Gibbs Sampling Technique Research Articles

Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values.

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

Gibbs Sampling for Damage Detection Using Complex Modal Data from Multiple Setups

This paper presents a novel Gibbs sampling approach for structural health monitoring (SHM) with detection of structural changes/damages using incomplete complex modal data measured with a limited number of sensors. The usual difficulty with the availability of sensors in SHM practices and enforcing data acquisition in multiple setups is thoroughly addressed. Structural modeling incorporated with damping is considered in this proposed inverse problem exercise to calibrate damping parameters along with the stiffness and mass parameters facilitating SHM. Both proportional and nonproportional viscous damping are adopted in structural modeling. Detailed formulations on the probabilistic detection of changes/damages are presented in detail. Moreover, a Gibbs sampling technique is introduced to quantify uncertainties of the various sets of uncertain parameters, where samples of the conditional probability density function of a parameter set are obtained iteratively. The proposed approach retains the typical advantage of the nonrequirement of mode-matching. A validation exercise is performed using a three-dimensional building structure (attached with supplementary viscous dampers) and a laboratory steel structure considering multiple damage cases and different sensor placements. The proposed methodology is observed to be efficient for SHM using incomplete complex modal data measured with a limited number of sensors.

Meta-analysis of a step-stress experiment under Weibull distribution

ABSTRACT In this article, we mainly focus on the meta-analysis of several simple step-stress experimental data sets. It is assumed that independent data sets are obtained from s simple step-stress experiments. It is further assumed that the lifetime of the experimental units follow two parameter Weibull distribution with different shape and scale parameters at different stress levels. The classical and Bayesian inference of the model parameters have been provided. Since the closed-form solution of maximum-likelihood estimators of the model parameters do not exist, asymptotic properties of the estimators have been used to construct confidence intervals. On the other hand, Gibbs sampling technique has been used to obtain the Bayes estimates and the associated credible intervals of the model parameters. Extensive simulation experiments have been performed to assess the performance of the proposed methods, and the analyses of two data sets have been presented for illustrative purpose.

Estimating and Testing Skewness in a Stochastic Volatility Model

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.

Simulated tempering with irreversible Gibbs sampling techniques.

We present here two novel algorithms for simulated tempering simulations, which break the detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we present here are based on Gibbs sampling and concern breaking DBC at the update scheme of the temperature swaps. We utilize three systems as a test bed for our methods: a Markov chain Monte Carlo simulation on a simple system described by a one-dimensional double well potential, the Ising model, and molecular dynamics simulations on alanine pentapeptide (ALA5). The relaxation times of inverse temperature, magnetic susceptibility, and energy density for the Ising model indicate clear gains in sampling efficiency over conventional Gibbs sampling techniques with DBC and also over the conventionally used simulated tempering with the Metropolis-Hastings (MH) scheme. Simulations on ALA5 with a large number of temperatures indicate distinct gains in mixing times for inverse temperature and consequently the energy of the system compared to conventional MH. With no additional computational overhead, our methods were found to be more efficient alternatives to the conventionally used simulated tempering methods with DBC. Our algorithms should be particularly advantageous in simulations of large systems with many temperature ladders, as our algorithms showed a more favorable constant scaling in Ising spin systems as compared with both reversible and irreversible MH algorithms. In future applications, our irreversible methods can also be easily tailored to utilize a given dynamical variable other than temperature to flatten rugged free energy landscapes.

Inference for two‐parameter Rayleigh competing risks data under generalized progressive hybrid censoring

AbstractIn this paper, a competing risks model based on the generalized progressive hybrid censored two‐parameter Rayleigh distributions is studied under the assumption that the lifetime distributions of failure causes are identically distributed with same location and different scale parameters. We obtain maximum likelihood estimates of unknown parameters with associated existence uniqueness. The approximate confidence intervals are constructed using the asymptotic distribution of maximum likelihood estimates via the observed information matrix. Further, Bayes point estimates and the highest probability density credible intervals of unknown parameters are presented, and the Gibbs sampling technique is used to approximate corresponding estimates. A Monte Carlo simulation study is conducted to compare the accuracy of proposed estimates. Finally, a real‐life example is presented for illustration purpose.

Application of degradation growth model in the estimation of Bayesian system reliability

In real life situations, for example, in case of concrete structures and mechanical devises, failure occurs due to accumulation of stress over time, and the consequent degradation causes the system to under-perform, thereby failure occurs completely, when the accumulated stress exceeds a critical threshold. The degradation path is known for some systems and in such cases useful information on product reliability can be obtained from these measurements. This work considers a degradation model having exponential degradation path with positive degradation rate, which follows Weibull distribution with known shape parameter β, and unknown scale parameter α. The Bayesian analysis is performed by considering noninformative (Quasi) and informative (Gamma) prior distributions for the scale parameter α. The Bayesian estimators of α and the system reliability are presented as well. The standard error for estimated α corresponding to both informative and noninformative priors are calculated using bootstrap method. It is observed that for larger bootstrap sample, the Bayes estimator of α, tends to have minimum standard error. It is also seen from the simulation study carried out by making use of Gibbs sampling technique that the Bayesian reliability of the system approaches the actual reliability for increasing sample size.

An Extended Burr-XII Distribution with Application to Lifetime Data

Abstract In this article, a new distribution named the extended Burr-XII distribution is developed. This new distribution combines the Burr-XII and Weibull distributions by using the method of T-X family. Probability density, hazard rate, residual and reversed residual lifetime functions, and the s th raw moment of the distribution are studied. We obtain the stress-strength reliability. The extended Burr-XII is able to model distributions with monotonically decreasing and upside down bathtub hazard rates. The maximum likelihood, ordinary least squares, weighted least squares, maximum product of spacings, Cramér-von Mises, Anderson-Darling, Kolmogorov-Smirnov, and Bayes methods are adopted for estimating the parameters of the model. The asymptotic confidence intervals of the parameters are obtained according to the observed Fisher’s information matrix. Also, the posterior density credible intervals of the parameters are obtained under gamma prior using Gibbs sampling technique. The new distribution and other distributions are fitted to two real data sets, and the results indicate that the new distribution is quite a reasonable model for the given data sets. Lastly, the performance of the proposed estimation methods is compared by a Monte Carlo simulation.

Inferences for two Lindley populations based on joint progressive type-II censored data

The joint censoring scheme is of great importance when the motive of study is to compare the relative merits of products in relation of their service times. In last few years, progressive censoring received considerable attention in order to save cost and time of the experiment. This paper deals with inferences for Lindley populations, when joint progressive type-II censoring scheme is applied on two samples in a joint manner. Here, the maximum likelihood estimators of parameters are derived along with their associated confidence intervals which are dependent on the Fisher’s information matrix. The boot-p and boot-t confidence intervals are also obtained. Bayes estimators of the unknown parameters assuming gamma priors are calculated. The concept of importance sampling technique and Gibbs sampling technique are used as the Bayes estimators cannot be calculated in closed form. HPD credible intervals are also constructed. A Monte Carlo simulation study is performed to measure the efficiency of the estimates. A real data set is given for illustrative purpose. Finally some criteria for an optimum censoring scheme are discussed.

Robust parameter design based on Gaussian process with model uncertainty

In robust parameter design, it is common to use computer models to simulate the relationships between input variables and output responses. However, for the contaminated experimental data, the model uncertainty between computer models and actual physical systems will seriously impair the robustness of the optimal input settings. In this paper, we propose a new weighted robust design approach concerning the model uncertainty from outliers based on the robust Gaussian process model with a Student-t likelihood (StGP). Firstly, to reduce the impact of outliers on the output means and variances, the StGP modelling technique is adopted to estimate the relationship models for contaminated data. Secondly, the Gibbs sampling technique is employed to estimate model parameters for better mixing and convergence. Finally, an optimisation scheme integrating the quality loss function and confidence interval analysis approach is built to find the feasible optimisation solution. Meanwhile, the hypersphere decomposition method and data-driven method are applied to determine the relative weights of objective functions. Two examples are used to demonstrate the effectiveness of the proposed approach. The comparison results show that the proposed approach can achieve better performance than other approaches by considering the model uncertainty from outliers.

On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor

Bayes factor is a major Bayesian tool for model comparison especially when the model priors are the same. In this paper, the Savage-Dickey Density Ratio (SDDR) is used to derive the Bayes factor to select a model from two competing models under consideration in a normal linear regression with an independent normal-gamma prior. The Gibbs sampling technique for the joint posterior distribution with equal prior precision for both the unrestricted and restricted models is used to obtain the model estimates. The result shows that the Bayes factor gave more support to the unrestricted model against the restricted and was consistent irrespective of changes in sample size.

Empirical Bayes Based on Squared Error Loss and Precautionary Loss Functions in Sequential Sampling Plan

An acceptance sampling plans are statistical tools in quality control which often used for lot inspection in several areas such as industry, engineering and business. It can be applied for preserving the quality of products in industry process and preserving the producer’s risk and consumer’s risk in the production process of manufactures. The objective of this study is to utilize the Empirical Bayes approach based on squared error loss and precautionary loss functions for parameter estimation in sequential sampling plans. The parameters are estimated using Lindley’s approximation technique, and hyper-parameters can be obtained via Gibbs sampling technique. Data are normally distributed under an unknown mean and variance. The proposed plans are compared with traditional approaches including a single sampling plan and sequential sampling plan. The probability of acceptance ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{a}$ </tex-math></inline-formula> ) and average sample number (ASN) are used as criterion for comparison. Results show that the proposed plans yielded the smaller ASN and higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P_{a}$ </tex-math></inline-formula> than both classical methods.

A dynamic financial distress forecast model with multiple forecast results under unbalanced data environment

Corporate financial distress forecasts are important for companies, investors and regulatory authorities. However, as most financial distress forecast (FDF) models in previous studies were based on a single time dimension, they have tended to ignore the two key financial distress data characteristics, imbalanced data sets and concept drift of data stream. To overcome these problems, this study proposes a new dynamic financial distress forecasting (DFDF) approach, the Adaptive Neighbor SMOTE-Recursive Ensemble Approach (ANS-REA), that allows for multiple forecast results from unbalanced data streams. An empirical experiment was conducted on 373 financially distressed samples and 1119 matching normal Chinese listed companies from 2007 to 2017. With an overall average AUC, it was found that the Random Forest (RF) classifier outperformed other commonly used classifiers such as Support Vector Machine (SVM), Decision Tree (DT), baggingDT, oblique random forests (obRF), Kernel ridge regression (KRR) and Bayes in the classification of DFDF data. In addition, the proposed ANS-REA algorithm had better performance than SMOTE, ANS, Random Walk Over-Sampling Approach (RWO), Rapidly Converging Gibbs sampling Technique (racog), SMOTEboost, RUSboost, SMOTEbagging, wRACOG and Majority Weighted Minority Oversampling Technique (MWMOTE) methods in dealing with imbalanced data sets classification. Further, we found that the proposed model that combined the multiple forecast results is the effective way to solve the financial distress forecast problem.

A joint model of place of residence (POR) and place of work (POW): Making use of Gibbs sampling technique to overcome arbitrary assumptions in contexts of data limitation

Place or residence (POR) and place of work (POW) are two spatial pivots defining patterns of travel behavior. These choices are considered part of long-term choice influencing short-term daily travel choices. Hence, POR-POW distributions are input into almost all daily travel demand models. However, in many cases, POW-POR is modelled in an ad-hoc way considering the gravity-based or entropy is maximizing aggregate modelling approach. Lack of data on the sequence of choices related to POR and POW is often blamed for avoiding using disaggregate choice model. Recognizing such data limitation, this paper presents an alternative methodology of modelling joint distribution of POW-POW that uses disaggregate choice models without necessarily knowing the sequence of POR and POW choices. It uses the conditional probability break downs of joint POR-POW choice probabilities as depicted in the Gibbs sampling approach. This allows capturing effects of household socioeconomic characteristics, zonal land-use characteristics, and modal accessibility factors in the POR-POW models. The model is applied for a case study in the city of Ottawa. Results reveal that the proposed methodology can replicate observed patterns of POR-POW with a high degree of accuracy.

A roadmap towards implementing parallel aspect level sentiment analysis

In the digital era, the importance of extracting the hidden sentiments from user reviews plays a prominent role, to increase the profitability of an organization. The interest among, the research community in Sentiment Analysis (SA) has grown exponentially. But there are enormous challenges still being faced in the field of SA namely: Identification of sarcasm/Irony/Conditional/Modifier statements present in the review, Identification of Aspects and sentiment word as a pair (Data Transformation), Rating the recognized Aspects towards predicting the overall aggregated sentiment, Analyzing and designing issues towards implementing the parallel Aspect Level sentiment. In the present research work, We have addressed each of this challenges using a serial hybridization model, Where, the output of each step, is input to the following stage. First, towards identification sarcasm. In which, the dictionary is updated with the set of sentiment words by manually crafted rules. Next, to mitigate the discovery of sentiment and aspect word pair. In which, Latent Dirichlet Allocation (LDA), Gibbs sampling techniques are used. Next, to present the result of sentiment analysis as the overall rating of data considered, Latent Aspect Rating Regression (LARR) model is proposed (Data Presentation). Finally, addressed the designing issues (deciding numbers of mappers and reducers needed) towards implementing the parallel Aspect Level sentiment Analysis with the objective of improving the resource utilization in Big Data clusters. This work can help the researchers doing research in the field of speech recognition, development of recommended systems. The evaluation Metric used in estimating the performance of each step in our research are F-score, Rand Index, Classification accuracy and Root Mean Absolute Error (RMAE), Throughput. The findings of our research work help the customer to directly use the result obtained from the proposed model in the form of Aspect level rating.

Assessing the effects of exchange rate depreciation on the US economy

PurposeThe purpose of this paper is to examine the effects of exchange rate shock on the broad spectrum of the US economy using a factor-augmented VAR model (FAVAR).Design/methodology/approachThe authors developed a two-factor FAVAR model and estimated it with the single-step Bayesian likelihood approach using the Gibbs sampling technique. The two factors represented, respectively, the economic activity and price pressures. The exchange rate shock was identified with the Choleski decomposition method for VARs. The authors used the data of 117 time series for the period from 1973:02 to 2007:12. Impulse responses and variance decompositions were computed as the main results.FindingsThe authors found that exchange rate shock has pervasive effects on the US economy as the following: depreciation does not appear to help reduce the US trade deficit as both import and export rise with the depreciation shock; in the short run, depreciation appears expansionary as industrial production, manufacturing and employment all increase within a year; in the medium run, depreciation appears inflationary, as consumer price, producer price, import price and export price all increase; and in the medium run, depreciation appears contractionary as personal consumption, consumer confidence, stock price and housing start tend to fall.Research limitations/implicationsSome caveats remain: first, our simple model symmetrically estimates depreciation shock and appreciation shock and, hence, cannot draw inferences for how exchange rate appreciation and depreciation may affect the US economy asymmetrically. Second, the simple model used did not distinguish the different possible sources of exchange rate depreciation shock, the knowledge of which may lead to richer policy implications and is the direction of research for the future.Originality/valueThis research contributes to the literature of whether exchange rate is expansionary or contractionary to the US economy using the FAVAR model. This is the first comprehensive study in the literature studying the pervasive effects of the exchange rate on the broad spectrum of the US economy in one integrated model.

Inference for Weibull Competing Risks Data Under Generalized Progressive Hybrid Censoring

A competing risks model is considered under a generalized progressive hybrid censoring. When the latent failure times are Weibull distributed, maximum-likelihood estimates for the unknown model parameters are established where the associated existence and uniqueness are shown. An asymptotic distribution of the maximum-likelihood estimators is used to construct approximate confidence intervals via the observed fisher information matrix. Moreover, Bayes point estimates and the highest probability density credible intervals of unknown parameters are also presented, and the Gibbs sampling technique is used to approximate corresponding estimates. Simulation studies and real-life example are presented for illustration purpose.

Multi-label classification using stacked hierarchical Dirichlet processes with reduced sampling complexity

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

IMS-DTM: Incremental Multi-Scale Dynamic Topic Models

Dynamic topic models (DTM) are commonly used for mining latent topics in evolving web corpora. In this paper, we note that a major limitation of the conventional DTM based models is that they assume a predetermined and fixed scale of topics. In reality, however, topics may have varying spans and topics of multiple scales can co-exist in a single web or social media data stream. Therefore, DTMs that assume a fixed epoch length may not be able to effectively capture latent topics and thus negatively affect accuracy. In this paper, we propose a Multi-Scale Dynamic Topic Model (MS-DTM) and a complementary Incremental Multi-Scale Dynamic Topic Model (IMS-DTM) inference method that can be used to capture latent topics and their dynamics simultaneously, at different scales. In this model, topic specific feature distributions are generated based on a multi-scale feature distribution of the previous epochs; moreover, multiple scales of the current epoch are analyzed together through a novel multi-scale incremental Gibbs sampling technique. We show that the proposed model significantly improves efficiency and effectiveness compared to the single scale dynamic DTMs and prior models that consider only multiple scales of the past.

Labeled Phrase Latent Dirichlet Allocation and its online learning algorithm

There is a mass of user-marked text data on the Internet, such as web pages with categories, papers with corresponding keywords, and tweets with hashtags. In recent years, supervised topic models, such as Labeled Latent Dirichlet Allocation, have been widely used to discover the abstract topics in labeled text corpora. However, none of these topic models have taken into consideration word order under the bag-of-words assumption, which will obviously lose a lot of semantic information. In this paper, in order to synchronously model semantical label information and word order, we propose a novel topic model, called Labeled Phrase Latent Dirichlet Allocation (LPLDA), which regards each document as a mixture of phrases and partly considers the word order. In order to obtain the parameter estimation for the proposed LPLDA model, we develop a batch inference algorithm based on Gibbs sampling technique. Moreover, to accelerate the LPLDA’s processing speed for large-scale stream data, we further propose an online inference algorithm for LPLDA. Extensive experiments were conducted among LPLDA and four state-of-the-art baselines. The results show (1) batch LPLDA significantly outperforms baselines in terms of case study, perplexity and scalability, and the third party task in most cases; (2) the online algorithm for LPLDA is obviously more efficient than batch method under the premise of good results.