Invariant Causal Prediction for Nonlinear Models

An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system's underlying causal structure. To this end, Invariant Causal Prediction (ICP) (Peters et al., 2016) has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence. In this work, we present and evaluate an array of methods for nonlinear and nonparametric versions of ICP for learning the causal parents of given target variables. We find that an approach which first fits a nonlinear model with data pooled over all environments and then tests for differences between the residual distributions across environments is quite robust across a large variety of simulation settings. We call this procedure "invariant residual distribution test". In general, we observe that the performance of all approaches is critically dependent on the true (unknown) causal structure and it becomes challenging to achieve high power if the parental set includes more than two variables. As a real-world example, we consider fertility rate modelling which is central to world population projections. We explore predicting the effect of hypothetical interventions using the accepted models from nonlinear ICP. The results reaffirm the previously observed central causal role of child mortality rates

What Does the Mass Accumulation of 100 Late Pleistocene Fallow Deer Skeletons (<em>Dama geiselana</em>) and Red Deer Skeletons (<em>Cervus elaphus</em>) from Neumark-Nord Reveal about the Cause of Death?

In the open-cast lignite mine of Neumark-Nord (Saxony-Anhalt, Germany, Eemian interglacial period) the richest fossil fallow deer material which has been found so far was collected. About 80 articulated skeletons and partial skeletons of Dama geiselana Pfeiffer, 1998 (Cervidae, Mammalia) and 20 partial skeletons of Cervus elaphus in perfect state of preservation were recovered, together with skeletons of Elephas antiquus, Stephanorhinus kirchbergensis and hemitoechus, Bos primigenius, and Panthera leo spelea. The extraordinary composition of the thanatocoenosis of the deer provided decisive information on the cause of death, which is presented here. The deer show the typical preservation of drowned carcasses; 75% of the deer skeletons belong to strong males, while juveniles and females are rare, and very old individuals are missing in the deer assemblage. Several disasters in different years have led to the mass occurrence of deer. The individual age determination of the juveniles, the stage of antler development, and the level of epiphyseal adhesion are explained here. They show that the majority most probably died in autumn. This information provided the crucial approach to investigate nitrifying toxic cyanobacterial blooms as a cause of death. The biochemical results obtained by absorption spectroscopy and RP-HPLC with UV-detection, published in 2002, showed that pigments, and probably toxins, characteristic of cyanobacteria are preserved in the sediment

Verwendung von Einzeldaten aus der Verbraucherpreisstatistik für regionale Preisvergleiche

Mit der Berechnung des Verbraucherpreisindex für Deutschland liegen in der amtlichen Statistik monatlich umfassende und detaillierte Informationen über die Preisentwicklung im Zeitablauf vor. Besteht die Fragestellung jedoch darin, zu einem gegebenen Zeitpunkt die Unterschiede im Preisniveau verschiedener Regionen innerhalb von Deutschland zu untersuchen, so sind gegenwärtig keine ausreichenden Informationen verfügbar. Für den zeitlichen Preisvergleich werden in den verschiedenen Städten unterschiedliche Produkte als „Preisrepräsentanten“ ausgewählt. Wegen dieser regionalen Unterschiede bei den ausgewählten Produkten sind die Preisbeobachtungen des Verbraucherpreisindex nicht direkt für einen räumlichen Preisvergleich geeignet. Bisher wurden daher für den Zweck der räumlichen Preisniveaumessung in unregelmäßigen Abständen eigenständige Erhebungen durchgeführt, die speziell auf den regionalen Preisvergleich zugeschnitten und sehr aufwändig waren. Eine solche Erhebung wurde zuletzt 1993 durchgeführt (im Folgenden als „Zwischenörtlicher Preisvergleich von 1993“ bezeichnet und fand seitdem aus Kostengründen nicht mehr statt. Da die Ergebnisse von 1993 mittlerweile veraltet sein dürften, besteht im System der deutschen amtlichen Preisstatistik eine Lücke im Hinblick auf Daten zum Vergleich der Preisniveaus verschiedener Regionen innerhalb von Deutschland.