Search results for: approximate entropy

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 126

Authors: Roven Tumaneng, Angelica Kristina Monzon, Ralph Sedricke Lapuz, Jose Don De Alban, Jennica Paula Masigan, Joanne Rae Pales, Laila Monera Pornel, Dennis Tablazon, Rizza Karen Veridiano, Jackie Lou Wenceslao, Edmund Leo Rico, Neil Aldrin Mallari

Abstract:

Most protected area management plans in the Philippines, particularly the smaller and more remote islands suffer from insufficient baseline data, which should provide the bases for formulating measureable conservation targets and appropriate management interventions for these protected areas. Attempts to synthesize available data particularly on cultural and socio-economic characteristic of local peoples within and outside protected areas also suffer from the lack of comprehensive and detailed inventories, which should be considered in designing adaptive management interventions to be used for those protected areas. Mt Guiting-guiting Natural Park (MGGNP) located in Sibuyan Island is one of the poorly studied protected areas in the Philippines. In this study, we determined the highly biologically important areas of the protected area using Maximum Entropy approach (MaxEnt) from environmental predictors (i.e., topographic, bioclimatic,land cover, and soil image layers) derived from global remotely sensed data and point occurrence data of species of birds and trees recorded during field surveys on the island. A total of 23 trigger species of birds and trees was modeled and stacked to generate species richness maps for biological high conservation value areas (HCVAs). Forest habitat change was delineated using dual-polarised L-band ALOS-PALSAR mosaic data at 25 meter spatial resolution, taken at two acquisition years 2007 and 2009 to provide information on forest cover ad habitat change in the island between year 2007 and 2009. Determining the livelihood guilds were also conducted using the data gathered from171 household interviews, from which demographic and livelihood variables were extracted (i.e., age, gender, number of household members, educational attainment, years of residency, distance from forest edge, main occupation, alternative sources of food and resources during scarcity months, and sources of these alternative resources).Using Principal Component Analysis (PCA) and Kruskal-Wallis test, the diversity and patterns of forest resource use by people in the island were determined with particular focus on the economic activities that directly and indirectly affect the population of key species as well as to identify levels of forest resource use by people in different areas of the park.Results showed that there are gaps in the area occupied by the natural park, as evidenced by the mismatch of the proposed HCVAs and the existing perimeters of the park. We found out that subsistence forest gathering was the possible main driver for forest degradation out of the eight livelihood guilds that were identified in the park. Determining the high conservation areas and identifyingthe anthropogenic factors that influence the species richness and abundance of key species in the different management zone of MGGNP would provide guidance for the design of a protected area management plan and future monitoring programs. However, through intensive communication and consultation with government stakeholders and local communities our results led to setting conservation targets in local development plans and serve as a basis for the reposition of the boundaries and reconfiguration of the management zones of MGGNP.

Keywords: conservation gaps, livelihood guilds, MaxEnt, protected area

Procedia PDF Downloads 378

Authors: Lauti Dwita Santy, Hermes Panggabean, Syahrir Andi Mangga

Abstract:

The Bengkulu Basin is part of the Sunda Arc system, which is a classic convergent type margin that occur around the southern rim of the Eurasian continental (Sundaland) plate. The basin is located between deep sea trench (Mentawai Outer Arc high) and the volvanic/ magmatic Arc of the Barisan Mountains Range. To the northwest it is bounded by Padang High, to the northest by Barisan Mountains (Sumatra Fault Zone) to the southwest by Mentawai Fault Zone and to the southeast by Semangko High/ Sunda Strait. The stratigraphic succession and tectonic development can be broadly divided into four stage/ periods, i.e Late Jurassic- Early Cretaceous, Late Eocene-Early Oligocene, Late Oligocene-Early Miocene, Middle Miocene-Late Miocene and Pliocene-Plistocene, which are mainly controlled by the development of subduction activities. The Pre Tertiary Basement consist of sedimentary and shallow water limestone, calcareous mudstone, cherts and tholeiitic volcanic rocks, with Late Jurassic to Early Cretaceous in age. The sedimentation in this basin is depend on the relief of the Pre Tertiary Basement (Woyla Terrane) and occured into two stages, i.e. transgressive stage during the Latest Oligocene-Early Middle Miocene Seblat Formation, and the regressive stage during the Latest Middle Miocene-Pleistocene (Lemau, Simpangaur and Bintunan Formations). The Pre-Tertiary Faults were more intensive than the overlying cover, The Tertiary Rocks. There are two main fault trends can be distinguished, Northwest–Southwest Faults and Northeast-Southwest Faults. The NW-SE fault (Ketaun) are commonly laterally persistent, are interpreted to the part of Sumatran Fault Systems. They commonly form the boundaries to the Pre Tertiary basement highs and therefore are one of the faults elements controlling the geometry and development of the Tertiary sedimentary basins.The Northeast-Southwest faults was formed a conjugate set to the Northwest–Southeast Faults. In the earliest Tertiary and reactivated during the Plio-Pleistocene in a compressive mode with subsequent dextral displacement. The Block Faulting accross these two sets of faults related to approximate North–South compression in Paleogene time and produced a series of elongate basins separated by basement highs in the backarc and forearc region. The Bengkulu basin is interpreted having evolved from pull apart feature in the area southwest of the main Sumatra Fault System related to NW-SE trending in dextral shear.Based on Pyrolysis Yield (PY) vs Total Organic Carbon (TOC) diagram show that Seblat and Lemau Formation belongs to oil and Gas Prone with the quality of the source rocks includes into excellent and good (Lemau Formation), Fair and Poor (Seblat Formation). The fine-grained carbonaceous sediment of the Seblat dan Lemau Formations as source rocks, the coarse grained and carbonate sediments of the Seblat and Lemau Formations as reservoir rocks, claystone bed in Seblat and Lemau Formation as caprock. The source rocks maturation are late immature to early mature, with kerogen type II and III (Seblat Formation), and late immature to post mature with kerogen type I and III (Lemau Formation). The burial history show to 2500 m in depthh with paleo temperature reached 80oC. Trapping mechanism occur during Oligo–Miocene and Middle Miocene, mainly in block faulting system.

Keywords: fore arc, bengkulu, sumatra, sundaland, hydrocarbon, trapping mechanism

Procedia PDF Downloads 533