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The theory and applications of the Akaike information criterion (AIC) Mixture model simulations and the application of the AIC to a large portion of a LANDSAT segment are presented.
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Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) infrared observations at 1.1-1.7 microns probe primarily the H2O absorption band at 1.4 microns, and have provided low-resolution transmission spectra for a wide range of exoplanets. We present the application of marginalization based on Gibson to analyze exoplanet transit light curves obtained from HST WFC3 to better determine important transit parameters such as "ramp" probability (R (sub p)) divided by "ramp" total (R (sub asterisk)), which are important for accurate detections of H2O. We approximate the evidence, often referred to as the marginal likelihood, for a grid of systematic models using the Akaike Information Criterion. We then calculate the evidence-based weight assigned to each systematic model and use the information from all tested models to calculate the final marginalized transit parameters for both the band-integrated and spectroscopic light curves to construct the transmission spectrum. We find that a majority of the highest weight models contain a correction for a linear trend in time as well as corrections related to HST orbital phase. We additionally test the dependence on the shift in spectral wavelength position over the course of the observations and find that spectroscopic wavelength shifts delta (sub lambda) times lambda) best describe the associated systematic in the spectroscopic light curves for most targets while fast scan rate observations of bright targets require an additional level of processing to produce a robust transmission spectrum. The use of marginalization allows for transparent interpretation and understanding of the instrument and the impact of each systematic evaluated statistically for each data set, expanding the ability to make true and comprehensive comparisons between exoplanet atmospheres.
National Meteorological Center data from midlatitudes for three Januaries is used in calculating time series of the zonal mean meridional eddy heat flux and the zonal mean baroclinic stability, as measured by the difference between the zonal wind shear and the critical value of the shear in two-level models. Time-lagged correlations between the two series reveal a highly significant negative correlation for short time lags, peaking at approximately -0.4 when the stability parameter lags one half day behind the eddy flux. They also reveal that strongly unstable conditions are not followed by significant increases in the eddy flux. These results are seen as indicating that the synoptic variations of the zonal mean eddy flux are not closely related to the degree of baroclinic instability of the zonal mean flow. The autocorrelation of the eddy flux is then compared with those expected for autoregressive processes. A Bayesian information criterion suggests that the behavior is represented best by a damped oscillation, with a damping time of 0.8 day and a period of five days.
The development of an accurate and efficient algorithm for analyzing the structure of MSS data, the application of the Akaiki information criterion to mixture models, and a research plan to delineate some of the technical issues and associated tasks in the area of rice scene radiation characterization are discussed. The AMOEBA clustering algorithm is refined and documented.
Lattice filters have properties which make them attractive for the application to the identification of the parameters of flexible structures. Here, the problem of both order and parameter estimation is addressed, where the numerical difficulties of an embedded lattice filter are avoided by applying a periodic lattice filter. With this formulation, it is quite natural to estimate system order by applying Akaike's (1976) information criterion to each channel of the periodic lattice filter. Several examples including nonstationary cases are simulated to demonstrate these facts.
The diurnal pattern of growth hormone (GH) serum levels depends on the frequency and amplitude of GH secretory events, the kinetics of GH infusion into and clearance from the circulation, and the feedback of GH on its secretion. We present a two-dimensional linear differential equation model based on these physiological principles to describe GH diurnal patterns. The model characterizes the onset times of the secretory events, the secretory event amplitudes, as well as the infusion, clearance, and feedback half-lives of GH. We illustrate the model by using maximum likelihood methods to fit it to GH measurements collected in 12 normal, healthy women during 8 h of scheduled sleep and a 16-h circadian constant-routine protocol. We assess the importance of the model components by using parameter standard error estimates and Akaike's Information Criterion. During sleep, both the median infusion and clearance half-life estimates were 13.8 min, and the median number of secretory events was 2. During the constant routine, the median infusion half-life estimate was 12.6 min, the median clearance half-life estimate was 11.7 min, and the median number of secretory events was 5. The infusion and clearance half-life estimates and the number of secretory events are consistent with current published reports. Our model gave an excellent fit to each GH data series. Our analysis paradigm suggests an approach to decomposing GH diurnal patterns that can be used to characterize the physiological properties of this hormone under normal and pathological conditions.
The plasma concentration-time profiles following oral administration of drugs are often irregular and cannot be interpreted easily with conventional models based on first- or zero-order absorption kinetics and lag time. Six new models were developed using a time-dependent absorption rate coefficient, ka(t), wherein the time dependency was varied to account for the dynamic processes such as changes in fluid absorption or secretion, in absorption surface area, and in motility with time, in the gastrointestinal tract. In the present study, the plasma concentration profiles of propranolol obtained in human subjects following oral dosing were analyzed using the newly derived models based on mass balance and compared with the conventional models. Nonlinear regression analysis indicated that the conventional compartment model including lag time (CLAG model) could not predict the rapid initial increase in plasma concentration after dosing and the predicted Cmax values were much lower than that observed. On the other hand, all models with the time-dependent absorption rate coefficient, ka(t), were superior to the CLAG model in predicting plasma concentration profiles. Based on Akaike's Information Criterion (AIC), the fluid absorption model without lag time (FA model) exhibited the best overall fit to the data. The two-phase model including lag time, TPLAG model was also found to be a good model judging from the values of sum of squares. This model also described the irregular profiles of plasma concentration with time and frequently predicted Cmax values satisfactorily. A comparison of the absorption rate profiles also suggested that the TPLAG model is better at prediction of irregular absorption kinetics than the FA model. In conclusion, the incorporation of a time-dependent absorption rate coefficient ka(t) allows the prediction of nonlinear absorption characteristics in a more reliable manner.
A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set.
In previous studies, a variety of unsupervised anomaly detection techniques for anomaly detection were applied to SSME (Space Shuttle Main Engine) data. The observed results indicated that the identification of certain anomalies were specific to the algorithmic method under consideration. This is the reason why one of the follow-on goals of these previous investigations was to build an architecture to support the best capabilities of all algorithms. We appeal to that goal here by investigating a cascade, serial architecture for the best performing and most suitable candidates from previous studies. As a precursor to a formal ROC (Receiver Operating Characteristic) curve analysis for validation of resulting anomaly detection algorithms, our primary focus here is to investigate the model fidelity as measured by variants of the AIC (Akaike Information Criterion) for state-space based models. We show that placing constraints on a state-space model during or after the training of the model introduces a modest level of suboptimality. Furthermore, we compare the fidelity of all candidate models including those embodying the cascade, serial architecture. We make recommendations on the most suitable candidates for application to subsequent anomaly detection studies as measured by AIC-based criteria.
In-situ measurements of interplanetary coronal mass ejections (ICMEs) display a wide range of properties. A distinct subset, "magnetic clouds" (MCs), are readily identifiable by a smooth rotation in an enhanced magnetic field, together with an unusually low solar wind proton temperature. In this study, we analyze Ulysses spacecraft measurements to systematically investigate five possible explanations for why some ICMEs are observed to be MCs and others are not: i) An observational selection effect; that is, all ICMEs do in fact contain MCs, but the trajectory of the spacecraft through the ICME determines whether the MC is actually encountered; ii) interactions of an erupting flux rope (PR) with itself or between neighboring FRs, which produce complex structures in which the coherent magnetic structure has been destroyed; iii) an evolutionary process, such as relaxation to a low plasma-beta state that leads to the formation of an MC; iv) the existence of two (or more) intrinsic initiation mechanisms, some of which produce MCs and some that do not; or v) MCs are just an easily identifiable limit in an otherwise corntinuous spectrum of structures. We apply quantitative statistical models to assess these ideas. In particular, we use the Akaike information criterion (AIC) to rank the candidate models and a Gaussian mixture model (GMM) to uncover any intrinsic clustering of the data. Using a logistic regression, we find that plasma-beta, CME width, and the ratio O(sup 7) / O(sup 6) are the most significant predictor variables for the presence of an MC. Moreover, the propensity for an event to be identified as an MC decreases with heliocentric distance. These results tend to refute ideas ii) and iii). GMM clustering analysis further identifies three distinct groups of ICMEs; two of which match (at the 86% level) with events independently identified as MCs, and a third that matches with non-MCs (68 % overlap), Thus, idea v) is not supported. Choosing between ideas i) and iv) is more challenging, since they may effectively be indistinguishable from one another by a single in-situ spacecraft. We offer some suggestions on how future studies may address this.
We characterize both nonlinear and high order linear responses of fiber-optic and optoelectronic components using spread spectrum temperature cycling methods. This Thermal Signature Identification System (TheSIS) provides much more detail than conventional narrowband or quasi-static temperature profiling methods. This detail allows us to match components more thoroughly, detect subtle reversible shifts in performance, and investigate the cause of instabilities or irreversible changes. In particular, we create parameterized models of athermal fiber Bragg gratings (FBGs), delay line interferometers (DLIs), and distributed feedback (DFB) lasers, then subject the alternative models to selection via the Akaike Information Criterion (AIC). Detailed pairing of components, e.g. FBGs, is accomplished by means of weighted distance metrics or norms, rather than on the basis of a single parameter, such as center wavelength.
The forest above-ground biomass (AGB) and spatial distribution of vegetation elements have profound effects on the productivity and biodiversity of terrestrial ecosystems. In this paper, we evaluated biomass estimation from L-band Synthetic Aperture Radar (SAR) data acquired by National Aeronautics and Space Administration (NASA) Uninhabited Aerial Vehicle SAR (UAVSAR) and the improvement of accuracy by adding canopy height information derived from stereo imagery acquired by Japan Aerospace Exploration Agency (JAXA) Panchromatic Remote Sensing Instrument for Stereo Mapping (PRISM) on-board the Advanced Land Observing Satellite (ALOS). Various models for prediction of forest biomass from UAVSAR data were investigated at pixel sizes of 1/4 ha (50 m x 50 m) and 1 ha. The variance inflation factor (VIF) was calculated for each of the explanatory variables in multivariable regression models to assess the multi-collinearity between explanatory variables. In addition, the t-and p-values were used to interpret the significance of the coefficients of each explanatory variables. The R(exp. 2), Root Mean Square Error (RMSE), bias and Akaike information criterion (AIC), and leave-one-out cross-validation (LOOCV) and bootstrapping were used to validate models. At 1/4-ha scale, the R(exp. 2) and RMSE of biomass estimation from a model using a single track of polarimetric UAVSAR data were 0.59 and 52.08 Mg/ha. With canopy height from PRISM as additional independent variable, R(exp. 2) increased to 0.76 and RMSE decreased to 39.74 Mg/ha (28.24%). At 1-ha scale, the RMSE of biomass estimation based on UAVSAR data of a single track was 39.42 Mg/ha with a R(exp. 2) of 0.77. With the canopy height from PRISM, R(exp. 2) increased to 0.86 and RMSE decreased to 29.47 Mg/ha (20.18%). The models using UAVSAR data alone underestimated biomass at levels above approximately 150 Mg/ha showing the saturation phenomenon. Adding canopy height from PRISM stereo imagery significantly improved the biomass estimation and elevated the saturation level in estimating biomass. Combined use of UAVSAR data acquired from opposite directions (odd and even tracks) slightly improved the biomass estimation.Combined use of UAVSAR data acquired from opposite directions (odd and even tracks) slightly improved the biomass estimation at 1/4-ha scale, R(exp. 2) increased from 0.59 to 0.66 and RMSE reduced from 52.08 to 48.57 Mg/ha. Averaging multiple acquisitions of UAVSAR data from the same look azimuth direction did not improve biomass estimation. A biomass map derived from NASA's LVIS (Laser Vegetation Imaging System) wave-form data was used as a reference for evaluation of the biomass maps from these models. The study has also shown that the errors decreased when deciduous, evergreen, and mixed forests were modeled separately but the improvement was not significant
Warming in arctic and boreal regions is increasing shrub cover and biomass. In southcentral Alaska, willow (Salix spp.) and alder (Alnus spp.) shrubs grow taller than many tree species and account for a substantial proportion of aboveground biomass, yet they are not individually measured as part of the operational Forest Inventory and Analysis (FIA) Program. The goal of this research was to test methods for landscape-scale mapping of tall shrub biomass in upper montane and subalpine environments using FIA-type plot measurements (n = 51) and predictor variables from imagery-based structure-from-motion (SfM) and airborne lidar. Specifically, we compared biomass models constructed from imagery acquired by unmanned aerial vehicle (UAV; ~1.7 cm pixels), imagery from the NASA Goddard's Lidar, Hyperspectral, and Thermal Airborne Imager (G-LiHT; ~3.1 cm pixels), and concomitant G-LiHT small-footprint lidar. Tall shrub biomass was most accurately predicted at 5 m resolution (R^2 = 0.81, RMSE = 1.09 kg/sq. m) using G-LiHT SfM color and structure variables. Lidar-only models had lower precision (R^2 = 0.74, RMSE = 1.26 kg/sq. m), possibly due to reduced model information content from variable multicollinearity or lower data density. Separate models for upper montane zones with trees and shrubs and subalpine zones with only shrubs were always chosen over single models based on minimization of Akaike's Information Criterion, indicating the need for variable sets robust to overhanging tree canopy. Decreasing point density from UAV (5000–8000 pts./sq. m) to the G-LiHT SfM point cloud (500–2000 pts./sq. m) had little impact on model fit, suggesting that high-resolution airborne imagery can extend SfM approaches well beyond line-of-sight restrictions for UAV platforms. Overall, our results confirmed that SfM from high-resolution imagery is a viable approach to estimate shrub biomass in the boreal region, especially when an existing lidar terrain model and local field calibration data are available to quantify uncertainty in the SfM point cloud and landscape-scale estimates of shrub biomass.
A criterion for characterizing an iteratively trained classifier is presented. The criterion is based on an information theoretic measure that is developed from modeling classifier training iterations as a set of cascaded channels. The criterion is formulated as a figure of merit and as a performance index to check the appropriateness of application of the characterized classifier to an unknown data base and for implementing classifier updates and data selection respectively.
A criterion for characterizing an iteratively trained classifier is presented. The criterion is based on an information theoretic measure that is developed from modeling classifier training iterations as a set of cascaded channels. The criterion is formulated as a figure of merit and as a performance index to check the appropriateness of application of the characterized classifier to an unknown data base and for implementing classifier updates and data selection, respectively.
A criterion, based on Bayes' theorem, is described that defines the optimal set of classes (a classification) for a given set of examples. This criterion is transformed into an equivalent minimum message length criterion with an intuitive information interpretation. This criterion does not require that the number of classes be specified in advance, this is determined by the data. The minimum message length criterion includes the message length required to describe the classes, so there is a built in bias against adding new classes unless they lead to a reduction in the message length required to describe the data. Unfortunately, the search space of possible classifications is too large to search exhaustively, so heuristic search methods, such as simulated annealing, are applied. Tutored learning and probabilistic prediction in particular cases are an important indirect result of optimal class discovery. Extensions to the basic class induction program include the ability to combine category and real value data, hierarchical classes, independent classifications and deciding for each class which attributes are relevant.
Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.