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Scan inheritor calculated

welcome back in this third set of slides related to the clustering of rage we're going to focus on scan statistics and scan statistics are a different perspective on what is a cluster in the previous lecture dealing with the local moran adjusted for rate variance instability a cluster was there always a location with its neighbors so you didn't really have clusters that consisted of a single location in the scan statistics that is a valid notion of a cluster so in a scan statistic you don't necessarily have to have the neighbors you can find a cluster that is a single aerial unit which is a little bit different so what we're going to do is first i'll talk a little bit about the the general perspective the general concept of a scan statistic and then provide some technical detail on two uh well-known cases the b sag newell approach and then arguably the most popular most well-known approach is kuldorf's scan statistic which has its own specialized software in the satscan software package okay what what is a scan statistic what is a scan first of all a scan is very simple it's it's some aerial shape typically a circle but it doesn't have to be a circle it could be a square it could be in an ellipse it could be something based on networks and uh it's some shape and you count the number of events within that shape so let's say it's a circle with a given radius and you count the number of events within that radius we've already seen this in different guises in fact we saw the uniform kernel which was a disc with a given radius and we counted the number of events in that kernel that is the same principle underlying what is known as the gam or geographical analysis machine which was a way suggested by openshaw and co-workers to try to find clusters now the problem with the open show approach is that it didn't really have a way to assess significance and both the scan statistics or the families of scan statistics that we'll discuss here do have a way of assessing significance so in other words with the open saw open shaw gam approach you had circles and with varying intensity but you couldn't really have you didn't really have a formal way to decide which one was significant and which one was not and so how does a scan statistic work it's like a bullseye you focus it typically on the centroid of an aerial unit and you increase the radius of the circle and count how many events are happening within that shape within that radius of the circle and and you continue until you reach a stopping criterion and as we'll see the two different approaches use a different stopping criterion so the scan statistics count events they increase the size of the shape until they reach a stopping point as i...