Integrating remote sensing datasets into ecological modelling: a Bayesian approach

Process-based models have been used to simulate 3-dimensional complexities of forest ecosystems and their temporal changes, but their extensive data requirement and complex parameterisation have often limited their use for practical management applications. Increasingly, information retrieved using remote sensing techniques can help in model parameterisation and data collection by providing spatially and temporally resolved forest information. In this paper, we illustrate the potential of Bayesian calibration for integrating such data sources to simulate forest production. As an example, we use the 3-PG model combined with hyperspectral, LiDAR, SAR and field-based data to simulate the growth of UK Corsican pine stands. Hyperspectral, LiDAR and SAR data are used to estimate LAI dynamics, tree height and above ground biomass, respectively, while the Bayesian calibration provides estimates of uncertainties to model parameters and outputs. The Bayesian calibration contrasts with goodness-of-fit approaches, which do not provide uncertainties to parameters and model outputs. Parameters and the data used in the calibration process are presented in the form of probability distributions, reflecting our degree of certainty about them. After the calibration, the distributions are updated. To approximate posterior distributions (of outputs and parameters), a Markov Chain Monte Carlo sampling approach is used (25 000 steps). A sensitivity analysis is also conducted between parameters and outputs. Overall, the results illustrate the potential of a Bayesian framework for truly integrative work, both in the consideration of field-based and remotely sensed datasets available and in estimating parameter and model output uncertainties

Entanglement entropy in fermionic Laughlin states

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the `total quantum dimension') characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.Comment: 4+ pages, 3 figures. Minor changes in v

Simple Measures of Individual Cluster-Membership Certainty for Hard Partitional Clustering

We propose two probability-like measures of individual cluster-membership certainty which can be applied to a hard partition of the sample such as that obtained from the Partitioning Around Medoids (PAM) algorithm, hierarchical clustering or k-means clustering. One measure extends the individual silhouette widths and the other is obtained directly from the pairwise dissimilarities in the sample. Unlike the classic silhouette, however, the measures behave like probabilities and can be used to investigate an individual's tendency to belong to a cluster. We also suggest two possible ways to evaluate the hard partition. We evaluate the performance of both measures in individuals with ambiguous cluster membership, using simulated binary datasets that have been partitioned by the PAM algorithm or continuous datasets that have been partitioned by hierarchical clustering and k-means clustering. For comparison, we also present results from soft clustering algorithms such as soft analysis clustering (FANNY) and two model-based clustering methods. Our proposed measures perform comparably to the posterior-probability estimators from either FANNY or the model-based clustering methods. We also illustrate the proposed measures by applying them to Fisher's classic iris data set