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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]