Search

Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases the number of variables used to parameterize these coefficients is large, and oobtaining meaningful statistics of their probability distributions is difficult using simple sampling methods such as the basic Metropolis- Hastings algorithm--in particular, if the inverse problem is ill-conditioned or ill-posed. As a consequence, many advanced sampling methods have been described in the literature that converge faster than Metropolis-Hastings, for example, by exploiting hierarchies of statistical models or hierarchies of discretizations of the underlying differential equation. At the same time, it remains difficult for the reader of the literature to quantify the advantages of these algorithms because there is no commonly used benchmark. This paper presents a benchmark Bayesian inverse problem--namely, the determination of a spatially variable coefficient, discretized by 64 values, in a Poisson equation, based on point measurements of the solution--that fills the gap between widely used simple test cases (such as superpositions of Gaussians) and real applications that are difficult to replicate for developers of sampling algorithms. We provide a complete description of the test case and provide an open-source implementation that can serve as the basis for further experiments. We have also computed 2 x 1011 samples, at a cost of some 30 CPU years, of the posterior probability distribution from which we have generated detailed and accurate statistics against which other sampling algorithms can be tested. [ABSTRACT FROM AUTHOR]

In this paper, we propose clustering algorithms based on finite mixture and infinite mixture models of exponential approximation to the Multinomial Generalized Dirichlet (EMGD), Multinomial Beta-Liouville (EMBL) and Multinomial Shifted- Scaled Dirichlet (EMSSD) with Bayesian inference. The finite mixtures have already shown superior performance in real data sets clustering using the Expectation--Maximization approach. The proposed approaches in this paper are based on a Monte Carlo simulation technique namely Gibbs sampling algorithm including an additional Metropolis--Hastings step, and we utilize exponential family conjugate prior information to construct their posterior relying on Bayesian theory. Furthermore, we also present the infinite models based on Dirichlet processes, which results in clustering algorithms that do not require the specification of the number of mixture components to be given in advance and selects it in a principled manner. The performance of our Bayesian approaches was evaluated in some challenging real-world applications concerning text sentiment analysis, fake news detection, and human face gender recognition. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to present a Bayesian analysis of Multivariate GARCH(l, m) (M-GARCH) models including estimation of the coefficient parameters as well as the model order, by combining a set of existing MCMC algorithms in the literature. The proposed algorithm focuses on the BEKK formulation of the multivariate GARCH model. The estimation procedure will be designed as a custom MCMC with embedded Reversible Jump MCMC (RJMCMC) and Delayed Rejection Metropolis-Hastings (DRMH) steps implemented using the statistical software R. The RJMCMC steps allow three variants of BEKK models (constant, diagonal and full) to be indexed and this index included as a parameter to be estimated. The proposed MCMC algorithms are validated using extensive simulation experiments followed by a case study using bivariate data derived from the daily share prices for BHP Group Limited, Rio Tinto Group, and Fortescue Metals Group Limited on the ASX over from September 2013 to December 2021. [ABSTRACT FROM AUTHOR]

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ABSTRACT FROM AUTHOR]

This paper examines the medical correspondence between the physician George Cheyne and the aristocrats Selina Hastings and Susan Keck. Written during the 1730s, these letters reveal that both Cheyne and his patients articulated a model of medical expertise based not on knowledge in any conventional sense, but rather on fellow feeling or intersubjectivity. Drawing on letters sent by Keck to Hastings that have yet to be noticed by historians, this paper tries to understand how Cheyne and Keck sought to convince Hastings that they had felt exactly the same symptoms under which she had suffered. In so doing, it draws on scholarship concerned with the sociology of taste. Whilst it does not claim that the intersubjective form of expertise modelled by Cheyne was a form of taste, it argues that the moves he and his patients made were analogous to the strategies used at other times and places by those concerned with taste. In both cases, the participants sought ways to obtain consensus about the supposedly subjective dimensions of human experience. [ABSTRACT FROM AUTHOR]

Conditional tests are constructed by conditioning a fit measure to a minimal sufficient statistic. To calculate the p-value of these tests, Monte Carlo methods with co-sufficient samples can be used. In this paper we show how to simulate co-sufficient samples when the data distribution belongs to the exponential family with doubly transitive sufficient statistics. The proposed method is illustrated using the beta distribution. [ABSTRACT FROM AUTHOR]

Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and Metropolis – Hastings algorithms. The proposed techniques are applied to simulated data following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method was well performed in all simulation scenarios with respect to different sample sizes. [ABSTRACT FROM AUTHOR]

In a breakthrough, Hastings showed that there exist quantum channels whose classical Holevo capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings’ proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate $n^{2/3}$ -design gives rise to a quantum channel with superadditive classical Holevo capacity, where $n$ is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate $t$ -design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low’s technique for proving concentration of measure for an approximate $t$ -design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work. Haar random unitaries require at least $\Omega (n^{2})$ random bits in order to describe them with good precision. In contrast, there exist exact $n^{2/3}$ -designs using only $O(n^{2/3} \log n)$ random bits. Thus, our work can be viewed as a partial derandomisation of Hastings’ result, and a step towards the quest of finding an explicit quantum channel with superadditive classical Holevo capacity. Finally we also show that for any $p > 1$ , approximate unitary $n^{1.7}$ -designs give rise to channels violating subadditivity of Rényi $p$ -entropy. In addition to stratified analysis, the proof of this result uses a new technique of approximating a monotonic differentiable function defined on a closed bounded interval and its derivative by moderate degree polynomials which should be of independent interest. [ABSTRACT FROM AUTHOR]

The generalized double semion (GDS) model, introduced by Freedman and Hastings, is a lattice system similar to the toric code, with a gapped Hamiltonian whose definition depends on a triangulation of the ambient manifold M, but whose space of ground states does not depend on the triangulation, but only on the underlying manifold. In this paper, we use topological quantum field theory (TQFT) to investigate the low-energy limit of the GDS model. We define and study a functorial TQFT Z GDS in every dimension n such that for every closed (n - 1) -manifold M, Z GDS (M) is isomorphic to the space of ground states of the GDS model on M; the isomorphism can be chosen to intertwine the actions of the mapping class group of M that arise on both sides. Throughout this paper, we compare our constructions and results with their known analogues for the toric code. [ABSTRACT FROM AUTHOR]

We study locality preserving automorphisms of operator algebras on D-dimensional uniform lattices of prime p-dimensional qudits quantum cellular automata (QCAs), specializing in those that are translation invariant (TI), and map every prime p-dimensional Pauli matrix to a tensor product of Pauli matrices (Clifford). We associate antihermitian forms of the unit determinant over Laurent polynomial rings to TI Clifford QCA with lattice boundaries and prove that the form determines the QCA up to Clifford circuits and shifts (trivial). It follows that every 2D TI Clifford QCA is trivial since the antihermitian form in this case is always trivial. Furthermore, we prove that for any D, the fourth power of any TI Clifford QCA is trivial. We present explicit examples of nontrivial TI Clifford QCA for D = 3 and any odd prime p and show that the Witt group of the finite field F p is a subgroup of the group C (D = 3 , p) of all TI Clifford QCA modulo trivial ones. That is, C (D = 3 , p ≡ 1 mod 4) ⊇ Z 2 × Z 2 and C (D = 3 , p ≡ 3 mod 4) ⊇ Z 4 . The examples are found by disentangling the ground state of a commuting Pauli Hamiltonian, which is constructed by coupling layers of prime dimensional toric codes such that an exposed surface has an anomalous topological order that is not realizable by commuting Pauli Hamiltonians strictly in two dimensions. In an appendix independent of the main body of this paper, we revisit a recent theorem of Freedman and Hastings that any two-dimensional QCA, which is not necessarily Clifford or translation invariant, is a constant depth quantum circuit followed by a shift. We give a more direct proof of the theorem without using any ancillas. [ABSTRACT FROM AUTHOR]

The use of critical slowing down as an early warning indicator for regime switching in observations from noisy dynamical systems and models has been widely studied and implemented in recent years. Some systems, however, have been shown to avoid critical slowing down prior to a transition between equilibria (Ditlevsen and Johnsen, Geophysical Research Letters, 37(19), 2010; Hastings and Wysham, Ecol Lett 13(4):464–472, 2010). Possible explanations include a non-smooth potential driving the dynamic (Hastings and Wysham, Ecol Lett 13(4):464–472, 2010) or large perturbations driving the system out of the initial basin of attraction (Boettiger and Batt 2020). In this paper, we discuss a phenomenon analogous to critical slowing down, where a slow parameter change leads to a high likelihood of a regime shift and creates signature warning signs in the statistics of the process's sample paths. This effect, which we dub "critical speeding up," is demonstrated using a simple population model exhibiting an Allee effect. In short, if a basin of attraction is compressed under a parameter change then the potential well steepens, leading to a drop in the time series' variance and autocorrelation; precisely the opposite warning signs exhibited by critical slowing down. The fact that either falling or rising variance / autocorrelation can indicate imminent state change should underline the need for reliable modeling of any empirical system where one desires to forecast regime change. [ABSTRACT FROM AUTHOR]

This paper studies Gaussian-based filters within the pseudo-marginal Metropolis Hastings (PM-MH) algorithm for posterior inference on parameters in nonlinear DSGE models. We implement two Gaussian-based filters to evaluate the likelihood of a DSGE model solved to second and third order and embed them into the PM-MH: Central Difference Kalman filter (CDKF) and Gaussian mixture filter (GMF). The GMF is adaptively refined by splitting a mixture component into new mixture components based on Binomial Gaussian mixture. The overall results indicate that the estimation accuracy of the CDKF and the GMF is comparable to that of the particle filter (PF), except that the CDKF generates biased estimates in the extremely nonlinear case. The proposed GMF generates the most accurate estimates among them. We argue that the GMF with PM-MH can converge to the true and invariant distribution when the likelihood constructed by infinite Gaussian mixtures weakly converges to the true likelihood. In addition, we show that the Gaussian-based filters are more efficient than the PF in terms of effective computing time. Finally, we apply the method to real data. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Markov chain Monte Carlo (MCMC) algorithm supported by a neural network. In particular, we use the neural network to substitute derivative calculations made during a Metropolis adjusted Langevin algorithm (MALA) step with inexpensive neural network evaluations. Using a complex, high-dimensional blood coagulation model and a set of measurements, we define a likelihood function on which we evaluate the new MCMC algorithm. The blood coagulation model is a dynamic model, where derivative calculations are expensive and hence limit the efficiency of derivative-based MCMC algorithms. The MALA adaptation greatly reduces the time per iteration, while only slightly affecting the sample quality. We also test the new algorithm on a 2-dimensional example with a non-convex shape, a case where the MALA algorithm has a clear advantage over other state of the art MCMC algorithms. To assess the impact of the new algorithm, we compare the results to previously generated results of the MALA and the random walk Metropolis Hastings (RWMH). [ABSTRACT FROM AUTHOR]

Optimization-based samplers such as randomize-then-optimize (RTO) [J. M. Bardsley et al., SIAM J. Sci. Comput., 36 (2014), pp. A1895--A1910] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw samples from an approximate posterior distribution. ''Correcting"" these samples, either by Metropolization or importance sampling, enables characterization of the original posterior distribution. This paper focuses on the scalability of RTO to problems with highor infinite-dimensional parameters. In particular, we introduce a new subspace strategy to reformulate RTO. For problems with intrinsic low-rank structures, this subspace acceleration makes the computational complexity of RTO scale linearly with the parameter dimension. Furthermore, this subspace perspective suggests a natural extension of RTO to a function space setting. We thus formalize a function space version of RTO and establish sufficient conditions for it to produce a valid Metropolis--Hastings proposal, yielding dimension-independent sampling performance. Numerical examples corroborate the dimension independence of RTO and demonstrate sampling performance that is also robust to small observational noise. [ABSTRACT FROM AUTHOR]

In a 1970 Biometrika paper, W. K. Hastings developed a broad class of Markov chain algorithms for sampling from probability distributions that are difficult to sample from directly. The algorithm draws a candidate value from a proposal distribution and accepts the candidate with a probability that can be computed using only the unnormalized density of the target distribution, allowing one to sample from distributions known only up to a constant of proportionality. The stationary distribution of the corresponding Markov chain is the target distribution one is attempting to sample from. The Hastings algorithm generalizes the Metropolis algorithm to allow a much broader class of proposal distributions instead of just symmetric cases. An important class of applications for the Hastings algorithm corresponds to sampling from Bayesian posterior distributions, which have densities given by a prior density multiplied by a likelihood function and divided by a normalizing constant equal to the marginal likelihood. The marginal likelihood is typically intractable, presenting a fundamental barrier to implementation in Bayesian statistics. This barrier can be overcome by Markov chain Monte Carlo sampling algorithms. Amazingly, even after 50 years, the majority of algorithms used in practice today involve the Hastings algorithm. This article provides a brief celebration of the continuing impact of this ingenious algorithm on the 50th anniversary of its publication. [ABSTRACT FROM AUTHOR]

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large-scale applications with high-dimensional parameter spaces, e.g., in uncertainty quantification in porous media flow. We propose a new multilevel Metropolis--Hastings algorithm and give an abstract, problem-dependent theorem on the cost of the new multilevel estimator based on a set of simple, verifiable assumptions. For a typical model problem in subsurface flow, we then provide a detailed analysis of these assumptions and show significant gains over the standard Metropolis--Hastings estimator. Numerical experiments confirm the analysis and demonstrate the effectiveness of the method with consistent reductions of more than an order of magnitude in the cost of the multilevel estimator over the standard Metropolis--Hastings algorithm for tolerances ϵ < 10-2. [ABSTRACT FROM AUTHOR]

One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions. [ABSTRACT FROM AUTHOR]

Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods. [ABSTRACT FROM AUTHOR]

With continued pressure upon fisheries, alongside improved fisheries management in some places, there has been a decline in fish catches with changes in the structure of the ecosystem affecting its' functionality. The use of scientific based indicator frameworks in an attempt to pursue sustainable fisheries is a common trend, however the management decisions are often socially driven and can deviate, or even, conflict with the science. This study aimed to investigate British Gen Z perceptions upon what creates a sustainable fishing industry through a series of three studies. A compilation of 82 statements, derived from practitioner indicator systems, was used by 23 participants in a concept mapping process consisting of five steps; create statements, sort & rate statements, multi-dimensional scaling of sorted units, cluster analysis, and label the clusters. The next stage of the study looked to refine the large number of statements by statistically verifying them with exploratory factor analysis and confirmatory composite analysis using split halves of a sample containing 657 participants and generating a three-factor solution of Community, Ecological Management and, Economic. The domain was then switched to the descriptive typology and a further 179 British Gen Z evaluated the fisheries at Hastings and Brixham based upon case studies which further validated the three-factor solution. The significance of this study demonstrates that consumers, who influence policy and management of fisheries through their purchasing behaviour, interpret sustainable fisheries differently to science which is evidenced by the merging of the elements of ecologically and management. [ABSTRACT FROM AUTHOR]

We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis--Hastings method. Our resulting algorithm is able to sample from a specified measure on partitions or spanning forests. Being able to sample from a specified measure is a requirement of what we consider as the gold standard in quantifying the extent to which a particular map is a gerrymander. Our proposal chain modifies the recently developed method called recombination (ReCom), which draws spanning trees on joined partitions and then randomly cuts them to repartition. We improve the computational efficiency by augmenting the statespace from partitions to spanning forests. The extra information accelerates the computation of the forward and backward proposal probabilities which are required for the Metropolis--Hastings algorithm. We demonstrate this method by sampling redistricting plans on several measures of interest and find promising convergence results on several key observables of interest. We also explore some limitations in the measures that are efficient to sample from and investigate the feasibility of using parallel tempering to extend this space of measures. [ABSTRACT FROM AUTHOR]

In this article, a new modification of the Weibull model with three parameters, the new exponential Weibull distribution (E-WD), is defined. The new model has many statistical advantages, the heavy-tailed behavior and the regular variation property were offered. Many of the important statistical functions of the modified model are presented in closed forms. The flexibility of E-WD has been improved. The proposed model can be used to fit data with different shapes, it can be right-skewed, left-skewed, decreasing, curved and symmetric. Some distribution properties of the proposed model, including moment generating function, characteristic function, moment, quantile and identifiability property, have been derived. In addition to the information generating function, the Shannon entropy and information energy are also discussed. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. In the Bayesian method, three different loss functions are used. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals and the observed variance-covariance matrix are obtained. Metropolis Hastings' MCMC procedure is used for the calculations. We apply the composite distribution to stock data for four variables. The goodness-of-fit results show that the model performs well compared to its competitors. The proposed model can be used for forecasting and decision making. [ABSTRACT FROM AUTHOR]

Markov Chain Monte Carlo simulations form an essential tool for exploring high‐dimensional target distributions. Metropolis developed a fundamental random walk algorithm which was improved by Hastings later. The result is known as the Metropolis‐Hastings algorithm, which enables the exploration of multi‐dimensional distributions. The main drawbacks of this algorithm are its high auto‐correlation and slow exploration of the target distribution space. In order to increase efficiency, researchers have proposed various modifications to this algorithm. In particular, the Hamiltonian Monte Carlo simulation enhances the efficient exploration of the target probability density. The algorithm uses mechanisms inspired by Hamiltonian dynamics to propose a new sample for the target distribution. For reliability analysis, the incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results. However, using the Hamiltonian Monte Carlo method to sample is computationally expensive, especially when dealing with high‐dimensional problems and performing several steps to propose a new state. In this contribution, we show the general applicability of Hamiltonian neural networks to speed up the proposal of new samples within the Hamiltonian Monte Carlo method. [ABSTRACT FROM AUTHOR]

Autism spectrum disorder (ASD) is a neurodevelopmental condition characterized by difficulties in socialization. The amount of scientific research results on motherhood related to ASD has grown exponentially; however, there are no bibliometric studies in this field. Objective: This article aimed to analyze scientific research on motherhood related to the autism spectrum published in WoS. Articles on motherhood related to ASD were retrieved from the Web of Science (WoS). The advanced search interface used was "Title of the article, Abstract, Keywords". The analysis and visualization of the selected documents and their data were performed using a wide range of tools and software such as MS Excel (v16.0), VOS viewer (version 1.6.15), and R packages (Biblioshiny, version 2.0). A total of 1660 articles were included in this study. Most of the publications were original articles. The United States published the most significant number of articles among the countries identified. P.R. Hastings, M.M. Seltzer, and J. Van de Water were the main authors. The Journal of Autism and Developmental Disorders was the most productive and impactful journal. The main research topics were related to mental health and social support in the role of motherhood. This desk study provides researchers with a comprehensive understanding of ASD-related maternity research trends by evaluating relevant publications in recent decades. The results of this bibliometric analysis can serve as a basis and orientation for new studies. [ABSTRACT FROM AUTHOR]

Based on Hastings and Powell's research, this paper extends a three-species food-chain system to fractional-order form, whose dynamics are analyzed and explored. The necessary conditions for generating chaos are confirmed by the stability theory of fractional-order systems, chaos is characterized by its phase diagrams, and bifurcation diagrams prove that the dynamic behaviors of the fractional-order food-chain system are affected by the order. Next, the chaotic control of the fractional-order system is realized by the feedback control method with a good effect in a relative short period. The stability margin of the controlled system is revealed by the theory and numerical analysis. Finally, the results of theory analysis are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

Ambient seismic noise tomography is a novel, low-impact method for investigating the earth's structure. Although most passive seismic studies focus on structures on crustal scales, there are only a few examples of this technique being applied in a mineral exploration context. In this study, we performed an ambient seismic experiment to ascertain the relationship between the shallow shear wave velocity and mineralized zones in the Erzgebirge in Germany, one of the most important metal provinces in Europe. Late Variscan mineralized greisen and veins occurring in the Geyer-Ehrenfriedersdorf mining district of the Central Erzgebirge were mined from medieval times until the end of the 19th century. These occurrences represent a significant resource for commodities of high economic importance, such as tin, tungsten, zinc, indium, bismuth and lithium. Based on ambient noise data from a dense "LARGE-N" network comprising 400 low-power, short-period seismic stations, we applied an innovative tomographic inversion technique based on Bayesian statistics (transdimensional, hierarchical Monte Carlo search with Markov Chains using a Metropolis/Hastings sampler) to derive a three-dimensional shear wave velocity model. An auxiliary 3D airborne time-domain electromagnetic dataset is used to provide additional insight into the subsurface architecture of the area. The velocity model shows distinct anomalies down to approximately 500 m depth that correspond to known geological features of the study area, such as (a) gneiss intercalations in the mica schist-dominated host rock, imaged by a SW–NE striking low-velocity zone with a moderately steep northerly dip, and (b) a NW-trending strike-slip fault, imaged as a subvertical linear zone cross-cutting and offsetting this low-velocity domain. Similar to the velocity data, the electromagnetic data exhibit north-dipping (high-conductivity) structures in the mica schists, corresponding to the strike and dip of the predominant metamorphic fabric. An unsupervised classification performed on the bivariate 3D dataset yielded nine spatially coherent classes, one of which shows a high correspondence with drilled greisen occurrences in the roof zone of a granite pluton. The relatively high mean shear velocity and resistivity values of this class could be explained by changes in density and composition during greisen formation, as observed in other areas of the Erzgebirge. Our study demonstrates the great potential of the cost-efficient and low-impact ambient noise technology for mineral exploration, especially when combined with other independent geophysical datasets. [ABSTRACT FROM AUTHOR]

Traditional Markov chain Monte Carlo (MCMC) algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis–Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each iteration. We propose a general framework for performing MH-MCMC using mini-batches of the whole dataset and show that this gives rise to approximately a tempered stationary distribution. We prove that the algorithm preserves the modes of the original target distribution and derive an error bound on the approximation with mild assumptions on the likelihood. To further extend the utility of the algorithm to high-dimensional settings, we construct a proposal with forward and reverse moves using stochastic gradient and show that the construction leads to reasonable acceptance probabilities. We demonstrate the performance of our algorithm in both low dimensional models and high dimensional neural network applications. Particularly in the latter case, compared to popular optimization methods, our method is more robust to the choice of learning rate and improves testing accuracy. for this article are available online. [ABSTRACT FROM AUTHOR]

Comments on behaviour-based approaches to people with learning disabilities and challenging behaviour. Challenges facing positive behavioural support; Demands made on the Intensive Support Service in Hastings, England.

Motivated by the application to German interest rates, we propose a time‐varying autoregressive model for short‐term and long‐term prediction of time series that exhibit a temporary nonstationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the model and thereby regularize predictions in the far future. We use MCMC‐based inference by deriving relevant full conditional distributions and employ a Metropolis‐Hastings within Gibbs sampler approach to sample from the posterior (predictive) distribution. In combining data‐driven short‐term predictions with long‐term distribution assumptions our model is competitive to the existing methods in the short horizon while yielding reasonable predictions in the long run. We apply our model to interest rate data and contrast the forecasting performance to that of a 2‐Additive‐Factor Gaussian model as well as to the predictions of a dynamic Nelson‐Siegel model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis‐Hastings algorithm, in conjunction with the Euler‐Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood, and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

We develop a Metropolized Multiscale Forest Recombination Markov Chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a partition with a specified number of elements each of which corresponds to a different district according to a specified probability measure. The districts satisfy a collection of hard constraints, and the probability measure may be weighted with regard to a number of other criteria. The multiscale algorithm is similar to our previously developed Metropolized Forest Recombination proposal; however, this algorithm provides improved scaling properties and may also be used to preserve nested communities of interest such as counties and precincts. Both works use a proposal which extends the ReCom algorithm [D. DeFord, M. Duchin, and J. Solomon, Harvard Data Sci. Rev., (2021)] which leveraged spanning trees to merge and split districts. In this work, we extend the state space so that each district is defined by a hierarchy of trees. In this sense, the proposal step in both algorithms can be seen as a "Forest ReCom." The collection of plans sampled by the MCMC algorithm can serve as a baseline against which a particular plan of interest is compared. If a given plan has different racial or partisan qualities than what is typical of the collection of plans, the given plan may have been gerrymandered and is labeled as an outlier. Metropolizing relative to a policy driven probability measure removes the possibility of algorithmically inserted biases. [ABSTRACT FROM AUTHOR]

Purpose: From the eleventh to the thirteenth century, three major events marked surgery in France: the appearance of an epidemic linked to ergotism which led to numerous amputations, the emergence of barber surgeons for civilian practice, and the organization of war surgery for the First Crusade. Material and methods: If a certain separation between medicine and surgery had appeared at the beginning of the Middle Ages, it would have been from 1215 (at the time of the Lateran Council) that the real separation between medicine and surgery was made. Before this date, the surgery was done by the clergy (monks) who had some experience of surgical practice. After the Council de Lateran, the barbers will take charge of the surgery. Results: In the Middle Ages, the first cause of amputation was linked to poisoning by ergot of rye, intoxication due to the ingestion of contaminated bread. Due to ergotamine-related vasoconstriction, many patients will die with a frequency ranging from 10 to 20% in times of starvation. For survivors, gangrenes will lead to amputations made at the beginning by monks, then by the barber surgeons after 1215. With the name of barber surgeon, barbers are initially responsible for small surgical procedures, then for amputations given the epidemics linked to ergotism which led to numerous amputations. By this practice, they will acquire the knowledge of anatomy and the knowledge of the surgery. Apart from this civilian practice of surgery carried out by barber surgeons, the military practice of surgery will appear with the conquests of England and the start of the crusades which will require a more professional organization of surgery. Conclusion: After 1371, as only barbers surgeons had some surgical practice, their knowledge surpassed knowledge of the university. This supremacy of the barber surgeon over the surgeons of the university will be demonstrated by Ambroise Paré. [ABSTRACT FROM AUTHOR]

Copyright of American Journal of Potato Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this article is to find a better technique for estimating the volatility of the price of bitcoin on the one hand and to check if this special kind of asset called cryptocurrency behaves like other stock market indices. We include five stock market indexes for different countries such as Standard and Poor's 500 composite Index (S&P), Nasdaq, Nikkei, Stoxx, and DowJones. Using daily data over the period 2010–2019. We examine two asymmetric stochastic volatility models used to describe the volatility dependencies found in most financial returns. Two models are compared, the first is the autoregressive stochastic volatility model with Student's t-distribution (ARSV-t), and the second is the basic SVOL. To estimate these models, our analysis is based on the Markov Chain Monte-Carlo method. Therefore, the technique used is a Metropolis–Hastings (Hastings in Biometrika 57:97–109, 1970), and the Gibbs sampler (Casella and George in Am Stat 46:167–174, 1992; Gelfand and Smith in J Am Stat Assoc 85:398–409, 1990; Gilks and Wild in 41:337–348, 1992). Model comparisons illustrate that the ARSV-t model performs better performances. We conclude that this model is better than the SVOL model on the MSE and AIC function. This result concerns bitcoin as well as the other stock market indices. Without forgetting that our finding proves the efficiency of Markov Chain for our sample and the convergence and stability for all parameters to a certain level. On the whole, it seems that permanent shocks have an effect on the volatility of the price of the bitcoin and also on the other stock market. Our results will help investors better diversify their portfolio by adding this cryptocurrency. [ABSTRACT FROM AUTHOR]

Sonny Eliot is listed tenth in the cast of characters under the name Sonny Schlossberg. In her presentation, "Sonny Eliot: From POW to Punster, " Nordberg explored Eliot's time as a POW during World War II and subsequent rise to fame. JHSM Bulletin | 21 Programming Spotlight Sonny Eliot was a beloved radio and television weathercaster in Metro Detroit for nearly 60 years, becoming a household name and a Detroit institution. [Extracted from the article]

Copyright of Scientific Bulletin of National Mining University is the property of National Mining University, State Higher Educational Institution and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We propose a fast potential splitting Markov chain Monte Carlo method which costs O(1) time each step for sampling from equilibrium distributions (Gibbs measures) corresponding to particle systems with singular interacting kernels. We decompose the interacting potential into two parts; one is of long range but is smooth, and the other one is of short range but may be singular. To displace a particle, we first evolve a selected particle using the stochastic differential equation (SDE) under the smooth part with the idea of random batches, as commonly used in stochastic gradient Langevin dynamics. Then, we use the short range part to do a Metropolis rejection. Different from the classical Langevin dynamics, we only run the SDE dynamics with a random batch for a short duration of time so that the cost in the first step is O(p), where p is the batch size and is often chosen to be O(1). The cost of the rejection step is O(1) since the interaction used is of short range. We justify the proposed random-batch Monte Carlo method, which combines the random batch and splitting strategies, both in theory and with numerical experiments. While giving comparable results for typical examples of the Dyson Brownian motion and Lennard-Jones fluids, our method can save more time when compared to the classical Metropolis-Hastings algorithm. [ABSTRACT FROM AUTHOR]

We consider a scenario in which a process of interest, evolving within an environment occupied by several agents, is well-described probablistically via a Markov model. The agents each have local views and observe only some limited partial aspects of the world, but their overall task is to fuse their data to construct an integrated, global portrayal. The problem, however, is that their communications are unreliable: network links may fail, packets can be dropped, and generally the network might be partitioned for protracted periods. The fundamental problem then becomes one of consistency as agents in different parts of the network gain new information from their observations but can only share this with those with whom they are able to communicate. As the communication network changes, different views may be at odds; the challenge is to reconcile these differences. The issue is that correlations must be accounted for, lest some sensor data be double counted, inducing overconfidence or bias. As a means to address these problems, a new recursive consensus filter for distributed state estimation on hidden Markov models is presented. It is shown to be well-suited to multi-agent settings and associated applications since the algorithm is scalable, robust to network failure, capable of handling non-Gaussian transition and observation models, and is, therefore, quite general. Crucially, no global knowledge of the communication network is ever assumed. We have dubbed the algorithm a Hybrid method because two existing pieces are used in concert: the first, iterative conservative fusion is used to reach consensus over potentially correlated priors, while consensus over likelihoods, the second, is handled using weights based on a Metropolis Hastings Markov chain. To attain a detailed understanding of the theoretical upper limit for estimator performance modulo imperfect communication, we introduce an idealized distributed estimator. It is shown that under certain general conditions, the proposed Hybrid method converges exponentially to the ideal distributed estimator, despite the latter being purely conceptual and unrealizable in practice. An extensive evaluation of the Hybrid method, through a series of simulated experiments, shows that its performance surpasses competing algorithms. [ABSTRACT FROM AUTHOR]

Magic-state distillation is a resource intensive subroutine for quantum computation. The ratio of noisy input states to output states with an error rate at most ε scales as O(logγ(1/ε)) [S. Bravyi and J. Haah, Magic-state distillation with low overhead, Phys. Rev. A 86, 052329 (2012)]. In a breakthrough paper, Hastings and Haah [Distillation with Sublogarithmic Overhead, Phys. Rev. Lett. 120, 050504 (2018)] showed that it is possible to construct distillation routines with a sublogarithmic overhead, achieving γ≈0.6779 and falsifying a conjecture that γ is lower bounded by 1. They then ask whether γ can be made arbitrarily close to 0. We answer this question in the affirmative for magic-state distillation routines using qudits of prime dimension (d dimensional quantum systems for prime d). [ABSTRACT FROM AUTHOR]

We extend the new perturbation formula of equilibrium states by Hastings to KMS states of general W ∗ -dynamical systems. [ABSTRACT FROM AUTHOR]

Coupling Bayes' Theorem with a two-dimensional (2D) groundwater solute advection-diffusion transport equation allows an inverse model to be established to identify a set of contamination source parameters including source intensity (M), release location (X0, Y0) and release time (T0), based on monitoring well data. To address the issues of insufficient monitoring wells or weak correlation between monitoring data and model parameters, a monitoring well design optimization approach was developed based on the Bayesian formula and information entropy. To demonstrate how the model works, an exemplar problem with an instantaneous release of a contaminant in a confined groundwater aquifer was employed. The information entropy of the model parameters posterior distribution was used as a criterion to evaluate the monitoring data quantity index. The optimal monitoring well position and monitoring frequency were solved by the two-step Monte Carlo method and differential evolution algorithm given a known well monitoring locations and monitoring events. Based on the optimized monitoring well position and sampling frequency, the contamination source was identified by an improved Metropolis algorithm using the Latin hypercube sampling approach. The case study results show that the following parameters were obtained: 1) the optimal monitoring well position (D) is at (445, 200); and 2) the optimal monitoring frequency (Δt) is 7, providing that the monitoring events is set as 5 times. Employing the optimized monitoring well position and frequency, the mean errors of inverse modeling results in source parameters (M, X0,Y0,T0) were 9.20%, 0.25%, 0.0061%, and 0.33%, respectively. The optimized monitoring well position and sampling frequency can effectively safeguard the inverse modeling results in identifying the contamination source parameters. It was also learnt that the improved Metropolis-Hastings algorithm (a Markov chain Monte Carlo method) can make the inverse modeling result independent of the initial sampling points and achieves an overall optimization, which significantly improved the accuracy and numerical stability of the inverse modeling results. [ABSTRACT FROM AUTHOR]

Nonparametric topic models based on hierarchical Dirichlet processes (HDPs) allow for the number of topics to be automatically discovered from the data. The computational complexity of standard Gibbs sampling techniques for model training is linear in the number of topics. Recently, it was reduced to be linear in the number of topics per word using a technique called alias sampling combined with Metropolis Hastings (MH) sampling. We propose a different proposal distribution for the MH step based on the observation that distributions on the upper hierarchy level change slower than the document-specific distributions at the lower level. This reduces the sampling complexity, making it linear in the number of topics per document by using an approximation based on Metropolis-Hastings sampling. By utilizing a single global distribution, we are able to further improve the test set log-likelihood of this approximation. Furthermore, we propose a novel model of stacked HDPs utilizing this sampling method. An extensive analysis reveals the importance of the correct setting of hyperparameters for classification and shows the convergence properties of our method. Experiments demonstrate the effectiveness of the proposed approach in the context of multi-label classification as compared to previous Dependency-LDA models. [ABSTRACT FROM AUTHOR]

The article provides information on the evolutionary awakening of French Jesuit Pierre Teilhard de Chardin, a scientist in geology and palaeontology. Teilhard first found the full meaning of evolution in Hastings, a coastal town of England where he resided from 1908-1912 in a Jesuit house of studies. It states that his evolutionary awakening was a transformative experience which resulted him to reinterpret his faith's understanding, resonating through all his religious and scientific writings.

Markov chain Monte Carlo (MCMC) techniques are usually used to infer model parameters when closed-form inference is not feasible, with one of the simplest MCMC methods being the random walk Metropolis–Hastings (MH) algorithm. The MH algorithm suffers from random walk behaviour, which results in inefficient exploration of the target posterior distribution. This method has been improved upon, with algorithms such as Metropolis Adjusted Langevin Monte Carlo (MALA) and Hamiltonian Monte Carlo being examples of popular modifications to MH. In this work, we revisit the MH algorithm to reduce the autocorrelations in the generated samples without adding significant computational time. We present the: (1) Stochastic Volatility Metropolis–Hastings (SVMH) algorithm, which is based on using a random scaling matrix in the MH algorithm, and (2) Locally Scaled Metropolis–Hastings (LSMH) algorithm, in which the scaled matrix depends on the local geometry of the target distribution. For both these algorithms, the proposal distribution is still Gaussian centred at the current state. The empirical results show that these minor additions to the MH algorithm significantly improve the effective sample rates and predictive performance over the vanilla MH method. The SVMH algorithm produces similar effective sample sizes to the LSMH method, with SVMH outperforming LSMH on an execution time normalised effective sample size basis. The performance of the proposed methods is also compared to the MALA and the current state-of-art method being the No-U-Turn sampler (NUTS). The analysis is performed using a simulation study based on Neal's funnel and multivariate Gaussian distributions and using real world data modeled using jump diffusion processes and Bayesian logistic regression. Although both MALA and NUTS outperform the proposed algorithms on an effective sample size basis, the SVMH algorithm has similar or better predictive performance when compared to MALA and NUTS across the various targets. In addition, the SVMH algorithm outperforms the other MCMC algorithms on a normalised effective sample size basis on the jump diffusion processes datasets. These results indicate the overall usefulness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The decline of coral reefs characterized by macroalgae increase has been a global threat. We consider a slightly modified version of an ordinary differential equation (ODE) model proposed in Blackwood, Hastings, and Mumby [Theor. Ecol. 5 (2012), pp. 105–114] that explicitly considers the role of parrotfish grazing on coral reef dynamics. We perform complete stability, bifurcation, and persistence analysis for this model. If the fishing effort (f) is in between two critical values f0 and f1, then the system has a unique interior equilibrium, which is stable if f0