 bit of an advanced sort of mapping topic, but it is something that I think if nothing else will show you the range of what can be done with crime data and mapping. If you're, if you really want to get into it, or if in fact you want to rope someone who is very technical into helping you do it, it can be very useful. All right. So what research am I presenting today? I will be featuring this package, Aerial. So this is the research. Jeremy Menace has presented a paper called Dacymetric Speciotemporal Interpolation, which is a huge multiple. And I have put some R Markdown sheets in the guest presentation folder of day three that includes SF, which which we already saw the R package SF and also Aerial. There's a link to his, the DOI if you want to see his original paper, which is quite well written I have to say. Clearly I haven't done the animations properly on this. So what's the basic idea of Dacymetrics? It could be daisy metrics could be death. I don't know. Never make fun to someone if they pronounce something differently because it just means they've learned by reading and that is to be applauded. I say that as I mispronounce things quite excessively. So basic concept works a bit like this. Imagine you have a group of 10 people. But you only know some things about this group of people, you know that five are men and five are women and that some of them live in London and some of them live in Manchester. Now, if you wanted to do some kind of analysis about the women who lived in Manchester. If you want to create a map, for example, that shows the breakdown of men and women in London and Manchester, these kinds of things, you might just off the top of your head say, well, we'll split it evenly. If we assume an even distribution, then two and a half of these women live in Manchester that is not very believable. If you know anything about how women are divided. So you might make a more reasonable assumption and say actually London is about four times the size of Manchester in terms of total population. So maybe we should shift our assumptions a little bit rather than an even distribution assuming an even distribution. Let's assume the distribution matches roughly the population distribution between these two places. In that case, we would have a one woman, if our group of 10 people, there's likely to be one woman living in Manchester. So how do we apply this kind of logic these kind of like using other things we know about a space to mapping? Well, Coropleth maps, which we worked with a bit, they tend to evenly colour a polygon according to a feature. So like population density or population totals or the number of people who own cars or whatever it is that you're looking to plot. But other sources can hint at the distribution within that polygon. So for example, if we're mapping population density for a polygon that we know includes a huge park. We can really say, right, nobody lives in the park or if it's a lake, no one lives on the lake. We can make really quite sensible assumptions based on things we know about the features within that polygon. So if we combine this information, the population or the population density or whatever we're plotting for the polygon, if we combine it with other sources of information about the spatial distribution of that polygon, we can get more accurate. So population density, for example, is much more accurate if we don't assume that people are living on the top of the lake or in the middle of a park. And if we take it a step further, and we apply this kind of assumptions that we know about how things are distributed across the space, we can also apply it to how things are distributed across time. We know, for example, at least in Manchester, that the weather in winter encourages people to stay indoors much more. So for example, people are much less likely to commit certain kinds of crimes in winter than they are in summer, just because it's raining or it's freezing cold or it's totally dark and people just aren't hanging around doing the same kinds of crimes. So we know some crimes are not evenly distributed in time. We apply the same kind of logic about how we know that uneven distributions are likely to apply to both space and time. And we know that population density, for example, doesn't necessarily change between summer and winter in a place like Manchester. But we do know that population density might change over time in some places. You know, seasonal workers in a rural area, those populations are definitely going to change over time. You know, and we can use information about maybe what crops are grown and what time they are harvested or stored or how much labour is needed to do that and at what time of the year, things like how much labour is available in the community full time versus how much needs to be brought in seasonally. And local demographics, how many people of working age are in the community to begin with, things like that. Vacation towns in the same way, so we might use information like holiday schedules or school breaks or local transport links to say, you know, are people likely to come in by plane or train or motorway or these kinds of things. And if so, where they likely to be coming from, what are these holiday schedules for those places. And even within like a day, you know, or a week, we might look at, you know, the flow of people in shopping centres or using public transport or things like that. And at that point, we would want information on, you know, what is the distribution of local businesses, are they shopping, are they offices, are they dentist offices, things like that. What kind of hours do they typically open, do they typically open on weekends or is this a community where people shop on a Sunday or not, things like that. So let's look at how Jeremy Menace, who produced the research that I linked to earlier, has applied these concepts. He actually had very detailed location about the place and time of crimes in, I believe this is Chicago, yeah, Chicago. But he deliberately anonymised and abstracted that to a very high level to see how accurate this desimetric mapping interpolation worked. So he abstracted out to very broad sort of regions of the city. And for an entire year, so this is how many incidents of battery, so people getting in fights basically. Occurred in these large neighbourhood sort of blocks, polygons, over an entire year of 2002. And then he took a map of the land use area of the same space in Chicago. And everything that is dark grey is likely to be a populated like a used area. Everything that is in light grey is not like a non-populated area. So this one down here, I think is a park with a lot of water features. This one is the airport, Chicago O'Hare Airport. And this is the waterfront. So here on this side is Lake Michigan. So all along the waterfront is a lot of industrial area. And these are major boulevards and industrial districts. So he put these together and he also broke it down into seasons according to the temperature and sort of weather habits. And using this method that only took the high level distributions and the assumptions based on spatial and temporal expectations. He broke it down and found that this is what these are the sort of high impact areas in winter. And then in spring, summer and autumn, they shift around a little bit. So there's interesting things here. And his results showed that in fact, this method was very, very accurate, certainly much more accurate than only using space or only using time. So combining both space and time reproduced very nearly the original low level data. And so he was quite pleased with that. And this means that people can get quite useful, accurate predictions or estimations of data without compromising the anonymity needed when things are published at very high levels. And why might this matter, of course, if you look back at this map. And if you're a police department, for example, saying like, well, where do we want to put officers to respond quickly to or to prevent incidents of battery? You might really just target these three red ones. And so those are the high incidents. You might think, well, maybe it will send someone occasionally through these orange ones. But if you look at these maps, you'd say actually winter doesn't need very much sort of additional patrol at all. But in summertime, you need much more extensive areas of active sort of patrol or intervention. And that's, you know, also pretty much the whole city, at least in summer is at least the orange range, if not the red. And that means really you have to you have to plan out your policy of how you're going to make interventions differently based on space and time than if you look at just the high level statistics over vague blocky areas. So the key contributions of his research are when supplemental data supports its use temporal dashi metric in interpolation is a valid technique. So if you have good reasons to suspect that things are not distributed equally by time, then temporal dashi metric interpolation is useful. I think spatial or temporal interpolation will not always improve your analysis, but that if you combine them both, you're very likely to improve your analysis. So obviously this only applies when it is reasonable to assume that things are not evenly distributed according to either space time or pulse.