NumericMatrix trials,
                        NumericMatrix phioffset, NumericVector denoffset,  
                        NumericMatrix Sigmainv, double rho, double phi_tune,
                        NumericMatrix missind)
{
    // Update the spatially correlated random effects 
    //Create new objects
    NumericMatrix fcprec(nvar, nvar);
    int rowstart=0, rowend=0, accept=0;
    NumericVector sumphi(nvar), fcmean(nvar), propphi(nvar), mala1(nvar), mala2(nvar);
    NumericVector diffcurrent(nvar), diffprop(nvar);        
    NumericVector quadcurrent(nvar), quadprop(nvar);  
    NumericVector pold(nvar), pnew(nvar);
    double oldpriorbit, newpriorbit, oldlikebit, newlikebit, acceptance, hastings;
    
    //  Update each random effect in turn
    for(int j = 0; j < nsites; j++)
    {      
    // Calculate the prior precision and mean
        for(int r=0; r<nvar; r++)
        {
            fcprec(_,r) = denoffset[j] * Sigmainv(_,r);  
        }
        
    rowstart = Wbegfin(j,0) - 1;
    rowend = Wbegfin(j,1);
    sumphi = rep(0,nvar);
        for(int l = rowstart; l < rowend; l++) sumphi += Wtriplet(l, 2) * phi((Wtriplet(l,1) - 1),_);
    fcmean = rho * sumphi / denoffset[j]; 
        
        
    // Generate the proposal distribution mean and propose a value
        for(int r=0; r<nvar; r++)
        {
        mala1[r] =  phi(j,r) + 0.5 * pow(phi_tune, 2) * (missind(j,r) * (Y(j,r) - (trials(j,r) * exp(phi(j,r) + phioffset(j,r))) / (1 + exp(phi(j,r) + phioffset(j,r)))) -sum(fcprec(r,_) * (phi(j,_) - fcmean)));
        propphi[r] = rnorm(1, mala1[r], phi_tune)[0];
        //propphi[r] = rnorm(1, phi(j,r), phi_tune)[0];
        }

     // Generate the mala mean in reverse
        for(int r=0; r<nvar; r++)
        {
        mala2[r] =  propphi[r] + 0.5 * pow(phi_tune, 2) * (missind(j,r) * (Y(j,r) - (trials(j,r) * exp(propphi[r] + phioffset(j,r))) / (1 + exp(propphi[r] + phioffset(j,r)))) -sum(fcprec(r,_) * (propphi - fcmean)));
        }  
            
    // Compute the prior ratio
    diffcurrent = phi(j,_) - fcmean;
    diffprop = propphi - fcmean;
        for(int r=0; r<nvar; r++)
        {
        quadcurrent[r] = sum(diffcurrent * fcprec(_,r));  
        quadprop[r] = sum(diffprop * fcprec(_,r));  
        }
    oldpriorbit = 0.5 * sum(quadcurrent * diffcurrent);
    newpriorbit = 0.5 * sum(quadprop * diffprop);      
              
    // Likelihood ratio
    pold = exp(phioffset(j,_) + phi(j,_)) / (1 + exp(phioffset(j,_) + phi(j,_)));
    pnew = exp(phioffset(j,_) + propphi) / (1 + exp(phioffset(j,_) + propphi));
    oldlikebit = sum(missind(j,_) * (Y(j,_) * log(pold) + failures(j,_) * log(1 - pold)));
    newlikebit = sum(missind(j,_) * (Y(j,_) * log(pnew) + failures(j,_) * log(1 - pnew)));

    // Hastings ratio   
    hastings = - (sum(pow(phi(j,_) - mala2,2)) - sum(pow(propphi - mala1,2))) / (2*pow(phi_tune,2));
     
     
    // Accept or reject the value
    acceptance = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit + hastings);
    //acceptance = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit);
    if(runif(1)[0] <= acceptance) 
        {
        phi(j,_) = propphi;
        accept = accept + 1;
        }
        else
        { 
        }
    }     
            
            
    // Return the results
    List out(2);
    out[0] = phi;
    out[1] = accept;
    return out;
}



// [[Rcpp::export]]
List poissonmcarupdate(NumericMatrix Wtriplet, NumericMatrix Wbegfin, 
                       const int nsites,  const int nvar, NumericMatrix phi, 
                       NumericMatrix Y, NumericMatrix phioffset, 
                       NumericVector denoffset, NumericMatrix Sigmainv, double rho, 
                       double phi_tune, NumericMatrix missind)
{
    // Update the spatially correlated random effects 
    //Create new objects
    NumericMatrix fcprec(nvar, nvar);
    int rowstart=0, rowend=0, accept=0;
    NumericVector sumphi(nvar), fcmean(nvar), propphi(nvar), mala1(nvar), mala2(nvar);
    NumericVector diffcurrent(nvar), diffprop(nvar);        
    NumericVector quadcurrent(nvar), quadprop(nvar);  
    NumericVector lpold(nvar), lpnew(nvar);
    double oldpriorbit, newpriorbit, oldlikebit, newlikebit, acceptance, hastings;
    
    //  Update each random effect in turn
    for(int j = 0; j < nsites; j++)
    {     
    // Calculate the prior precision and mean
        for(int r=0; r<nvar; r++)
        {
            fcprec(_,r) = denoffset[j] * Sigmainv(_,r);  
        }
        
        rowstart = Wbegfin(j,0) - 1;
        rowend = Wbegfin(j,1);
        sumphi = rep(0,nvar);
        for(int l = rowstart; l < rowend; l++) sumphi += Wtriplet(l, 2) * phi((Wtriplet(l,1) - 1),_);
        fcmean = rho * sumphi / denoffset[j]; 
        
    // Generate the proposal distribution mean and propose a value
        for(int r=0; r<nvar; r++)
        {
        mala1[r] =  phi(j,r) + 0.5 * pow(phi_tune, 2) * (missind(j,r) * (Y(j,r) - exp(phi(j,r) + phioffset(j,r))) -sum(fcprec(r,_) * (phi(j,_) - fcmean)));
        propphi[r] = rnorm(1, mala1[r], phi_tune)[0];
        }
        
    // Generate the mala mean in reverse
        for(int r=0; r<nvar; r++)
        {
        mala2[r] =  propphi[r] + 0.5 * pow(phi_tune, 2) * (missind(j,r) * (Y(j,r) - exp(propphi[r] + phioffset(j,r))) - sum(fcprec(r,_) * (propphi - fcmean)));
        }       
        
         
    // Compute the prior ratio
    diffcurrent = phi(j,_) - fcmean;
    diffprop = propphi - fcmean;
        for(int r=0; r<nvar; r++)
        {
        quadcurrent[r] = sum(diffcurrent * fcprec(_,r));  
        quadprop[r] = sum(diffprop * fcprec(_,r));  
        }
        oldpriorbit = 0.5 * sum(quadcurrent * diffcurrent);
        newpriorbit = 0.5 * sum(quadprop * diffprop);      
        
    // Likelihood ratio
    lpold = phioffset(j,_) + phi(j,_);
    lpnew = phioffset(j,_) + propphi;
    oldlikebit = sum(missind(j,_) * (Y(j,_) * lpold - exp(lpold)));
    newlikebit = sum(missind(j,_) * (Y(j,_) * lpnew - exp(lpnew)));
    
    // Hastings ratio   
    hastings = - (sum(pow(phi(j,_) - mala2,2)) - sum(pow(propphi - mala1,2))) / (2*pow(phi_tune,2));

    // Accept or reject the value
    acceptance = exp(oldpriorbit - newpriorbit - oldlikebit + newlikebit + hastings);
        if(runif(1)[0] <= acceptance) 
        {
        phi(j,_) = propphi;
        accept = accept + 1;
        }
        else
        { 
        }
    }     

    List out(2);
    out[0] = phi;
    out[1] = accept;
    return out;
}