Testing for Equivalence: A Methodology for Computational Cognitive Modelling
The equivalence test (Stewart and West, 2007; Stewart, 2007) is a statistical measure for evaluating the similarity between a model and the system being modelled. It is designed to avoid over-fitting and to generate an easily interpretable summary of the quality of a model. We apply the equivalence test to two tasks: Repeated Binary Choice (Erev et al., 2010) and Dynamic Stocks and Flows (Gonzalez and Dutt, 2007). In the first case, we find a broad range of statistically equivalent models (and win a prediction competition) while identifying particular aspects of the task that are not yet adequately captured. In the second case, we re-evaluate results from the Dynamic Stocks and Flows challenge, demonstrating how our method emphasizes the breadth of coverage of a model and how it can be used for comparing different models. We argue that the explanatory power of models hinges on numerical similarity to empirical data over a broad set of measures.
Late Quaternary andesitic magmas in New Zealand contain complexly zoned antecrysts and glomerocrysts that are not in equilibrium with either the host whole rock compositions or siliceous groundmass glass and glass inclusions. Glass inclusions represent partial melts of mafic to gabbroic cumulates in the lower crust that mix with restite crystals, or cumulates from earlier magma batches. Assimilation of partial melts of mid-crustal rocks, represented by glass in crustal xenoliths, contributes a crustal component to the andesites. Magmas at Egmont are stored at about the brittle/ductile transition at about 10 km depth and variability in the composition of erupted material is a function of the composition of the recharging magma, and which parts of the storage system are tapped during the eruption. At Taranaki recharge occurs on a c. 1400 year cycle while interactions within the storage give rise to shorter period events. A similar process on a less well constrained timescale operates at Ruapehu. Andesites are therefore complex mixtures of fractionated mantle basalts, siliceous partial melts of both the lower crust and underplated cumulates, restite and cumulate crystals. Further modification occurs by interaction with partial melts of lower to middle crustal basement as geotherms increase with time.
The Efate Pumice Formation (EPF) is a trachydacitic volcaniclastic succession widespread in the central part of Efate Island and also present on Hat and Lelepa islands to the north. The volcanic succession has been inferred to result from a major, entirely subaqueous explosive event north of Efate Island. The accumulated pumice-rich units were previously interpreted to be subaqueous pyroclastic density current deposits on the basis of their bedding, componentry and stratigraphic characteristics. Here we suggest an alternative eruptive scenario for this widespread succession. The major part of the EPF is distributed in central Efate, where pumiceous pyroclastic rock units several hundred meters thick are found within fault scarp cliffs elevated about 800 m above sea level. The basal 200 m of the pumiceous succession is composed of massive to weakly bedded pumiceous lapilli units, each 2-3 m thick. This succession is interbedded with wavy, undulatory and dune bedded pumiceous ash and fine lapilli units with characteristics of co-ignimbrite surges and ground surges. The presence of the surge beds implies that the intervening units comprise a subaerial ignimbrite-dominated succession. There are no sedimentary indicators in the basal units examined that are consistent with water-supported transportation and/or deposition. The subaerial ignimbrite sequence of the EPF is overlain by a shallow marine volcaniclastic Rentanbau Tuffs. The EPF is topped by reef limestone, which presumably preserved the underlying EPF from erosion. We here propose that the EPF was formed by a combination of initial subaerial ignimbrite-forming eruptions, followed by caldera subsidence. The upper volcaniclastic successions in our model represent intra-caldera pumiceous volcaniclastic deposits accumulated in a shallow marine environment in the resultant caldera. The present day elevated position of the succession is a result of a combination of possible caldera resurgence and ongoing arc-related uplift in the region.
The Bakony-Balaton Highland Volcanic Field (BBHVF) is located in the central part of Transdanubia, Pannonian Basin, with over 50 alkali basaltic volcanoes. The basanite plug of Hegyestu erupted in the first phase of volcanic activity. K/Ar and Ar/Ar ages were published for the BBHVF. K/Ar and Ar/Ar ages of the leucite-bearing basanite of Hegyestás were conflicting. This is caused by the special Ar retention feature of leucite in this basanite.
K/Ar ages measured in the usual way were 25–45% younger, but after HCl treatment of the rock, or after reducing the baking temperature of the argon extraction line from 250°C to 150°C, they became similar to the
Ar/Ar ages. All Ar/Ar determinations were performed after HF treatment. HCl treatment dissolved olivine, nepheline, leucite, magnetite and from 1-1 sample analcime or calcite. K dissolution studies from different locations of Hegyestü have shown that K content is mostly ≈2%, but it may decrease to ≈0.3%. HCl treatment dissolved 28.0–63.5% of the K content. The calculated K concentration for the dissolved part of samples with ~2%K was 4.02-6.42%: showing that leucite is responsible for the low temperature loss of 40Ar(rad). Ar may release at low temperature from very finegrained mineral, or when the Ar release mechanism changes. A 40Ar(rad) degassing spectrum has been recorded in the 55–295°C range of baking temperature and the data were plotted in the Arrhenius diagram. The diagram shows that a change of the structure in the 145–295°C range caused the loss of 40Ar(rad). On fractions of HCl treated rock 7.56±0.17 Ma isochron K/Ar age has been determined. This is regarded as minimum age of eruption and it is similar to the Ar/Ar isochron age (7.78±0.07 Ma).