AIC under the framework of least squares estimation

Banks, Harvey Thomas; Joyner, Michelle Lynn

doi:10.1016/j.aml.2017.05.005

Cited by 104 publications

(89 citation statements)

References 23 publications

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“…A small circle has three degrees of freedom (radius, and central latitude and longitude) while a great circle has only two (central latitude and longitude). To allow direct comparison, we adapted the least squares fit case of the AIC (Akaike, ) where the model estimator is the rms‐misfit that we obtained from fitting the geometric models (Banks & Joyner, ; Burnham & Anderson, ). The AIC is expressed as

italicAIC = n \log ()(, {\overset{σ}{true}}^{2}) + 2 K,

where n is the number of data points, K is the number of adjusted parameters, and

{\overset{truê}{σ}}^{2}

is the estimator.…”

Section: Methodsmentioning

confidence: 99%

Upper Plate Stress Controls the Distribution of Mariana Arc Volcanoes

2020

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We present a spatial analysis of volcano distribution and morphology in the young, intraoceanic Mariana Arc. Both the quality of fit to idealized models and the divergence from those ideals indicate that Mariana Arc volcanoes are arranged into five great circle segments, rather than a single small circle or multiple small circles. The alignment of magmatic centers suggests that magma transport is controlled by the stress regime in the deep crust and/or lithospheric mantle of the Philippine Sea Plate, into which the arc is emplaced, and that arc‐normal tension is the dominant process operating in the deep lithosphere along the whole arc. Volcano morphologies indicate that the stress regime in the shallow crust varies between arc‐normal tension and compression, which also implies that the stress field can vary with depth in the arc lithosphere. We show that this horizontal and vertical stress partitioning can be related to the changing dip of the subducting plate and the breadth of the zone where it is coupled with the overriding plate. The variation in stress regime is consistent with both the distribution of seismicity in the Philippine Sea Plate and with the structural fabrics of the nonvolcanic part of the plate margin to the south. Our analysis suggests that the upper plate exerts the principal control on the distribution of volcanoes in the Mariana Arc. Where tension in the deeper parts of arc lithosphere is sufficiently concentrated, then a distinct volcanic front is produced.

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italicAIC = n \log ()(, {\overset{σ}{true}}^{2}) + 2 K,

where n is the number of data points, K is the number of adjusted parameters, and

{\overset{truê}{σ}}^{2}

is the estimator.…”

Section: Methodsmentioning

confidence: 99%

Upper Plate Stress Controls the Distribution of Mariana Arc Volcanoes

2020

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“…To compare the relative predictive quality between our relation for bankfull Shields number including bank material size against previous models obtained via different regression techniques (Li et al, 2015), the Akaike Information Criterion (AIC) is used (Akaike, 1974). For linear least square regressions, AIC is expressed as (Banks & Joyner, 2017):…”

Section: Akaike Information Criterionmentioning

confidence: 99%

Roles of Bank Material in Setting Bankfull Hydraulic Geometry as Informed by the Selenga River Delta, Russia

Dong

Nittrouer

Czapiga

et al. 2019

Water Resources Research

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A semi‐empirical bankfull Shields number relation as a function of slope, bed, and bank sediment grain size is obtained based on a field data set that includes the delta of the Selenga River, Russia, and other rivers from around the globe. The new Shields number relation is used in conjunction with continuity, flow resistance, and sediment transport equations to deduce predictive relations for bankfull width, depth, and slope of sand‐bed rivers. In addition, hydraulic geometry relations are obtained specifically for the Selenga River delta. Key results of this study are as follows: (1) bankfull width is strongly dependent on water discharge and is directly related to bank sediment size; (2) bankfull shear velocity is weakly dependent on bed sediment size and is inversely related to bank sediment size; (3) sand‐bed deltas with multiple distributary channels maintain smaller bankfull Shields numbers than is typical of alluvial rivers. This analysis is the first of its kind to include bank sediment size into a predictive bankfull Shields number relation to obtain relations for bankfull hydraulic geometry. The relations presented here can be utilized in morphodynamic models that explore how fluvial and deltaic systems respond to a range of imposed conditions, such as variable base level, sediment, and water supply.

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“…The question arises whether the improvement of the fit is significant enough to justify the increase in complexity. One way to answer this question is to compare the values of the Akaike information criterium (AIC) for the model residuals (e.g., Banks and Joyner , Equation 6):

AIC = (2 k + 1) + N \log (S / N)

…”

Section: Results Of Standard Time Series Analysismentioning

confidence: 99%

Identification and Explanation of a Change in the Groundwater Regime using Time Series Analysis

Obergfell¹,

Bakker

Maas³

2019

Groundwater

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Time series analysis is applied to identify and analyze a transition in the groundwater regime in the aquifer below the sand ridge of Salland in the Netherlands, where groundwater regime refers to the range of head variations throughout the seasons. Standard time series analysis revealed a discrepancy between modeled and observed heads in several piezometers indicating a possible change in the groundwater regime. A new time series modeling approach is developed to simulate the transition from the initial regime to the altered regime. The transition is modeled as a weighted sum of two responses, one representing the initial state of the system, the other representing the altered state. The inferred timing and magnitude of the change provided strong evidence that the transition was the result of significant dredging works that increased the river bed conductance of the main river draining the aquifer. The plausibility of this explanation is corroborated by an analytical model. This case study and the developed approach to identify a change in the groundwater regime are meant to stimulate a more systematic application of time series analysis to detect and understand changes in groundwater systems which may easily go unnoticed in groundwater flow modeling.

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AIC under the framework of least squares estimation

Cited by 104 publications

References 23 publications

Upper Plate Stress Controls the Distribution of Mariana Arc Volcanoes

Upper Plate Stress Controls the Distribution of Mariana Arc Volcanoes

Roles of Bank Material in Setting Bankfull Hydraulic Geometry as Informed by the Selenga River Delta, Russia

Identification and Explanation of a Change in the Groundwater Regime using Time Series Analysis

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