(Un)Conditional Sample Generation Based on Distribution Element Trees

Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples similar to a smooth bootstrap. These samples can be generated unconditionally, but also, without further complications, conditionally utilizing available information about certain probability-space components.Comment: published online in the Journal of Computational and Graphical Statistic

Maximum Likelihood Estimation of Log-Concave Densities on Tree Space

Phylogenetic trees are key data objects in biology, and the method of phylogenetic reconstruction has been highly developed. The space of phylogenetic trees is a nonpositively curved metric space. Recently, statistical methods to analyze the set of trees on this space are being developed utilizing this property. Meanwhile, in Euclidean space, the log-concave maximum likelihood method has emerged as a new nonparametric method for probability density estimation. In this paper, we derive a sufficient condition for the existence and uniqueness of the log-concave maximum likelihood estimator on tree space. We also propose an estimation algorithm for one and two dimensions. Since various factors affect the inferred trees, it is difficult to specify the distribution of sample trees. The class of log-concave densities is nonparametric, and yet the estimation can be conducted by the maximum likelihood method without selecting hyperparameters. We compare the estimation performance with a previously developed kernel density estimator numerically. In our examples where the true density is log-concave, we demonstrate that our estimator has a smaller integrated squared error when the sample size is large. We also conduct numerical experiments of clustering using the Expectation-Maximization (EM) algorithm and compare the results with k-means++ clustering using Fr\'echet mean.Comment: 41 pages, 10 figure

Estimasi Biomasa Dan Karbon Tersimpan Pada Pinus Merkusii Jungh. & De Vriese Di Hutan Pinus Gn. Bunder, Tn. Gn. Halimun Salak [Biomass Estimation and Carbon Stock on Pinus Merkusii Jungh. & De Vriese in Pine Forest at Bunder Mount, Gunung Halimun Salak National Park]

A study on the biomass and carbon stock estimation of Pinus merkusii Jungh. & de Vriese plantation has been conducted on 17-years and 30-years old pine forest in Gunung Bunder, Halimun Salak National Park. The method used was the allometric with non destructive technique. The results showed that pine trees density of 30-years old pine was 542 trees ha-1 ; the basal area (BA) was 26.8 m2 ha-1; trees density of 17-years old pine was 1,398 tree ha-1 with BA was 36.2 m2 ha-1. The estimation of biomass, carbon sinks and CO2 sequestration of 30-years old pine were 203.7, 96.5 and 354.2 ton ha-1, respectively. Meanwhile, the estimation of biomass, carbon sinks and CO2 sequestration of 17-years old pine were 188.3, 86.8 and 318.5 ton ha-1, respectively. Value of the environmental services derived from the CO2 absorption for the development of a pine forest ranged from US.$ 1,847.09 to 2,054.22, at two ages of pine trees

Density Trees for Efficient Nonlinear State Estimation

In this paper, a new class of nonlinear Bayesian estimators based on a special space partitioning structure, generalized Octrees, is presented. This structure minimizes memory and calculation overhead. It is used as a container framework for a set of node functions that approximate a density piecewise. All necessary operations are derived in a very general way in order to allow for a great variety of Bayesian estimators. The presented estimators are especially well suited for multi-modal nonlinear estimation problems. The running time performance of the resulting estimators is first analyzed theoretically and then backed by means of simulations. All operations have a linear running time in the number of tree nodes

Cascaded High Dimensional Histograms: A Generative Approach to Density Estimation

We present tree- and list- structured density estimation methods for high dimensional binary/categorical data. Our density estimation models are high dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the density is constant, similar to the flat density within the bin of a histogram. Histograms, however, cannot easily be visualized in higher dimensions, whereas our models can. The accuracy of histograms fades as dimensions increase, whereas our models have priors that help with generalization. Our models are sparse, unlike high-dimensional histograms. We present three generative models, where the first one allows the user to specify the number of desired leaves in the tree within a Bayesian prior. The second model allows the user to specify the desired number of branches within the prior. The third model returns lists (rather than trees) and allows the user to specify the desired number of rules and the length of rules within the prior. Our results indicate that the new approaches yield a better balance between sparsity and accuracy of density estimates than other methods for this task.Comment: 27 pages, 13 figure