A Global Irrigated Area Map (GIAM) has been produced for the end of the last millennium using multiple satellite sensor, secondary, Google Earth and groundtruth data. The data included: (a) Advanced Very High Resolution Radiometer (AVHRR) 3-band and Normalized Difference Vegetation Index (NDVI) 10 km monthly time-series for 1997-1999, (b) Syste`me pour l'Observation de la Terre Vegetation (SPOT VGT) NDVI 1 km monthly time series for 1999, (c) East Anglia University Climate Research Unit (CRU) rainfall 50km monthly time series for 1961-2000, (d) Global 30 Arc-Second Elevation Data Set (GTOPO30) 1 km digital elevation data of the World, (e) Japanese Earth Resources Satellite-1 Synthetic Aperture Radar (JERS-1 SAR) data for the rain forests during two seasons in 1996 and (f) University of Maryland Global Tree Cover 1 km data for 1992-1993. A single mega-file data-cube (MFDC) of the World with 159 layers, akin to hyperspectral data, was composed by re-sampling different data types into a common 1 km resolution. The MFDC was segmented based on elevation, temperature and precipitation zones. Classification was performed on the segments. Quantitative spectral matching techniques (SMTs) used in hyperspectral data analysis were adopted to group class spectra derived from unsupervised classification and match them with ideal or target spectra. A rigorous class identification and labelling process involved the use of: (a) space-time spiral curve (ST-SC) plots, (b) brightness-greenness-wetness (BGW) plots, (c) time series NDVI plots, (d) Google Earth very-high-resolution imagery (VHRI) 'zoom-in views' in over 11 000 locations, (e) groundtruth data broadly sourced from the degree confluence project (3 864 sample locations) and from the GIAM project (1 790 sample locations), (f) high-resolution Landsat-ETM+ Geocover 150m mosaic of the World and (g) secondary data (e.g. national and global land use and land cover data). Mixed classes were resolved based on decision tree algorithms and spatial modelling, and when that did not work, the problem class was used to mask and re-classify the MDFC, and the class identification and labelling protocol repeated. The sub-pixel area (SPA) calculations were performed by multiplying full-pixel areas (FPAs) with irrigated area fractions (IAFs) for every class. A 28 class GIAMwas produced and the area statistics reported as: (a) annualized irrigated areas (AIAs), which consider intensity of irrigation (i.e. sum of irrigated areas from different seasons in a year plus continuous year-round irrigation or gross irrigated areas), and (b) total area available for irrigation (TAAI), which does not consider intensity of irrigation (i.e. irrigated areas at any given point of time plus the areas left fallow but 'equipped for irrigation' at the same point of time or net irrigated areas). The AIA of the World at the end of the last millennium was 467million hectares (Mha), which is sum of the non-overlapping areas of: (a) 252Mha from season one, (b) 174Mha from season two and (c) 41Mha from continuous yea...
Bayesian inference plays an important role in phylogenetics, evolutionary biology, and in many other branches of science. It provides a principled framework for dealing with uncertainty and quantifying how it changes in the light of new evidence. For many complex models and inference problems, however, only approximate quantitative answers are obtainable. Approximate Bayesian computation (ABC) refers to a family of algorithms for approximate inference that makes a minimal set of assumptions by only requiring that sampling from a model is possible. We explain here the fundamentals of ABC, review the classical algorithms, and highlight recent developments. [ABC; approximate Bayesian computation; Bayesian inference; likelihood-free inference; phylogenetics; simulator-based models; stochastic simulation models; tree-based models.]
Increasingly complex generative models are being used across disciplines as they allow for realistic characterization of data, but a common difficulty with them is the prohibitively large computational cost to evaluate the likelihood function and thus to perform likelihood-based statistical inference. A likelihood-free inference framework has emerged where the parameters are identified by finding values that yield simulated data resembling the observed data. While widely applicable, a major difficulty in this framework is how to measure the discrepancy between the simulated and observed data. Transforming the original problem into a problem of classifying the data into simulated versus observed, we find that classification accuracy can be used to assess the discrepancy. The complete arsenal of classification methods becomes thereby available for inference of intractable generative models. We validate our approach using theory and simulations for both point estimation and Bayesian inference, and demonstrate its use on real data by inferring an individual-based epidemiological model for bacterial infections in child care centers.
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