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New article on spatial autocorrelation and stochastic point processes

A graph from the paper Westerholt (2022), published in Geographical Analysis. © René Westerholt

Estimating spatial autocorrelation is a statistical means of identifying and characterising structures in georeferenced data sets. Inference procedures for spatial autocorrelation statistics are based on the assumption of fixed configurations of spatial units. Sometimes, however, this assumption can prove disadvantageous, for example, when analysing social media posts or moving objects, where the geometric units to which attributes are assigned are also subject to a certain degree of randomness. In a newly published article in the journal Geographical Analysis by Jun.-Prof. Dr René Westerholt, it is investigated for the case of point geometries how the change from fixed to random spatial units affects inferences about global Moran's I, a popular spatial autocorrelation measure. Homogeneous and inhomogeneous Matérn and Thomas cluster processes are studied, and 10,000 random point patterns are simulated for each of these processes. These point processes are widely used to model a wide variety of phenomena such as the distribution of trees in forests, the study of crowds at large events and similar processes involving geometric randomness. Based on the simulations generated, three aspects are investigated that are central to inference about Moran's I: the null distributions of I under variation of the underlying geometries; the effect of the latter on critical values used to reject null hypotheses; and the effect of the presence of point processes on the statistical power of Moran's I. The results show that point processes affect all three properties. Inferences about spatial structure in relevant application contexts may therefore differ from conventional inferences when this additional source of randomness is taken into account.

Westerholt, R. (2022). A simulation study to explore inference about global Moran’s I with random spatial indexes. Geographical Analysis. DOI: 10.1111/gean.12349


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The campus of TU Dort­mund University is located close to interstate junction Dort­mund West, where the Sauerlandlinie A 45 (Frankfurt-Dort­mund) crosses the Ruhrschnellweg B 1 / A 40. The best interstate exit to take from A 45 is "Dort­mund-Eichlinghofen" (closer to Campus Süd), and from B 1 / A 40 "Dort­mund-Dorstfeld" (closer to Campus Nord). Signs for the uni­ver­si­ty are located at both exits. Also, there is a new exit before you pass over the B 1-bridge leading into Dort­mund.

To get from Campus Nord to Campus Süd by car, there is the connection via Vogelpothsweg/Baroper Straße. We recommend you leave your car on one of the parking lots at Campus Nord and use the H-Bahn (suspended monorail system), which conveniently connects the two campuses.

TU Dort­mund University has its own train station ("Dort­mund Uni­ver­si­tät"). From there, suburban trains (S-Bahn) leave for Dort­mund main station ("Dort­mund Hauptbahnhof") and Düsseldorf main station via the "Düsseldorf Airport Train Station" (take S-Bahn number 1, which leaves every 20 or 30 minutes). The uni­ver­si­ty is easily reached from Bochum, Essen, Mülheim an der Ruhr and Duisburg.

You can also take the bus or subway train from Dort­mund city to the uni­ver­si­ty: From Dort­mund main station, you can take any train bound for the Station "Stadtgarten", usually lines U41, U45, U 47 and U49. At "Stadtgarten" you switch trains and get on line U42 towards "Hombruch". Look out for the Station "An der Palmweide". From the bus stop just across the road, busses bound for TU Dort­mund University leave every ten minutes (445, 447 and 462). Another option is to take the subway routes U41, U45, U47 and U49 from Dort­mund main station to the stop "Dort­mund Kampstraße". From there, take U43 or U44 to the stop "Dort­mund Wittener Straße". Switch to bus line 447 and get off at "Dort­mund Uni­ver­si­tät S".

The AirportExpress is a fast and convenient means of transport from Dort­mund Airport (DTM) to Dort­mund Central Station, taking you there in little more than 20 minutes. From Dort­mund Central Station, you can continue to the uni­ver­si­ty campus by interurban railway (S-Bahn). A larger range of in­ter­na­tio­nal flight connections is offered at Düsseldorf Airport (DUS), which is about 60 kilometres away and can be directly reached by S-Bahn from the uni­ver­si­ty station.

The H-Bahn is one of the hallmarks of TU Dort­mund University. There are two stations on Campus Nord. One ("Dort­mund Uni­ver­si­tät S") is directly located at the suburban train stop, which connects the uni­ver­si­ty directly with the city of Dort­mund and the rest of the Ruhr Area. Also from this station, there are connections to the "Technologiepark" and (via Campus Süd) Eichlinghofen. The other station is located at the dining hall at Campus Nord and offers a direct connection to Campus Süd every five minutes.

The facilities of TU Dort­mund University are spread over two campuses, the larger Campus North and the smaller Campus South. Additionally, some areas of the uni­ver­si­ty are located in the adjacent "Technologiepark".

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