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In this paper we propose a novel approach to estimating and testing skewness in a stochastic volatility (SV) model. Our key idea is to replace a normal return error in the standard SV model with a split normal error. We show that this simple variation in the model brings about two large computational advantages. First, the SV can be simulated fast and efficiently using a one-block Gibbs sampling technique. Second, more importantly, this is the first to provide a marginal likelihood calculation method to formally test the skewness and SV in a Bayesian framework. We subsequently demonstrate the efficiency and reliability of our posterior sampling and model comparison methods through a simulation study. The simulation study results also show that neglecting skewness leads to inaccurate SV estimates and conditional expected returns. Our empirical applications to daily stock return data also show strong evidence of negative skewness.

For multimodal representation learning, traditional black-box approaches often fall short of extracting interpretable multilayer hidden structures, which contribute to visualize the connections between different modalities at multiple semantic levels. To extract interpretable multimodal latent representations and visualize the hierarchial semantic relationships between different modalities, based on deep topic models, we develop a novel multimodal Poisson gamma belief network (mPGBN) that tightly couples the observations of different modalities via imposing sparse connections between their modality-specific hidden layers. To alleviate the time-consuming Gibbs sampler adopted by traditional topic models in the testing stage, we construct a Weibull-based variational inference network (encoder) to directly map the observations to their latent representations, and further combine it with the mPGBN (decoder), resulting in a novel multimodal Weibull variational autoencoder (MWVAE), which is fast in out-of-sample prediction and can handle large-scale multimodal datasets. Qualitative evaluations on bimodal data consisting of image-text pairs show that the developed MWVAE can successfully extract expressive multimodal latent representations for downstream tasks like missing modality imputation and multimodal retrieval. Further extensive quantitative results demonstrate that both MWVAE and its supervised extension sMWVAE achieve state-of-the-art performance on various multimodal benchmarks.

Nonconvex Stochastic Optimization Nonconvex stochastic optimization problems arise in many machine learning problems, including deep learning. The stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradients with a momentum method in which a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates toward a global minimum. SGHMC has shown empirical success in practice for solving nonconvex stochastic optimization problems. In “Global convergence of stochastic gradient Hamiltonian Monte Carlo for nonconvex stochastic optimization: Nonasymptotic performance bounds and momentum-based acceleration,” Gao, Gürbüzbalaban, and Zhu provide, for the first time, the finite-time performance bounds for the global convergence of SGHMC in the context of both population and empirical risk minimization problems and show that acceleration with momentum is possible in the context of global nonconvex stochastic optimization.

Topic modeling is a significant branch of natural language processing and machine learning focused on inferring the generative process of text. Traditionally, algorithms for estimating topic models have relied on Bayesian inference and Gibbs sampling. This paper proposes a novel “acceptable set” framework for formulating topic modeling problems inspired by ideas from discrete component analysis and data-driven robust optimization. Our approach not only simplifies the design and inference of topic models, but also allows for extensions and generalizations that are challenging to integrate into traditional approaches. Different restrictions (e.g., sparsity) and assumptions (e.g., alternative generative processes) can be easily incorporated into our formulations through additional or modified constraints. Our formulations also naturally control a widely used metric of model quality, perplexity. We adapt state-of-the-art stochastic gradient methods to find good local optima for the optimization formulations. The algorithms are efficient, scaling to realistic problem sizes with runtimes comparable to existing methods. Through extensive computational experiments, we show that our methods have improved solution quality compared to baseline methods and reconstruct more reliably the underlying generative models. Our framework overcomes known vulnerabilities of traditional topic modeling algorithms: our methods are effective in low-data settings, register good out-of-sample performance, and perform well for a variety of initial assumptions on input parameter values.

N6-methyladenosine (m6A) has been shown to play crucial roles in RNA metabolism, physiology, and pathological processes. However, the specific regulatory mechanisms of most methylation sites remain uncharted due to the complexity of life processes. Biological experimental methods are costly to solve this problem, and computational methods are relatively lacking. The discovery of local co-methylation patterns (LCPs) of m6A epi-transcriptome data can benefit to solve the above problems. Based on this, we propose a novel biclustering algorithm based on the beta distribution (BDBB), which realizes the mining of LCPs of m6A epi-transcriptome data. BDBB employs the Gibbs sampling method to complete parameter estimation. In the process of modeling, LCPs are recognized as sharp beta distributions compared to the background distribution. Simulation study showed BDBB can extract all the three actual LCPs implanted in the background data and the overlap conditions between them with considerable accuracy (almost close to 100%). On MeRIP-Seq data of 69,446 methylation sites under 32 experimental conditions from 10 human cell lines, BDBB unveiled two LCPs, and Gene Ontology (GO) enrichment analysis showed that they were enriched in histone modification and embryo development, etc. important biological processes respectively. The GOE_Score scoring indicated that the biclustering results of BDBB in the m6A epi-transcriptome data are more biologically meaningful than the results of other biclustering algorithms.

In this article, considering the supervised dimensionality reduction, we first propose a model, called infinite Bayesian max-margin linear discriminant projection (iMMLDP), by assembling a set of local regions, where we make use of Bayesian nonparametric priors to handle the model selection problem, for example, the underlying number of local regions. In each local region, our model jointly learns a discriminative subspace and the corresponding classifier. Under this framework, iMMLDP combines dimensionality reduction, clustering, and classification in a principled way. Moreover, to deal with more complex data, for example, a local nonlinear separable structure, we extend the linear projection to a nonlinear case based on the kernel trick and develop an infinite kernel max-margin discriminant projection (iKMMDP) model. Thanks to the conjugate property, the parameters in these two models can be inferred efficiently via the Gibbs sampler. Finally, we implement our models on synthesized and real-world data, including multimodally distributed datasets and measured radar image data, to validate their efficiency and effectiveness.

Probabilistic topic models, such as latent Dirichlet allocation (LDA), are often used to discover hidden semantic structure of a collection of documents. In recent years, various inference algorithms have been developed to cope with learning of topic models, among which Gibbs sampling methods remain a popular choice. In this paper, we aim to improve the inference of topic models based on the Gibbs sampling framework. We extend a state augmentation based Gibbs sampling method by maximizing the replications of latent states, and propose a new generic deterministic inference method, named maximal latent state replication (MAX), for learning of a family of probabilistic topic models. One key benefit of the proposed method lies in the deterministic nature for inference, which may help to improve its running efficiency as well as predictive perplexity. We have conducted extensive experiments on real-life publicly available datasets, and the results have validated that our proposed method MAX significantly outperforms state-of-the-art baselines for inference of existing well-known topic models.

Feature selection is of great importance to make prediction for process variables in industrial production. An embedded feature selection method, based on relevance vector machines with an approximated marginal likelihood function, is proposed in this study. By setting hierarchical prior distributions over the model weights and the parameters of the automatic relevance determination kernel function, respectively, a Gaussian approximation method is designed to approximate the intractable exact marginal likelihood by using the law of the total expectation and the total covariance. Furthermore, in this study, the joint posterior distribution over the model weights and the kernel parameters is estimated by combining the Gibbs sampling with a Laplace approximation. Thus, feature selection is performed by examining the posterior over the kernel parameters. To verify the performance of the proposed method, a series of benchmark datasets and two practical industrial datasets are employed. The experimental results demonstrate that the proposed method not only produces higher prediction accuracy than other methods but also performs better in feature selection, especially in industrial case.

Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive evidence received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network’s topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. A case study of several real-world distribution systems is presented to validate the proposed method.

In this study, we present a novel framework called Community-based sentiment Extraction and NeTwork Embedding for POI Recommendation (CENTER) in order to suggesting impressive POIs in an effective and efficient fashion. The CENTER framework integrates two essential techniques: (1) a latent probabilistic generative model called Community-based Sentiment Extraction (CSE), which can accurately capture the review contents in LBSNs by taking into consideration the characteristics of social communities. The parameters of the CSE model are inferred effectively by the Gibbs sampling method. The primary sentiments are obtained based on the probability distribution of sentiments; (2) a network embedding model called Sentiment-aware Nework Embedding for POI Recommendation (SNER) is employed to learn the representation of important factors including POIs, users and textual sentiments in a low-dimensional embedding space. The joint training is utilized to alternatively sample all sets of edges in a heterogeneous network. Extensive experiments were conducted on two large-scale real datasets, in order to evaluate the performance of CENTER. The results demonstrate that CENTER outperforms the state-of-the-art baseline methods in the effectiveness and efficiency of POI suggestion.

The emergence of computer-based assessments has made response times, in addition to response accuracies, available as a source of information about test takers’ latent abilities. The development of substantively meaningful accounts of the cognitive process underlying item responses is critical to establishing the validity of psychometric tests. However, existing substantive theories such as the diffusion model have been slow to gain traction due to their unwieldy functional form and regular violations of model assumptions in psychometric contexts. In the present work, we develop an attention-based diffusion model based on process assumptions that are appropriate for psychometric applications. This model is straightforward to analyse using Gibbs sampling and can be readily extended. We demonstrate our model’s good computational and statistical properties in a comparison with two well-established psychometric models.

In this article, we consider a network with a hybrid access point (HAP) and radio frequency (RF)-energy harvesting wireless devices. The HAP is responsible for charging these devices and receiving their data. Our problem is to select a set of devices to transmit in each time slot so as to maximize a given reward over a planning horizon. In contrast to prior works, we consider the challenging case whereby the HAP has imperfect channel state information (CSI) nor information about the battery state of devices. We also consider nonlinear RF-energy conversion rates and battery leakage. We propose a cross entropy approach to identify the best set of devices to select in each time slot over random channel gains. In addition, we propose a fast Gibbs sampling approach, called Gibbs $^+$ , that incorporates a novel step to evict noncompetitive devices. We compare our solutions against random pick, round robin, original Gibbs sampling, and perfect information selection (PIS). Our results show that CE and Gibbs $^+$ algorithm produce a higher reward than RR, RP, and OGS. Advantageously, our CE and Gibbs $^+$ algorithms, respectively, achieve $\text{99\%}$ and $\text{98\%}$ of the theoretical maximum throughput as computed by PIS, which has perfect information.

This work proposes a data sampling algorithm for smart cities applications based on sensor network infrastructure. Our algorithm identifies the sensor data behavior through the Causality Complexity-Entropy Plane and performs data reduction by removing redundant data without losing the system’s properties. For this, we recognize the systems’ dynamic changes in real-time through a delimiter, named Maximum Complexity Point (MCP). Thus, we determine when to update the sampling period to maximize the system’s information content, i.e., the statistical complexity quantifier. To confirm the sampling adaptability, we apply our method in three different chaotic attractors: Rossler, Lorenz, and ${B}_{7}$ . We compared our solution with two other sampling algorithms: (i) random histogram-based sampling and the ${L}$ algorithm. We use the K-S test, the average Data Error, and the Causality Complexity-Entropy Plane to compare the results. Using our sampling approach, we observed K-S test distances less than 3% for chaotic maps and 1% for natural environments data. The best results were in the Data Error, showing an average error rate up to 13.4% lower when evaluating chaotic data and 15.7% lower when evaluating natural environments. Regarding the dispersion of points in the Causality Complexity-Entropy Plane, the sampled time-series reached regions of higher statistical complexity, indicating that they preserved information content, hence the original data’s dynamics.

Pilots' brain fatigue status recognition faces two important issues. They are how to extract brain cognitive features and how to identify these fatigue characteristics. In this article, a gamma deep belief network is proposed to extract multilayer deep representations of high-dimensional cognitive data. The Dirichlet distributed connection weight vector is upsampled layer by layer in each iteration, and then the hidden units of the gamma distribution are downsampled. An effective upper and lower Gibbs sampler is formed to realize the automatic reasoning of the network structure. In order to extract the 3-D instantaneous time-frequency distribution spectrum of electroencephalogram (EEG) signals and avoid signal modal aliasing, this article also proposes a smoothed pseudo affine Wigner-Ville distribution method. Finally, experimental results show that our model achieves satisfactory results in terms of both recognition accuracy and stability.

The advent of single-cell sequencing opens new avenues for personalized treatment. In this paper, we address a two-level clustering problem of simultaneous subject subgroup discovery (subject level) and cell type detection (cell level) for single-cell expression data from multiple subjects. However, current statistical approaches either cluster cells without considering the subject heterogeneity or group subjects without using the single-cell information. To bridge the gap between cell clustering and subject grouping, we develop a nonparametric Bayesian model, Subject and Cell clustering for Single-Cell expression data (SCSC) model, to achieve subject and cell grouping simultaneously. SCSC does not need to prespecify the subject subgroup number or the cell type number. It automatically induces subject subgroup structures and matches cell types across subjects. Moreover, it directly models the single-cell raw count data by deliberately considering the data's dropouts, library sizes, and over-dispersion. A blocked Gibbs sampler is proposed for the posterior inference. Simulation studies and the application to a multi-subject iPSC scRNA-seq dataset validate the ability of SCSC to simultaneously cluster subjects and cells.

Recently, listwise collaborative filtering (CF) algorithms are attracting increasing interest due to their efficiency and prediction quality. Different from rating-oriented (pointwise) CF, they recommend a preference ranking of items to each user without estimating the absolute value of the ratings. In practice, there are extensive side information about users and items in many corpora that can improve recommendation performance and specially help CF methods to address the cold-start problem. However, a model has not been proposed that incorporates side information to listwise CF. Therefore, in this work, a Bayesian graphical model, called Content-Aware Listwise Collaborative Filtering (CALCF), is developed which incorporates text information, represented as a bag of words, to listwise CF using topic models. We propose a Gibbs sampler with closed-form samples using data augmentation techniques to infer the latent variables. CALCF has been validated by comparison with previous listwise and pointwise algorithms on implicit (click, view, purchase) and explicit (numeric ratings) feedback data in both cold-start and warm-start scenarios. The results demonstrate that in most cases CALCF achieves better Normalized Discounted Cumulative Gain (NDCG) and Recall at top M recommendation compared with the previous models.

Community detection using statistical models is a promising research area in network analysis. Most existing statistical models for this task cannot be fitted well for various community structures. In this paper, we propose a model incorporating the latent link patterns for detecting effectively various community structures. It can automatically discover the number and the sizes of communities by grouping the vertices owning the same latent link pattern, which is meaningful and explainable. An inference approach based on collapsed Gibbs sampling is proposed to estimate the parameters of our model. Experiments on 13 real-world networks demonstrate our model outperforms four state-of-the-art approaches on most of the datasets and is competent to explore various community structures. In addition, our model can detect some hidden link patterns that offer extra information for network analysis.

The properties of a learning-based system are particularly relevant to the process study of the unknown behavior of a system or environment. In the semiconductor industry, there is regularly a partially observable system in which the entire state of the process is not directly or fully visible due to uncertainties or disturbances. The model for studying such a system that permits uncertainties regarding the stochastic (Markov) process for state information acquisition is called a partially observable Markov decision process (POMDP). This study aims to deal with the optimization issue of compensation control bias of a dynamic multilayer lithography process in wafer fabrication with prior information, the existence of high-dimensionality, and unmeasurable uncertainties. We show how the POMDP on a linear state-space model with uncertainties can encode the information from past runs and layers, and deal with accumulated overlay error at the current run and layer. The Gibbs sampling is applied to optimize the belief function of POMDP optimization approach. Note to Practitioners —The multilayer overlay error of the photolithography process is one of the remarkable and challenging issues in wafer fabrication. In a multilevel manufacturing process, errors occur at each level, which would be accumulated in the upstream operations. The optimization objective will be even more critical in a high-mixed fabrication process. In this study, the learning-based control system emerged with the state-space model compensates the multilayer overlay error. The Gibbs sampling as a Bayesian approach as a core structure of optimization algorithm is utilized, which can be updated with information from engineering’s domain knowledge or estimated information about previous runs. The robustness of the proposed optimization algorithm is shown by comparing the distribution of overlay error with conventional methods and with a fast convergence rate of the learning algorithm.

The accelerated failure time mixture cure (AFTMC) model is widely used for survival data when a portion of patients can be cured. In this paper, a Bayesian semiparametric method is proposed to obtain the estimation of parameters and density distribution for both the cure probability and the survival distribution of the uncured patients in the AFTMC model. Specifically, the baseline error distribution of the uncured patients is nonparametrically modeled by a mixture of Dirichlet process. Based on the stick-breaking formulation of the Dirichlet process, the techniques of retrospective and slice sampling, an efficient and easy-to-implement Gibbs sampler is developed for the posterior calculation. The proposed approach can be easily implemented in commonly used statistical softwares, and its performance is comparable to fully parametric method via comprehensive simulation studies. Besides, the proposed approach is adopted to the analysis of a colorectal cancer clinical trial data.

Relevance vector machine (RVM) is a popular sparse Bayesian learning model typically used for prediction. Recently it has been shown that improper priors assumed on multiple penalty parameters in RVM may lead to an improper posterior. Currently in the literature, the sufficient conditions for posterior propriety of RVM do not allow improper priors over the multiple penalty parameters. In this article, we propose a single penalty relevance vector machine (SPRVM) model in which multiple penalty parameters are replaced by a single penalty and we consider a semi Bayesian approach for fitting the SPRVM. The necessary and sufficient conditions for posterior propriety of SPRVM are more liberal than those of RVM and allow for several improper priors over the penalty parameter. Additionally, we also prove the geometric ergodicity of the Gibbs sampler used to analyze the SPRVM model and hence can estimate the asymptotic standard errors associated with the Monte Carlo estimate of the means of the posterior predictive distribution. Such a Monte Carlo standard error cannot be computed in the case of RVM, since the rate of convergence of the Gibbs sampler used to analyze RVM is not known. The predictive performance of RVM and SPRVM is compared by analyzing three real life datasets., 25 pages

In this study, non-homogeneous Poisson processes (NHPP) are used to analyze climate data. The data were collected over a certain period time and consist of the yearly average precipitation, yearly average temperature and yearly average maximum temperature for some regions of the world. Different existing parametric forms depending on time and on unknown parameters are assumed for the intensity/rate function $$\lambda (t), t \ge 0$$ of the NHPP. In the present context, the Poisson events of interest are the numbers of years that a climate variable measurement has exceeded a given threshold of interest. The threshold corresponds to the overall average measurements of each climate variable taking into account here. Two versions of the NHPP model are considered in the study, one version without including change points and one version including a change point. The parameters included in the model are estimated under a Bayesian approach using standard Markov chain Monte Carlo (MCMC) methods such as the Gibbs sampling and Metropolis–Hastings algorithms. The models are applied to climate data from Kazakhstan and Uzbekistan, in Central Asia and from the USA obtained over several years.

Beta regression models have become a popular tool for describing and predicting limited-range continuous data such as rates and proportions. However, these models can be severely affected by outlying observations that the beta distribution does not handle well. A robust alternative to the modeling with the beta distribution is considering the rectangular beta (RB) distribution, which is an extension of the former one. The RB distribution can deal with heavy tails and is therefore more flexible than the beta distribution. Regression modeling where covariates are measured with error is a frequent issue in different areas. This paper derives robust regression modeling for proportions with errors-in-variables using the RB distribution under a new parametrization recently proposed in the literature. We use a Bayesian approach to estimate the model parameters with a specification of prior distributions and a computational implementation carried out via the Gibbs sampling. Monte Carlo simulations allow us to conduct numerical evaluation to detect the statistical performance of the approach considered. Then, an illustration with real-world data is presented to show its potential uses.

This paper proposes an effective unsupervised Bayesian framework for learning a finite mixture of asymmetric generalized Gaussian distributions (AGGD). The parameters are estimated by a hybrid Markov Chain Monte Carlo (MCMC) approach, which is a combination of Metropolis-Hastings and Gibbs sampling techniques. The motivation of this research is to add modeling flexibility to Gaussian distribution and enhance its ability to fit asymmetric and non-Gaussian data by introducing additional parameters. In order to examine the performance of the proposed model, several experiments are conducted, and the model is evaluated on various real world applications. The performance of our model is measured using a wide range of evaluation techniques and compared with the performance of benchmark models to investigate the goodness of fit. From the results, it is observed that proposed model has performed better in clustering applications as compared to Bayesian Gaussian and Bayesian asymmetric Gaussian mixture models.

Multilevel modeling is a modern approach to deal with hierarchical or a nested data structure which can assess the variability between clusters. Bayesian Markov Chain Monte Carlo (MCMC) methods of ...

Scientific journals develop very rapidly along with the development of science. Reporting from labs.semanticscholar.org/corpus, the number of scientific journals has reached over 39 million. The large number of scientific journals makes it challenging to grouping scientific journals. Grouping become more difficult because each scientific journal can have more than one topic. Therefore, special methods are needed to group the scientific journals.One of the well-known topic modeling methods is Latent Dirichlet Allocation (LDA). This research is an implementation of the LDA algorithm to do topic modeling in scientific journals. The topic modeling in this study uses the title as a corpus. Various titles are processed into bag of words in the pre-processing process so that they can be used to distribute. The results of the distribution stage are used for sampling with the Gibbs Sampling method. Through the sampling process, testing can also be done to determine the optimal parameters. The testing in this study used perplexity to find the most optimal number of iterations and topics. The result from this research are that LDA Algorithm successfully performs topic modeling in scientific journals by generating a list of keywords for each topic and grouping documents on each topic. The optimal parameters based on the results of perplexity comparison are 3 topics and 500 iterations.

In this article, we introduce two quantile autoregressive models with explanatory variables. The Bayesian quantile estimation method is considered in estimating the model parameters based on an asy...

Combined heteroscedasticity and multicollinearity as dual non-spherical disturbances were experimented asymptotically. A Gibbs Sampler technique was used to investigate the asymptotic properties of hetero-elasticnet estimator with mean squares error (MSE) and bias as performance metrics. The seed was set to 12345; is set at ; Xs variables were generated as follow: the design matrix was generated from the multivariate normal distribution with mean > 0 and variance . and are truncated with Harvey (1976) heteroscedastic error structure; are collinear covariate with pairwise correlation between 0.6 and 0.9, the sample sizes were 25, 100 and 1000. The number of replications of the experiment was set at 10,000 with burn-in of 1000 which specified the draws that were discarded to remove the effects of the initial values. The thinning was set at 5 to ensure the removal of the effects of autocorrelation in the MCMC simulation. The study found that there is consistency of estimator asymptotically as the sample sizes increases from 25 to 50 so also to 1000, the larger sample size depicted least bias. The estimator exhibited efficiency asymptotically as larger sample sizes depicted least mean squares error. The study therefore recommended Bayesian hetero-elasticnet when data exhibit both heteroscedasticity and multicollinearity. Keywords: Elasticnet; Bayesian Inference and Gibbs sampler

Models with distal outcomes have been commonly used to evaluate the effect of categorical latent variables on an observed dependent variable, which can be binary, counting, or continuous. Several a...

Gibbs samplers are common Markov chain Monte Carlo (MCMC) algorithms that are used to sample from intractable probability distributions when sampling directly from full conditional distributions is possible. These types of MCMC algorithms come up frequently in many applications, and because of their popularity it is important to have a sense of how long it takes for the Gibbs sampler to become close to its stationary distribution. To this end, it is common to rely on the values of drift and minorization coefficients to bound the mixing time of the Gibbs sampler. This manuscript provides a computational method for estimating these coefficients. Herein, we detail the several advantages of the proposed methods, as well as the limitations of this approach. These limitations are primarily related to the “curse of dimensionality”, which for these methods is caused by necessary increases in the numbers of initial states from which chains need be run and the need for an exponentially increasing number of grid points for estimation of minorization coefficients.

In this article, we use exponentiated exponential distribution as a suitable statistical lifetime model for novel corona virus (covid-19) Kerala patient data. The suitability of the model has been followed by different statistical tools like the value of logarithm of likelihood, Kolmogorov–Smirnov distance, Akaike information criterion, Bayesian information criterion. Moreover, likelihood ratio test and empirical posterior probability analysis are performed to show its suitability. The maximum-likelihood and asymptotic confidence intervals for the parameters are derived from Fisher information matrix. We use the Markov Chain Monte Carlo technique to generate samples from the posterior density function. Based on generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct highest posterior density credible intervals. Further we discuss the Bayesian prediction for future observation based on the observed sample. The Gibbs sampling technique has been used for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.

From the simulation perspective, spinning reserve risk evaluation of power system is commonly a rare‐event assessing issue, for which importance sampling is an appealing solution technique. This paper proposes a hybrid importance sampling method for tracing spinning reserve inadequacy risk of power system integrating with renewables. The proposed method is oriented towards a generic high‐dimensional integral calculus, which allows for continuous and discrete random variables mixed together for casting kinds of risk indices. To improve the robustness in high‐dimensional applications, a partially collapsed Gibbs sampler is devised to help in exploring adaptive training samples which feature typical rare outage events. Interestingly, the originators engendering extreme spinning reserve inadequacy events can be traced using the sampling information of the proposed method. The performance of the proposed method is tested in an updated RTS‐79 system vis‐à‐vis several existing methods. Spinning reserve inadequacy risk tracing is explained by uncovering a scenario frequency distribution concerning the short‐term expected energy not supplied.

The paper introduces a Bayesian estimation method for quantile regression in univariate ordinal models. Two algorithms are presented that utilize the latent variable inferential framework of Albert and Chib (1993) and the normal-exponential mixture representation of the asymmetric Laplace distribution. Estimation utilizes Markov chain Monte Carlo simulation - either Gibbs sampling together with the Metropolis-Hastings algorithm or only Gibbs sampling. The algorithms are employed in two simulation studies and implemented in the analysis of problems in economics (educational attainment) and political economy (public opinion on extending "Bush Tax" cuts). Investigations into model comparison exemplify the practical utility of quantile ordinal models., 24 pages

As a principled dimension reduction technique, factor models have been widely adopted in applications. However, conducting a proper Bayesian factor analysis can be subtle in high-dimensional settings since it requires both a careful prescription of the prior distribution and a suitable computational strategy. We analyze issues of posterior inconsistency and sensitivity under different priors for high-dimensional sparse normal factor models, and show why adopting the n-orthonormal factor assumption can resolve these issues and lead to a more robust and efficient Bayesian analysis. We also provide an efficient Gibbs sampler to conduct the required computation, and show that it can be orders of magnitude more efficient than compared existing algorithms.

Today, people first make their complaints and compliments on internet about a product which they use or a company they are a customer of. Therefore, when they are going to buy a new product, they first analyze the complaints made by other users of the product. These complaints play an important role in helping people make decision of purchasing or not purchasing product. It is impossible to analyze online complaints manually due to the huge data size. However, companies are still losing a lot of time by analyzing and reading thousands of complaints one by one. In this article, online text based customer complaints are analyzed with Latent Dirichlet Allocation (LDA), GenSim LDA, Mallet LDA and Gibbs Sampling for Dirichlet Multinomial Mixture model (GSDMM) and the performances of them are compared. It is observed that GSDMM gives much more successful results than LDA. The obtained topics of the complaints are presented to users with a mobile application developed in React Native. With the developed application not only the customers will be able to see the topics of complaint from the application interface but also the companies will be able to view the distribution and statistics of the topics of complaints.

Rao–Blackwellisation is a notion often occurring in the MCMC literature, with possibly different meanings and connections with the original Rao–Blackwell theorem as established by C.R. Rao in 1945 and D. Blackwell in 1947, including a reduction of the variance of the resulting Monte Carlo approximations. This survey reviews some of the meanings of the term.

The runout distance of landslides is a critical factor that influences landslide risk quantification and mitigation designs. Nevertheless, empirical correlation models developed in a region may be ...

Social relations between users have been proven to be a good type of auxiliary information to improve the recommendation performance. However, it is a challenging issue to sufficiently exploit the social relations and correctly determine the user preference from both social and rating information. In this article, we propose a unified Bayesian Additive Matrix Approximation model (BAMA), which takes advantage of rating preference and social network to provide high-quality recommendation. The basic idea of BAMA is to extract social influence from social networks, integrate them to Bayesian additive co-clustering for effectively determining the user clusters and item clusters, and provide an accurate rating prediction. In addition, an efficient algorithm with collapsed Gibbs Sampling is designed to inference the proposed model. A series of experiments were conducted on six real-world social datasets. The results demonstrate the superiority of the proposed BAMA by comparing with the state-of-the-art methods from three views, all users, cold-start users, and users with few social relations. With the aid of social information, furthermore, BAMA has ability to provide the explainable recommendation.

In epidemiological studies where subjects are seen periodically on follow-up visits, interval-censored data occur naturally. The exact time the change of state (such as HIV seroconversion) occurs is not known exactly, only that it occurred sometime within a specific time interval. This paper considers estimation of parameters when HIV infection times are interval- censored and correlated. It is assumed that each sexual partnership has a specific unobservable random effect that induces association between infec- tion times. Parameters are estimated using the expectation-maximization algorithm and the Gibbs sampler. The results from the two methods are compared. Both methods yield fixed effects and baseline hazard estimates that are comparable. However, standard errors and frailty variance estimates are underestimated in the expectation-maximization algorithm compared to those from the Gibbs sampler. The Gibbs sampler is considered a plausible alternative to the expectation-maximization algorithm.

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.

We have extended some previous works by applying the product partition model (PPM) to identify multiple change points in the variance of normal data sequence assuming mean equal to zero. This type of problem is very common in applied economics and finance. We consider the Gibbs sampling scheme proposed in the literature to obtain the posterior estimates or product estimates for the variance and the posterior distributions for the instants when changes take place and also for the number of change points in the sequence. The PPM is used to obtain the posterior behavior of the volatility (measured as the variance) in the series of returns of four important Latin American stock indexes (MERVAL-Argentina, IBOVESPA- Brazil, IPSA-Chile and IPyC-Mexico). The posterior number of change point as well as the posterior most probable partition for each index series are also obtained.

Researchers are often interested in linking individuals between two datasets that lack a common unique identifier. Matching procedures often struggle to match records with common names, birthplaces or other field values. Computational feasibility is also a challenge, particularly when linking large datasets. We develop a Bayesian method for automated probabilistic record linkage and show it recovers more than 50% more true matches, holding accuracy constant, than comparable methods in a matching of military recruitment data to the 1900 US Census for which expert-labelled matches are available. Our approach, which builds on a recent state-of-the-art Bayesian method, refines the modelling of comparison data, allowing disagreement probability parameters conditional on non-match status to be record-specific in the smaller of the two datasets. This flexibility significantly improves matching when many records share common field values. We show that our method is computationally feasible in practice, despite the added complexity, with an R/C++ implementation that achieves significant improvement in speed over comparable recent methods. We also suggest a lightweight method for treatment of very common names and show how to estimate true positive rate and positive predictive value when true match status is unavailable.

In this paper, we propose an effective Bayesian subset selection method for the double-threshold-variable autoregressive moving-average (DT-ARMA) models. The usual complexity of estimation is increased mainly by capturing the correlation between two threshold variables and including moving-average terms in the model. By adopting the stochastic search variable selection method, combined with the Gibbs sampler and Metropolis-Hastings algorithm, we can simultaneously estimate the unknown parameters and select the best subset model from a large number of possible models. The simulation experiments illustrate that the proposed approach performs well. In applications, two real data sets are analyzed by the proposed method, and the fitted DT-ARMA model is better than the double-threshold autoregressive (DT-AR) model from the view of parsimony.

The study of factor analytic models often has to address two im- portant issues: (a) the determination of the "optimum" number of factors and (b) the derivation of a unique simple structure whose interpretation is easy and straightforward. The classical approach deals with these two tasks separately, and sometimes resorts to ad-hoc methods. This paper proposes a Bayesian approach to these two important issues, and adapts ideas from stochastic geometry and Bayesian finite mixture modelling to construct an ergodic Markov chain having the posterior distribution of the complete col- lection of parameters (including the number of factors) as its equilibrium distribution. The proposed method uses an Automatic Relevance Determi- nation (ARD) prior as the device of achieving the desired simple structure. A Gibbs sampler updating scheme is then combined with the simulation of a continuous-time birth-and-death point process to produce a sampling scheme that efficiently explores the posterior distribution of interest. The MCMC sample path obtained from the simulated posterior then provides a flexible ingredient for most of the inferential tasks of interest. Illustrations on both artificial and real tasks are provided, while major difficulties and challenges are discussed, along with ideas for future improvements.

In this paper, we propose a nonparametric approach using the Dirichlet processes (DP) as a class of prior distributions for the distribution G of the random effects in the hierarchical generalized linear mixed model (GLMM). The support of the prior distribution (and the posterior distribution) is large, allowing for a wide range of shapes for G. This provides great flexibility in estimating G and therefore produces a more flexible estimator than does the parametric analysis. We present some computation strategies for posterior computations involved in DP modeling. The proposed method is illustrated with real examples as well as simulations.