Table 1:

A comparison between the key equations in DP and how they can be implemented in R. The last column covers the primary R functions that carry out the calculations. The newly observed data entry is evaluated by the dmvnormO function to obtain its log density, given appropriate input parameters for the predictive distributions. Readers who prefer a different computer programming language may use these to guide their implementation.

Equations for DP	Line(s)	R code
$\frac{n_{-i,k}}{n-1+\alpha }\mathcal{N}\left({\tilde{y}}_i;\frac{{\stackrel{‒}{y}}_k{n}_k{\tau }_k+{\mu }_0{\tau }_0}{n_k{\tau }_k+{\tau }_0},\frac{1}{n_k{\tau }_k+{\tau }_0}+{\sigma }_y^2\right)$ Equation (12)	108 – 110	mean_p <- sig_p %*% (tau_y %*% sum_data + tauO %*% t(muO)) logp[c_i] <- log(n_k[c_i]) + dmvnorm(data[n,], mean = mean_p, sigma = sig_p + sigma_y, log = TRUE)
$\frac{\alpha }{n-1+\alpha }\mathcal{N}({\tilde{y}}_i;{\mu }_0,{\sigma }_0^2+{\sigma }_y^2)$ Equation (13)	117 – 118	logp[ Nclust+1 ] >- log(alpha) + dmvnorm(data[n,] , mean mu0, sigma = sigma0 + sigma_y, log = TRUE)