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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]

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]

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]

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 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]

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]

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]

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]

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]

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]