Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

A method of assessing air toxics concentrations in urban areas using mobile platform measurements.

The objective of this paper is to demonstrate an approach to characterize the spatial variability in ambient air concentrations using mobile platform measurements. This approach may be useful for air toxics assessments in Environmental Justice applications, epidemiological studies, and environmental health risk assessments. In this study, we developed and applied a method to characterize air toxics concentrations in urban areas using results of the recently conducted field study in Wilmington, DE. Mobile measurements were collected over a 4- x 4-km area of downtown Wilmington for three components: formaldehyde (representative of volatile organic compounds and also photochemically reactive pollutants), aerosol size distribution (representing fine particulate matter), and water-soluble hexavalent chromium (representative of toxic metals). These measurements were,used to construct spatial and temporal distributions of air toxics in the area that show a very strong temporal variability, both diurnally and seasonally. An analysis of spatial variability indicates that all pollutants varied significantly by location, which suggests potential impact of local sources. From the comparison with measurements at the central monitoring site, we conclude that formaldehyde and fine particulates show a positive correlation with temperature, which could also be the reason that photochemically generated formaldehyde and fine particulates over the study area correlate well with the fine particulate matter measured at the central site.

On the multiple ecological roles of water in river networks

The distribution and movement of water can influence the state and dynamics of terrestrial and aquatic ecosystems through a diversity of mechanisms. These mechanisms can be organized into three general categories wherein water acts as (1) a resource or habitat for biota, (2) a vector for connectivity and exchange of energy, materials, and organisms, and (3) as an agent of geomorphic change and disturbance. These latter two roles are highlighted in current models, which emphasize hydrologic connectivity and geomorphic change as determinants of the spatial and temporal distributions of species and processes in river systems. Water availability, on the other hand, has received less attention as a driver of ecological pattern, despite the prevalence of intermittent streams, and strong potential for environmental change to alter the spatial extent of drying in many regions. Here we summarize long-term research from a Sonoran Desert watershed to illustrate how spatial patterns of ecosystem structure and functioning reflect shifts in the relative importance of different 'roles of water' across scales of drainage size. These roles are distributed and interact hierarchically in the landscape, and for the bulk of the drainage network it is the duration of water availability that represents the primary determinant of ecological processes. Only for the largest catchments, with the most permanent flow regimes, do flood-associated disturbances and hydrologic exchange emerge as important drivers of local dynamics. While desert basins represent an extreme case, the diversity of mechanisms by which the availability and flow of water influence ecosystem structure and functioning are general. Predicting how river ecosystems may respond to future environmental pressures will require clear understanding of how changes in the spatial extent and relative overlap of these different roles of water shape ecological patterns. © 2013 Sponseller et al.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).

Fission dynamics for capture reactions in 58,64ni + 208pb systems: New results in terms of thermal energy and neutron multiplicity correlated distributions

The neutron multidetector DéMoN has been used to investigate the symmetric splitting dynamics in the reactions 58.64Ni + 208Pb with excitation energies ranging from 65 to 186 MeV for the composite system. An analysis based on the new backtracing technique has been applied on the neutron data to determine the two-dimensional correlations between the parent composite system initial thermal energy (EthCN) and the total neutron multiplicity (νtot), and between pre- and post-scission neutron multiplicities (νpre and νpost, respectively). The νpre distribution shape indicates the possible coexistence of fast-fission and fusion-fission for the system 58Ni + 208Pb (Ebeam = 8.86 A MeV). The analysis of the neutron multiplicities in the framework of the combined dynamical statistical model (CDSM) gives a reduced friction coefficient β = 23 ± 2512 × 1021 s-1, above the one-body dissipation limit. The corresponding fission time is τf = 40 ± 4620 × 10-21 s. © 1999 Elsevier Science B.V. All rights reserved.

Particle size distributions from Fraunhofer diffraction

info:eu-repo/semantics/published

Discussion of "On families of distributions with shape parameters", by M.C. Jones

SCOPUS: ar.j

Contribution of SO3 to the acid neutralizing capacity of Andosols exposed to strong volcanogenic acid and SO2 deposition

info:eu-repo/semantics/published

Hydrocarbon field size distributions: a case study in mixed integer nonlinear programming

Of key importance to oil and gas companies is the size distribution of fields in the areas that they are drilling. Recent arguments suggest that there are many more fields yet to be discovered in mature provinces than had previously been thought because the underlying distribution is monotonic not peaked. According to this view the peaked nature of the distribution for discovered fields reflects not the underlying distribution but the effect of economic truncation. This paper contributes to the discussion by analysing up-to-date exploration and discovery data for two mature provinces using the discovery-process model, based on sampling without replacement and implicitly including economic truncation effects. The maximum likelihood estimation involved generates a high-dimensional mixed-integer nonlinear optimization problem. A highly efficient solution strategy is tested, exploiting the separable structure and handling the integer constraints by treating the problem as a masked allocation problem in dynamic programming.

Measuring distributions of jump rates in disordered metal–hydrogen systems by nuclear magnetic relaxation

Monte Carlo calculations of the nuclear magnetic relaxation rate in a disordered metal–hydrogen system having a distribution of jump rates are reported. The calculations deal specifically with the spin-locked rotating-frame relaxation time T1ρ. The results demonstrate that the temperature variation of the rate is only weakly dependent on the distribution and it is therefore unlikely that the jump rate distribution can be extracted from relaxation measurements in which temperature is the main variable. It is shown that the alternative of measuring the relaxation rate over a wide range of spin-locking field strengths at a constant temperature can lead to an evaluation of the distribution.

Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

The Richit-Richards family of distributions and its use in forestry

Johnson's SB and the logit-logistic are four-parameter distribution models that may be obtained from the standard normal and logistic distributions by a four-parameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logit-logistic with a one-parameter “standard Richards” distribution and transforming by a five-parameter Richards function, we obtain a new six-parameter distribution model, the “Richit-Richards”. The Richit-Richards includes the “logit-Richards”, the “Richit-logistic”, and the logit-logistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the Richit-Richards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the four-parameter logit-logistic for large data sets.