Hi, I am trying to figure out how to evaluate the density function of multivariate normal efficiently for a large data set, the data set should look like this (take d=2 for example): data mean sigma 2.131, 3.000 1.000,1.000 1 0 0 1 1.231,5.141 2.000,2.000 .5 -.1 ............. ............. -.1 .4 ......... that is , I need SUM_i (log(dmvnorm(d[i], mu[i], sigma[i])). tried to rewrite the dmvnorm function from mvtnorm package, but could not find a satisfactory method to avoid using loops. ( using those "apply" functions seem to be slower than loops) . May I get some suggestion on this ? Thanks a lot in advance. best