Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

scholarly journals Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 111-120 ◽  
Author(s):  
Dewi Rahardja
Keyword(s):  
Bayesian Inference ◽  
Closed Form ◽  
Bayesian Approach ◽  
Interval Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Posterior Distributions ◽  
Binomial Data ◽  
The Difference ◽  
Data Subject

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

scholarly journals A Bayesian Analysis of Spectral ARMA Model

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Manoel I. Silvestre Bezerra ◽  
Fernando Antonio Moala ◽  
Yuzo Iano
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Confidence Interval ◽  
Bayesian Analysis ◽  
Least Squares ◽  
Bayesian Approach ◽  
Arma Model ◽  
New Method ◽  
Posterior Distributions ◽  
Numerical Illustration

Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model. In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967). The Bayesian computations, simulation via Markov Monte Carlo (MCMC) is carried out and characteristics of marginal posterior distributions such as Bayes estimator and confidence interval for the parameters of the ARMA model are derived. Both methods are also compared with the traditional least squares and maximum likelihood approaches and a numerical illustration with two examples of the ARMA model is presented to evaluate the performance of the procedures.

scholarly journals A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 929
Author(s):  
Mohammad Reza Mahmoudi ◽  
Mohsen Maleki ◽  
Dumitru Baleanu ◽  
Vu-Thanh Nguyen ◽  
Kim-Hung Pho
Keyword(s):  
Bayesian Analysis ◽  
Heavy Tails ◽  
Linear Time ◽  
Real Data ◽  
Finite Mixture ◽  
Stochastic Representation ◽  
Bayesian Approaches ◽  
Proposed Model ◽  
Heavy Tailed ◽  
Informative Prior Distributions

In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN–MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.

An integrated strategy for fleet maintenance planning

2017 ◽  
Vol 23 (4) ◽  
pp. 457-478 ◽  
Author(s):  
Manish Rawat ◽  
Bhupesh Kumar Lad
Keyword(s):  
Failure Rate ◽  
Real Life ◽  
Complex Problem ◽  
General Assumption ◽  
Point Of View ◽  
System Structure ◽  
Imperfect Maintenance ◽  
Content Type ◽  
Integrated Strategy

Purpose Conventionally, fleet maintenance decisions are made based on the level of repair (LOR) analysis. A general assumption made during LOR analysis is the consideration of the lifetime distribution with constant failure rate (CFR). However, industries do use preventive maintenance (PM) to extend the life of such components, which in turn may affect the LOR decisions such as repair/move/discard. The CFR assumption does not allow the consideration of effect of PM in LOR analysis. The purpose of this paper is to develop a more practical LOR analysis approach, considering the time-dependent failure rate (TDFR) of components and the effect of PM. Design/methodology/approach In the proposed methodology, first, a detailed life cycle model considering the effect of various parameters related to LOR and PM is developed. A simulation-based genetic algorithm approach is then used to obtain an integrated solution for LOR and PM schedule decisions. The model is also evaluated for the various cases of quality of maintenance measured in terms of degree of restoration. Findings The results, from the illustrative example for a multi-indenture and multi-echelon fleet maintenance network, show that the proposed integrated strategy leads to better LCC performance compare to the conventional approach. Additionally, it is identified that the degree of restoration also affects the PM schedule as well as LOR decisions of the fleet system. Therefore, consideration of TDFR is important to truly optimize the LOR decisions. The proposed approach can be applied to fleet of any equipment. Research limitations/implications The approach is illustrated using a hypothetical example of an industrial system. A more complex system structure in terms of number of machines, types of machines (identical vs non-identical), number of echelons, possible repair actions at various echelons, etc. may be present for a particular industrial case. However, the approach presented is generic and can be extended to any system. Moreover, the aim of the paper is to highlight the importance of the considering PM and quality of maintenance in LOR decision making. Originality/value To the best of the authors’ knowledge, this is the first work which considers the effect of PM and quality of maintenance on LOR analysis. Consideration of TDFR and imperfect maintenance while optimizing LOR decisions is a complex problem. Thus, the work is of high significance from the research point of view. Also, most of the real life fleet systems use PM to extend the life of the equipment. Thus, present paper is a more practical approach for LOR analysis of such systems.

The first flush in sewer systems

1996 ◽  
Vol 33 (9) ◽  
pp. 101-108 ◽  
Author(s):  
Agnès Saget ◽  
Ghassan Chebbo ◽  
Jean-Luc Bertrand-Krajewski
Keyword(s):  
Treatment Strategy ◽  
Real Data ◽  
First Flush ◽  
Clear Definition ◽  
Controversial Subject ◽  
Sewer Systems ◽  
Wet Weather ◽  
Definition Of ◽  
Appearance Frequency

The first flush phenomenon of urban wet weather discharges is presently a controversial subject. Scientists do not agree with its reality, nor with its influences on the size of treatment works. Those disagreements mainly result from the unclear definition of the phenomenon. The objective of this article is first to provide a simple and clear definition of the first flush and then to apply it to real data and to obtain results about its appearance frequency. The data originate from the French database based on the quality of urban wet weather discharges. We use 80 events from 7 separately sewered basins, and 117 events from 7 combined sewered basins. The main result is that the first flush phenomenon is very scarce, anyway too scarce to be used to elaborate a treatment strategy against pollution generated by urban wet weather discharges.

scholarly journals Benchmarking Unsupervised Outlier Detection with Realistic Synthetic Data

2021 ◽  
Vol 15 (4) ◽  
pp. 1-20
Author(s):  
Georg Steinbuss ◽  
Klemens Böhm
Keyword(s):  
Outlier Detection ◽  
Synthetic Data ◽  
Real Data ◽  
Detection Methods ◽  
Quality Of Data ◽  
Benchmark Data ◽  
Core Idea ◽  
Generic Process ◽  
Unsupervised Outlier Detection

Benchmarking unsupervised outlier detection is difficult. Outliers are rare, and existing benchmark data contains outliers with various and unknown characteristics. Fully synthetic data usually consists of outliers and regular instances with clear characteristics and thus allows for a more meaningful evaluation of detection methods in principle. Nonetheless, there have only been few attempts to include synthetic data in benchmarks for outlier detection. This might be due to the imprecise notion of outliers or to the difficulty to arrive at a good coverage of different domains with synthetic data. In this work, we propose a generic process for the generation of datasets for such benchmarking. The core idea is to reconstruct regular instances from existing real-world benchmark data while generating outliers so that they exhibit insightful characteristics. We propose and describe a generic process for the benchmarking of unsupervised outlier detection, as sketched so far. We then describe three instantiations of this generic process that generate outliers with specific characteristics, like local outliers. To validate our process, we perform a benchmark with state-of-the-art detection methods and carry out experiments to study the quality of data reconstructed in this way. Next to showcasing the workflow, this confirms the usefulness of our proposed process. In particular, our process yields regular instances close to the ones from real data. Summing up, we propose and validate a new and practical process for the benchmarking of unsupervised outlier detection.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Bayesian analysis of data from segmented super-resolution images for quantifying protein clustering

2020 ◽  
Vol 22 (3) ◽  
pp. 1107-1114
Author(s):  
Tina Košuta ◽  
Marta Cullell-Dalmau ◽  
Francesca Cella Zanacchi ◽  
Carlo Manzo
Keyword(s):  
Bayesian Analysis ◽  
Relative Abundance ◽  
Bayesian Approach ◽  
Super Resolution ◽  
Molecular Aggregates ◽  
Protein Clustering ◽  
Precise Quantification

A Bayesian approach enables the precise quantification of the relative abundance of molecular aggregates of different stoichiometry from segmented super-resolution images.

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