The carbon balance of tropical ecosystems remains uncertain, with top-down atmospheric studies suggesting an overall sink and bottom-up ecological approaches indicating a modest net source. Here we use 12 years (2003 to 2014) of MODIS pantropical satellite data to quantify net annual changes in the aboveground carbon density of tropical woody live vegetation, providing direct, measurement-based evidence that the world's tropical forests are a net carbon source of 425.2 ± 92.0 teragrams of carbon per year (Tg C year). This net release of carbon consists of losses of 861.7 ± 80.2 Tg C year and gains of 436.5 ± 31.0 Tg C year Gains result from forest growth; losses result from deforestation and from reductions in carbon density within standing forests (degradation or disturbance), with the latter accounting for 68.9% of overall losses.

Maximum likelihood estimators and other direct optimizationbased estimators dominated statistical estimation and prediction for decades. Yet, the principled foundations supporting their dominance do not apply to the discrete high-dimensional inference problems of the 21st century. As it is well known, statistical decision theory shows that maximum likelihood and related estimators use data only to identify the single most probable solution. Accordingly, unless this one solution so dominates the immense ensemble of all solutions that its probability is near one, there is no principled reason to expect such an estimator to be representative of the posterior-weighted ensemble of solutions, and thus represent inferences drawn from the data. We employ statistical decision theory to find more representative estimators, centroid estimators, in a general high-dimensional discrete setting by using a family of loss functions with penalties that increase with the number of differences in components. We show that centroid estimates are obtained by maximizing the marginal probabilities of the solution components for unconstrained ensembles and for an important class of problems, including sequence alignment and the prediction of RNA secondary structure, whose ensembles contain exclusivity constraints. Three genomics examples are described that show that these estimators substantially improve predictions of ground-truth reference sets.prediction ͉ statistical inference ͉ computational biology ͉ discrete decoding I n the past decade, high-throughput data-acquisition technologies have rendered datasets with sizes unimaginable to our predecessors, including the sequence of the human genome (1) and the products of numerous high-throughput technologies of the post-genome era (2), data warehouses of commercial and internet transactions (3), and surveys of the objects of the universe (4). Although the emergence of such large datasets seems to imply more precise parameter estimation, paradoxically just the opposite is becoming increasingly common. This paradox emerged because these technologies simultaneously opened opportunities to draw inferences on previously unanswerable high-dimensional questions.Estimation and prediction have long been dominated by procedures that identify the most probable point, including maximum likelihood estimation (5), maximum a posteriori (MAP) estimates such as Viterbi decoding of hidden Markov models, and minimum ''free-energy'' structure predictions (6, 7). These types of estimators are referred as ML estimators (maximum likelihood-family estimators) in the remainder of this article. In addition, many algorithms that optimize scoring functions to produce estimates or predictions correspond to equivalent maximum likelihood estimation procedures (8, 9), and thus also yield ML estimators.Historically, there have been good reasons for this dominance. ML estimates are intuitively appealing because they identify the point in the space of the unknowns for which the data have highest probability. In the predi...

Supplementary data are available at Bioinformatics online.