scholarly journals Joint estimation of Robin coefficient and domain boundary for the Poisson problem

2021 ◽  
Author(s):  
Ruanui Nicholson ◽  
Matti Niskanen
Keyword(s):  
Gaussian Approximation ◽  
Domain Boundary ◽  
Simulated Data ◽  
Robin Boundary Condition ◽  
Thermal Parameter ◽  
Joint Estimation ◽  
Invariance Property ◽  
Boundary Shape ◽  
Poisson Problem ◽  
Adjoint Approach

Abstract We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem arises in, for example, corrosion detection, and thermal parameter estimation. We carry out both linearised uncertainty quantification, based on a local Gaussian approximation, and full exploration of the joint posterior using Markov chain Monte Carlo (MCMC) sampling. By exploiting a known invariance property of the Poisson problem, we are able to circumvent the need to re-mesh as the shape of the boundary changes. The linearised uncertainty analysis presented here relies on a local linearisation of the parameter-to-observable map, with respect to both the Robin coefficient and the boundary shape, evaluated at the maximum a posteriori (MAP) estimates. Computation of the MAP estimate is carried out using the Gauss-Newton method. On the other hand, to explore the full joint posterior we use the Metropolis-adjusted Langevin algorithm (MALA), which requires the gradient of the log-posterior. We thus derive both the Fréchet derivative of the solution to the Poisson problem with respect to the Robin coefficient and the boundary shape, and the gradient of the log-posterior, which is efficiently computed using the so-called adjoint approach. The performance of the approach is demonstrated via several numerical experiments with simulated data.

scholarly journals Joint Estimation of Pedigrees and Effective Population Size Using Markov Chain Monte Carlo

2018 ◽  
Author(s):  
Amy Ko ◽  
Rasmus Nielsen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Population Size ◽  
Effective Population Size ◽  
Simulated Data ◽  
Composite Likelihood ◽  
Joint Estimation ◽  
Pedigree Information ◽  
Effective Population

Pedigrees provide a fine resolution of the genealogical relationships among individuals and serve an important function in many areas of genetic studies. One such use of pedigree information is in the estimation of short-term effective population size (Ne), which is of great relevance in fields such as conservation genetics. Despite the usefulness of pedigrees, however, they are often an unknown parameter and must be inferred from genetic data. In this study, we present a Bayesian method to jointly estimate pedigrees and Ne from genetic markers using Markov Chain Monte Carlo. Our method supports analysis of a large number of markers and individuals with the use of composite likelihood, which significantly increases computational efficiency. We show on simulated data that our method is able to jointly estimate relationships up to first cousins and Ne with high accuracy. We also apply the method on a real dataset of house sparrows to reconstruct their previously unreported pedigree.

scholarly journals Estimation of dynamic SNP-heritability with Bayesian Gaussian process models

2020 ◽  
Vol 36 (12) ◽  
pp. 3795-3802
Author(s):  
Arttu Arjas ◽  
Andreas Hauptmann ◽  
Mikko J Sillanpää
Keyword(s):  
Gaussian Process ◽  
Variance Components ◽  
Simulated Data ◽  
Joint Estimation ◽  
Process Models ◽  
Random Regression ◽  
Superior Performance ◽  
Supplementary Information ◽  
Time Points ◽  
Heritability Estimation

Abstract Motivation Improved DNA technology has made it practical to estimate single-nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth- and development-related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty. Results We introduce a completely tuning-free Bayesian Gaussian process (GP)-based approach for estimating dynamic variance components and heritability as their function. For parameter estimation, we use a modern Markov Chain Monte Carlo method which allows full uncertainty quantification. Several datasets are analysed and our results clearly illustrate that the 95% credible intervals of the proposed joint estimation method (which ‘borrows strength’ from adjacent time points) are significantly narrower than of a two-stage baseline method that first estimates the variance components at each time point independently and then performs smoothing. We compare the method with a random regression model using MTG2 and BLUPF90 software and quantitative measures indicate superior performance of our method. Results are presented for simulated and real data with up to 1000 time points. Finally, we demonstrate scalability of the proposed method for simulated data with tens of thousands of individuals. Availability and implementation The C++ implementation dynBGP and simulated data are available in GitHub: https://github.com/aarjas/dynBGP. The programmes can be run in R. Real datasets are available in QTL archive: https://phenome.jax.org/centers/QTLA. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Efficient inference, potential, and limitations of site-specific substitution models

2020 ◽  
Author(s):  
Vadim Puller ◽  
Pavel Sagulenko ◽  
Richard A. Neher
Keyword(s):  
Phylogenetic Trees ◽  
Simulated Data ◽  
Branch Length ◽  
Large Data ◽  
Joint Estimation ◽  
Rate Variation ◽  
Evolutionary Patterns ◽  
Site Specific ◽  
Branch Lengths ◽  
Substitution Models

AbstractNatural selection imposes a complex filter on which variants persist in a population resulting in evolutionary patterns that vary greatly along the genome. Some sites evolve close to neutrally, while others are highly conserved, allow only specific states or only change in concert with other sites. Most commonly used evolutionary models, however, ignore much of this complexity and at best account for variation in the rate at which different sites change. Here, we present an efficient algorithm to estimate more complex models that allow for site-specific preferences and explore the accuracy at which such models can be estimated from simulated data. We find that an iterative approximate maximum likelihood scheme uses information in the data efficiently and accurately estimates site-specific preferences from large data sets with moderately diverged sequences. Ignoring site-specific preferences during estimation of branch length of phylogenetic trees – an assumption of most phylogeny software – results in substantial underestimation comparable to the error incurred when ignoring rate variation. However, the joint estimation of branch lengths, site-specific rates, and site-specific preferences can suffer from identifiability problems and is typically unable to recover the correct branch lengths. Site-specific preferences estimated from large HIV pol alignments show qualitative concordance with intra-host estimates of fitness costs. Analysis of site-specific HIV substitution models suggests near saturation of divergence after a few hundred years. Such saturation can explain the inability to infer deep divergence times of HIV and SIVs using molecular clock approaches and time-dependent rate estimates.

Evidence Evaluation for Bayesian Neural Networks Using Contour Monte Carlo

2005 ◽  
Vol 17 (6) ◽  
pp. 1385-1410 ◽  
Author(s):  
Faming Liang
Keyword(s):  
Neural Networks ◽  
Monte Carlo ◽  
Gaussian Approximation ◽  
Simulated Data ◽  
Real Data ◽  
New Method ◽  
Monte Carlo Algorithm ◽  
Multilayer Perceptrons ◽  
Nonlinear Phenomena ◽  
Bayesian Neural Networks

Bayesian neural networks play an increasingly important role in modeling and predicting nonlinear phenomena in scientific computing. In this article, we propose to use the contour Monte Carlo algorithm to evaluate evidence for Bayesian neural networks. In the new method, the evidence is dynamically learned for each of the models. Our numerical results show that the new method works well for both the regression and classification multilayer perceptrons. It often leads to an improved estimate, in terms of overall accuracy, for the evidence of multiple MLPs in comparison with the reversible-jump Markov chain Monte Carlo method and the gaussian approximation method. For the simulated data, it can identify the true models, and for the real data, it can produce results consistent with those published in the literature.

scholarly journals Joint Estimation of Pedigrees and Effective Population Size Using Markov Chain Monte Carlo

Genetics ◽  
2019 ◽  
Vol 212 (3) ◽  
pp. 855-868 ◽  
Author(s):  
Amy Ko ◽  
Rasmus Nielsen
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Population Size ◽  
Effective Population Size ◽  
Simulated Data ◽  
Composite Likelihood ◽  
Joint Estimation ◽  
Pedigree Information ◽  
Effective Population

Pedigrees provide the genealogical relationships among individuals at a fine resolution and serve an important function in many areas of genetic studies. One such use of pedigree information is in the estimation of the short-term effective population size (Ne), which is of great relevance in fields such as conservation genetics. Despite the usefulness of pedigrees, however, they are often an unknown parameter and must be inferred from genetic data. In this study, we present a Bayesian method to jointly estimate pedigrees and Ne from genetic markers using Markov Chain Monte Carlo. Our method supports analysis of a large number of markers and individuals within a single generation with the use of a composite likelihood, which significantly increases computational efficiency. We show, on simulated data, that our method is able to jointly estimate relationships up to first cousins and Ne with high accuracy. We also apply the method on a real dataset of house sparrows to reconstruct their previously unreported pedigree.

scholarly journals Ohana: detecting selection in multiple populations by modelling ancestral admixture components

2019 ◽  
Author(s):  
Jade Yu Cheng ◽  
Fernando Racimo ◽  
Rasmus Nielsen
Keyword(s):  
Native American ◽  
Allele Frequency ◽  
Mexican Americans ◽  
Gaussian Approximation ◽  
Simulated Data ◽  
Fat Distribution ◽  
Likelihood Method ◽  
Multiple Populations ◽  
Frequency Changes ◽  
Candidate Regions

AbstractOne of the most powerful and commonly used methods for detecting local adaptation in the genome is the identification of extreme allele frequency differences between populations. In this paper, we present a new maximum likelihood method for finding regions under positive selection. The method is based on a Gaussian approximation to allele frequency changes and it incorporates admixture between populations. The method can analyze multiple populations simultaneously and retains power to detect selection signatures specific to ancestry components that are not representative of any extant populations. We evaluate the method using simulated data and compare it to related methods based on summary statistics. We also apply it to human genomic data and identify loci with extreme genetic differentiation between major geographic groups. Many of the genes identified are previously known selected loci relating to hair pigmentation and morphology, skin and eye pigmentation. We also identify new candidate regions, including various selected loci in the Native American component of admixed Mexican-Americans. These involve diverse biological functions, like immunity, fat distribution, food intake, vision and hair development.

scholarly journals Efficient inference, potential, and limitations of site-specific substitution models

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Vadim Puller ◽  
Pavel Sagulenko ◽  
Richard A Neher
Keyword(s):  
Phylogenetic Reconstruction ◽  
Simulated Data ◽  
Branch Length ◽  
Large Data ◽  
Joint Estimation ◽  
Model Complexity ◽  
Sequence Evolution ◽  
Evolutionary Patterns ◽  
Site Specific ◽  
Substitution Models

Abstract Natural selection imposes a complex filter on which variants persist in a population resulting in evolutionary patterns that vary greatly along the genome. Some sites evolve close to neutrally, while others are highly conserved, allow only specific states, or only change in concert with other sites. On one hand, such constraints on sequence evolution can be to infer biological function, one the other hand they need to be accounted for in phylogenetic reconstruction. Phylogenetic models often account for this complexity by partitioning sites into a small number of discrete classes with different rates and/or state preferences. Appropriate model complexity is typically determined by model selection procedures. Here, we present an efficient algorithm to estimate more complex models that allow for different preferences at every site and explore the accuracy at which such models can be estimated from simulated data. Our iterative approximate maximum likelihood scheme uses information in the data efficiently and accurately estimates site-specific preferences from large data sets with moderately diverged sequences and known topology. However, the joint estimation of site-specific rates, and site-specific preferences, and phylogenetic branch length can suffer from identifiability problems, while ignoring variation in preferences across sites results in branch length underestimates. Site-specific preferences estimated from large HIV pol alignments show qualitative concordance with intra-host estimates of fitness costs. Analysis of these substitution models suggests near saturation of divergence after a few hundred years. Such saturation can explain the inability to infer deep divergence times of HIV and SIVs using molecular clock approaches and time-dependent rate estimates.

TEM study of lanthanum aluminate

1990 ◽  
Vol 48 (4) ◽  
pp. 1060-1061
Author(s):  
C.Y. Yang ◽  
Z.R. Huang ◽  
Y.Q. Zhou ◽  
C.Z. Li ◽  
W.H. Yang ◽  
...  
Keyword(s):  
Domain Boundary ◽  
Point Group ◽  
Optical Microscope ◽  
Dark Field ◽  
Zone Axis ◽  
Superconducting Film ◽  
Ion Milling ◽  
Lanthanum Aluminate ◽  
Ring Diameter ◽  
Diffraction Patterns

Lanthanum aluminate(LaAlO3) single crystal as a substrate for high Tc superconducting film has attracted attention recently. We report here a transmission electron microscopy(TEM) study of the crystal structure and phase transformation of LaAlO3 by using Philips EM420 and EM430 microscopes. Single crystals of LaAlO3 were investigated first by optical microscope. Stripe-shaped domains of mm size are clearly seen(Fig.1a), and 90° domain boundary is also obvious. TEM specimens were prepared by mechanical grinding and polishing followed by ion-milling.Fig.lb shows μm size stripe domains of LaAlO3. Convergent beam electron diffraction patterns (CBED) from single domain were taken.Fig. 2a and Fig. 2c are [001] zone axis patterns which show a 4mm symmetry, and the (200) dark field of this zone axis gives 2mm symmetry(fig.2b). Therefore the point group of this crystal is either 4/mmm or m3m. The projection of the first order Laue zone(FOLZ) reflections on zero layer (fig. 2c) shows that the unit cell is face centered. A tetragonal unit ceil is chosen, with a=0.532nm and c=0.753nm, c being determined from the FOLZ ring diameter.

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