Search results for: numerical validation

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 152

Authors: Ananya Barui, Provas Banerjee, Jyotirmoy Chatterjee

Abstract:

Application of optical technology in medicine and biology has a long track-record. In this endeavor, OCT is able to attract both engineers and biologists to work together in the field of photonics for establishing a striking non-invasive imaging technology. In contrast to other in vivo imaging modalities like Raman imaging, confocal imaging, two-photon microscopy etc. which can perform in vivo imaging upto 100-200 micron depth due to limitation in numerical aperture or scattering, however, OCT can achieve high-resolution imaging upto few millimeters of tissue structures depending on their refractive index in different anatomical location. This tomographic system depends on interference of two light waves in an interferometer to produce a depth profile of specimen. In wound healing, frequent collection of biopsies for follow-up of repair process could be avoided by such imaging technique. Real time skin OCT (the optical biopsy) has efficacy in deeper and faster illumination of cutaneou tissue to acquire high resolution cross sectional images of their internal micro-structure. Swept Source-OCT (SS-OCT), a novel imaging technique, can generate high-speed depth profile (~ 2 mm) of wound at a sweeping rate of laser with micron level resolution and optimum coherent length of 5-6 mm. Normally multi-layered skin tissue depicts different optical properties along with variation in thickness, refractive index and composition (i.e. keratine layer, water, fat etc.) according to their anatomical location. For instance, stratum corneum, the upper-most and relatively dehydrated layer of epidermis reflects more light and produces more lucid and a sharp demarcation line with rest of the hydrated epidermal region. During wound healing or regeneration, optical properties of cutaneous tissue continuously altered with maturation of wound bed. More mature and less hydrated tissue component reflects more light and becomes visible as a brighter area in comparison to immature region which content higher amount water or fat that depicts as a darker area in OCT image. Non-healing wound possess prolonged inflammation and inhibits nascent proliferative stage. Accumulation of necrotic tissues also prevents the repair of non-healing wounds. Due to high resolution and potentiality to reflect the compositional aspects of tissues in terms of their optical properties, this tomographic method may facilitate in differentiating non-healing and acute wounds in addition to clinical observations. Non-invasive OCT offers better insight regarding specific biological status of tissue in health and pathological conditions, OCT images could be associated with histo-pathological ‘gold standard’. This correlated SS-OCT and microscopic evaluation of the wound edges can provide information regarding progressive healing and maturation of the epithelial components. In the context of searching analogy between two different imaging modalities, their relative performances in imaging of healing bed were estimated for probing an alternative approach. Present study validated utility of SS-OCT in revealing micro-anatomic structure in the healing bed with newer information. Exploring precise correspondence of OCT images features with histo-chemical findings related to epithelial integrity of the regenerated tissue could have great implication. It could establish the ‘optical biopsy’ as a potent non-invasive diagnostic tool for cutaneous pathology.

Keywords: histo-pathology, non invasive imaging, OCT, wound healing

Procedia PDF Downloads 275

Authors: Pablo Reche

Abstract:

Since 1980’s aquaculture has become the biggest economic activity in southern Chile, being Salmo salar and Oncorhynchus mykiss the main finfish species. High fish density makes both species prone to contract diseases, what drives the industry to big losses, affecting greatly the local economy. Three are the most concerning infective agents, the infectious salmon anemia virus (ISAv), the bacteria Piscirickettsia salmonis and the copepod Caligus rogercresseyi. To regulate the industry the government arranged the salmon farms within management areas named as barrios, which coordinate the fallowing periods and antibiotics treatments of their salmon farms. In turn, barrios are gathered into larger management areas, named as macrozonas whose purpose is to minimize the risk of disease transmission between them and to enclose the outbreaks within their boundaries. However, disease outbreaks still happen and transmission to neighbor sites enlarges the initial event. Salmon disease agents are mostly transported passively by local currents. Thus, to understand how transmission occurs it must be firstly studied the physical environment. In Chile, salmon farming takes place in the inner seas of the southernmost regions of western Patagonia, between 41.5ºS-55ºS. This coastal marine system is characterised by western winds, latitudinally modulated by the position of the South-Eats Pacific high-pressure centre, high precipitation rates and freshwater inflows from the numerous glaciers (including the largest ice cap out of Antarctic and Greenland). All of these forcings meet in a complex bathymetry and coastline system - deep fjords, shallow sills, narrow straits, channels, archipelagos, inlets, and isolated inner seas- driving an estuarine circulation (fast outflows westwards on surface and slow deeper inflows eastwards). Such a complex system is modelled on the numerical model MIKE3, upon whose 3D current fields particle-track-biological models (one for each infective agent) are decoupled. Each agent biology is parameterized by functions for maturation and mortality (reproduction not included). Such parameterizations are depending upon environmental factors, like temperature and salinity, so their lifespan will depend upon the environmental conditions those virtual agents encounter on their way while passively transported. CLIC (Connectivity-Langrangian–IFOP-Chile) is a service platform that supports the graphical visualization of the connectivity matrices calculated from the particle trajectories files resultant of the particle-track-biological models. On CLIC users can select, from a high-resolution grid (~1km), the areas the connectivity will be calculated between them. These areas can be barrios and macrozonas. Users also can select what nodes of these areas are allowed to release and scatter particles from, depth and frequency of the initial particle release, climatic scenario (winter/summer) and type of particle (ISAv, Piscirickettsia salmonis, Caligus rogercresseyi plus an option for lifeless particles). Results include probabilities downstream (where the particles go) and upstream (where the particles come from), particle age and vertical distribution, all of them aiming to understand how currently connectivity works to eventually propose a minimum risk zonation for aquaculture purpose. Preliminary results in Chiloe inner sea shows that the risk depends not only upon dynamic conditions but upon barrios location with respect to their neighbors.

Keywords: aquaculture zonation, Caligus rogercresseyi, Chilean Patagonia, coastal oceanography, connectivity, infectious salmon anemia virus, Piscirickettsia salmonis

Procedia PDF Downloads 151