 So in this video, we're going to look at the general concept behind calculating predictive densities. So in general, what you want is the density of a new observation, say, yn plus 1, given your previously observed data, y1 to yn. So we think about breaking this down in terms of all the different components, we have the joint density of all of our data, including the new observation given our parameter. So that's yf of y1 to yn and yn plus 1 given our parameter, let's call it theta. And each of these are independent observations, so they can be each written like this, this f of y2 given theta, all the way up to f of yn given theta and f of yn plus 1 given theta. And this is quite important that they can be split because of independence. Now we also would think of that our f of our new observation yn plus 1 and our parameter given our data is the distribution of the new observation given the parameter and the previous data times the posterior distribution which is at g of theta given our previously observed data. So this is our posterior distribution which you should have previously found and there are several videos showing you how to find the posterior distribution if you're working with conjugate priors on this channel. So suppose we have the distribution of yn plus 1 given theta where theta represents whatever our parameter is and our data that we've previously observed, so y1 to yn, it only depends on theta. As yn plus 1 is another random draw from this underlying distribution, gy, y given theta. So our joint posterior in this case f of yn plus 1 and our parameter theta given our data is f of yn plus 1 given our parameter times g of theta given our observed data. This is quite important so we look at the distribution of our parameter and then we look at how new observation relates to that parameter. We integrate out the parameter theta f of yn plus 1 given our data is the integral over the relevant range f of yn plus 1 and theta given y1 up to yn d theta which is the integral of f of yn plus 1 given our observation times the posterior distribution of our parameter and that's the general concept of how to calculate the predictive distribution and the predictive densities. And we'll take a look in the next few videos about how to do this in specific distributions.