Path storage in the particle filter

This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N \log N$ where $T$ is the time horizon, $N$ is the number of particles and $C$ is a constant, as well as an efficient algorithm to realise this. The theoretical result and the algorithm are illustrated with numerical experiments.Comment: 9 pages, 5 figures. To appear in Statistics and Computin

Using parallel computation to improve Independent Metropolis--Hastings based estimation

In this paper, we consider the implications of the fact that parallel raw-power can be exploited by a generic Metropolis--Hastings algorithm if the proposed values are independent. In particular, we present improvements to the independent Metropolis--Hastings algorithm that significantly decrease the variance of any estimator derived from the MCMC output, for a null computing cost since those improvements are based on a fixed number of target density evaluations. Furthermore, the techniques developed in this paper do not jeopardize the Markovian convergence properties of the algorithm, since they are based on the Rao--Blackwell principles of Gelfand and Smith (1990), already exploited in Casella and Robert (1996), Atchade and Perron (2005) and Douc and Robert (2010). We illustrate those improvements both on a toy normal example and on a classical probit regression model, but stress the fact that they are applicable in any case where the independent Metropolis-Hastings is applicable.Comment: 19 pages, 8 figures, to appear in Journal of Computational and Graphical Statistic

Parallel resampling in the particle filter

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle filter, or more generally Sequential Monte Carlo (SMC), which are increasingly used in statistical inference. SMC methods carry a set of weighted particles through repeated propagation, weighting and resampling steps. The propagation and weighting steps are straightforward to parallelise, as they require only independent operations on each particle. The resampling step is more difficult, as standard schemes require a collective operation, such as a sum, across particle weights. Focusing on this resampling step, we analyse two alternative schemes that do not involve a collective operation (Metropolis and rejection resamplers), and compare them to standard schemes (multinomial, stratified and systematic resamplers). We find that, in certain circumstances, the alternative resamplers can perform significantly faster on a GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover, in single precision, the standard approaches are numerically biased for upwards of hundreds of thousands of particles, while the alternatives are not. This is particularly important given greater single- than double-precision throughput on modern devices, and the consequent temptation to use single precision with a greater number of particles. Finally, we provide auxiliary functions useful for implementation, such as for the permutation of ancestry vectors to enable in-place propagation.Comment: 21 pages, 6 figure

Extent of stacking disorder in diamond

Hexagonal diamond has been predicted computationally to display extraordinary physical properties including a hardness that exceeds cubic diamond. However, a recent electron microscopy study has shown that so-called hexagonal diamond samples are in fact not discrete materials but faulted and twinned cubic diamond. We now provide a quantitative analysis of cubic and hexagonal stacking in diamond samples by analysing X-ray diffraction data with the DIFFaX software package. The highest fractions of hexagonal stacking we find in materials which were previously referred to as hexagonal diamond are below 60%. The remainder of the stacking sequences are cubic. We show that the cubic and hexagonal sequences are interlaced in a complex way and that naturally occurring Lonsdaleite is not a simple phase mixture of cubic and hexagonal diamond. Instead, it is structurally best described as stacking disordered diamond. The future experimental challenge will be to prepare diamond samples beyond 60% hexagonality and towards the so far elusive 'perfect' hexagonal diamond

Longleaf Pine Restoration in the South Carolina Sandhills Wiregrass Gap

Longleaf pine restoration has been a topic of great concern and intrigue in the southeast and has taken on new fervor in recent decades as restoration methods continue to develop. Many landowners and forest managers are now pursuing ecological forestry and restoration ecology in great numbers as a new form of land management. However, niche regions can often be overlooked, as is the case with the Carolina Sandhills Wiregrass Gap, an area devoid of wiregrass and one that is on the outskirt regions of the historical longleaf pine range. Field studies were conducted pre- and post-harvest during two growing seasons in dense loblolly pine stands, actively being converted to longleaf pine habitat through restoration timber harvesting. Located in Camden, South Carolina, the study site was positioned directly in the heart of the South Carolina Sandhills Wiregrass Gap. We conducted an abiotic environmental inventory to monitor disturbance responses and ecological trends following restoration timber harvesting. Then, using ecological criteria characteristic of longleaf-sandhill ecology, we developed a series of habitat suitability models for longleaf pine restoration across the region using spatial modeling applications. Finally, harvesting productivity was investigated as a logistical approach to test the economic feasibility of restoration harvesting in South Carolina. Our findings indicate that logging slash manipulation significantly affects abiotic responses following disturbances and that this type of restoration approach is profitable for both landowners and loggers. Moreover, almost 30% of this unique ecoregion could support such an operation based on our model outputs, indicating strong restoration potential

Boston University School of Medicine Alumni News

Newsletter for Boston University School of Medicine alumni

Mixing apples and oranges: Assessing ecological status and its confidence from multiple and diverse indicators

Ecosystem responses to increasing human pressures are complex and diverse, affecting organisms across all trophic levels. This has prompted the development of methods that integrate information across many indicators for environmental management. Legislative frameworks such as the European Water Framework Directive (WFD), specifically prescribe that integrated assessme nt (IA) of ecological status must consider indicators representing various biological and supporting quality elements. We present a general approach for an IA system based on a piece-wise linear transformation of indicator distributions to a standardized scale, allowing for integrating information from multiple and diverse indicators through a policy-dependent aggregation scheme. Uncertainties associated with monitoring data used for calculating indicators and their propagation throughout the integration scheme allow for confidence assessment at all levels of the hierarchical integration. Specific pressures leading to ecological impact can be identified through the most impaired indicators in the hierarchical and transparent aggregation scheme. The IA and its confidence are facilitated though the development of an online tool that accesses information from monitoring databases and presents the outcome at all levels of the assessment, ensuring consistency and transparency in the calculations for all potential stakeholders. We demonstrate the versality and applicability of the approach using indicators and aggregation principles from the Swedish national guidelines for assessing ecological status of rivers, lakes and coastal waters according to the WFD. Although the approach and the tool were developed specifically for the WFD ecological status assessment in Sweden, the generality of the approach implies that it can easily be adapted to the WFD assessment methods of other countries as well as other policies, where an integrated assessment is required.publishedVersio

An Innovative Take on Filtering Carbon Dioxide Through CryoCapture

Overview (Air Mover): Carbon dioxide plays an important role in the earth's ecosystem; the lives of many organisms are based on the balancing of this gas. Plants and animals need it for survival however, an excess of carbon dioxide can also end the organism’s life. The production of the gas mostly comes from the combustion of fossil fuel, power plants, big industries, vehicles, and processes involving natural gasses. One of the most known issues of carbon dioxide pollution is global warming. The greenhouse gas essentially traps heat in the atmosphere, increasing the global temperature. The methodology provided is an innovative solution towards the creation of an environmentally friendly carbon dioxide filter. Current air filtration systems are restricted to industrial environments limiting the ability to filter the air. Due to the large noise and low range of operation of axial fans the filtration systems need controlled environments for longevity. The paper presents a versatile air mover that can be mounted onto multiple surfaces due to its low profile and bracket mounts. Furthermore, the usage of a diagonal fan inside of a PVC pipe allows for a durable system that can operate at high efficiency and low noise. The main challenge in designing the air mover was figuring out how to quantify the scalability of the device and what parameters could be changed in order to make the device more viable. The designs most prominent feature are the inclusion of a modular enclosure that can be adapted to multiple areas and environments while withstanding harsh conditions due to the PVC piping that can be coated with a diagonal fan for high volumetric flow rates and pressure differential for versatility in environments the device is placed in as well as efficiency. Overview (Carbon Storer): The Civil and Environmental Engineering team is responsible for finding a cost effective and sustainable way to transport, store and recycle the carbon caught in the air from the Carbon Catcher designed by the other engineering teams. In the team’s design, the Carbon Catcher will reduce the harmful emissions in the air by capturing CO2, store it and then utilize it in another industry which will reduce the need to mine for more raw materials which would thus further reduce the pollution emitted into the environment. Our plan is to recycle the carbon emitted from a factory and utilize it in CO2 dry ice. It's the Civil and Environmental Engineers’ job to find a way to connect a sustainable solution with a solution that improves the public’s quality of life. There are many industries that pollute immense amounts from the mining of raw material or the emission of pollutants. The team wants to show industries that the economic solution can also be the sustainable solution. Overview (Membrane) The team’s solution focuses on the use of cryogenic carbon capture, a method in which the selective freezing points of the gaseous components of air are used to separate out carbon dioxide. For this process, the team will be utilizing a 4 step filtration process. First, the flue gas will be run through a particulate filter to catch all macroscopic particles that may be present within the air. Afterwards, the gas is then passed through a dehumidifier where a majority of water content will be extracted. Following this, The gas was then run through a long pipe and progressively cool it down to the freezing point of carbon dioxide. Finally, the filtered gas is extracted, and a bubbler is used to separate the solid carbon dioxide. The carbon dioxide is then compressed and recycled around the feed pipe to help in the cooling process. Along the process of this design, the team encountered problems finding the optimum materials for temperatures this low. As well, coming up with a way to eliminate heat transfer from the outside posed a huge problem. Through the experience, the team was able to gain a greater view of what benefits and drawbacks must be balanced, along with the economic interest that comes with designing an efficient process. Unlike how most designs are focused, It was understood that using a membrane only provided so much creativity when it came to filtration. As a result, the team researched other successful methods and arrived at utilizing cryogenics to filter. Goal Research to provide a single solution to remove levels of carbon dioxide in the immediate atmosphere, transport it to a storage mechanism, and find a way to recycle it. Powerful research is required to ensure effective methodologies, material usage, and flexible scalability of the overall device. This particular team seeks to find an alternative separation process to membrane filtration, the efficacy of which has not been demonstrated beyond the scale of a laboratory