Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation

2001 ◽  
Vol 63 (2) ◽  
pp. 339-355 ◽  
Author(s):  
Ming Gao Gu ◽  
Hong-Tu Zhu
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Approximation ◽  
Spatial Models ◽  
Likelihood Estimation

scholarly journals Efficient stochastic optimisation by unadjusted Langevin Monte Carlo

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Valentin De Bortoli ◽  
Alain Durmus ◽  
Marcelo Pereyra ◽  
Ana F. Vidal
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stochastic Approximation ◽  
Likelihood Estimation ◽  
Stochastic Optimisation ◽  
Monte Carlo Algorithms ◽  
Wide Range ◽  
Optimisation Methods ◽  
Langevin Monte Carlo

AbstractStochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric empirical Bayesian estimation. Combined with Markov chain Monte Carlo algorithms, these stochastic optimisation methods have been successfully applied to a wide range of problems in science and industry. However, this strategy scales poorly to large problems because of methodological and theoretical difficulties related to using high-dimensional Markov chain Monte Carlo algorithms within a stochastic approximation scheme. This paper proposes to address these difficulties by using unadjusted Langevin algorithms to construct the stochastic approximation. This leads to a highly efficient stochastic optimisation methodology with favourable convergence properties that can be quantified explicitly and easily checked. The proposed methodology is demonstrated with three experiments, including a challenging application to statistical audio analysis and a sparse Bayesian logistic regression with random effects problem.

Failure rate analysis of jaw crusher using Weibull model

2016 ◽  
Vol 231 (4) ◽  
pp. 760-772 ◽  
Author(s):  
RS Sinha ◽  
AK Mukhopadhyay
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Jaw Crusher ◽  
Two Parameter

The primary crusher is essential equipment employed for comminuting the mineral in processing plants. Any kind of failure of its components will accordingly hinder the performance of the plant. Therefore, to minimize sudden failures, analysis should be undertaken to improve performance and operational reliability of the crushers and its components. This paper considers the methods for analyzing failure rates of a jaw crusher and its critical components application of a two-parameter Weibull distribution in a mineral processing plant fitted using statistical tests such as goodness of fit and maximum likelihood estimation. Monte Carlo simulation, analysis of variance, and artificial neural network are also applied. Two-parameter Weibull distribution is found to be the best fit distribution using Kolmogorov–Smirnov test. Maximum likelihood estimation method is used to find out the shape and scale parameter of two-parameter Weibull distribution. Monte Carlo simulation generates 40 numbers of shape parameters, scale parameters, and time. Further, 40 numbers of Weibull distribution parameters are evaluated to examine the failure rate, significant difference, and regression coefficient using ANOVA. Artificial neural network with back-propagation algorithm is used to determine R2 and is compared with analysis of variance.

scholarly journals PERBANDINGAN METODE MAXIMUM LIKELIHOOD DAN METODE BAYES DALAM MENGESTIMASI PARAMETER MODEL REGRESI LINIER BERGANDA UNTUK DATA BERDISTRIBUSI NORMAL

2019 ◽  
Vol 4 (2) ◽  
pp. 100
Author(s):  
Catrin Muharisa ◽  
Ferra Yanuar ◽  
Hazmira Yozza
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Maximum Likelihood ◽  
Gibbs Sampler

Analisis regresi merupakan salah satu metode untuk melihat hubungan antara variabel bebas (independent) dengan variabel terikat (dependent) yang dinyatakan dalam model regresi. Beberapa metode yang bisa digunakan untuk mengestimasi parameter model regresi, diantaranya adalah metode klasik dan metode Bayes. Salah satu metode klasik adalah metode maximum likelihood. Penelitian ini membahas tentang perbandingan metode maximum likelihood dan metode Bayes dalam mengestimasi parameter model regresi linear berganda untuk data berdistribusi normal. Adapun rumus untuk mengestimasi parameter dengan metode maximum likelihood adalah βˆ=(XTX)-1XTY dan ˆσ2 = 1 n P∞ k=1 ei. Sedangkan untuk mengestimasi parameter dengan metode Bayes adalah dengan menggunakan distribusi prior dan fungsi likelihood. Distribusi prior yag dipilih pada kajian ini adalah f(β, σ2 ) = Qn i=1 f(βj |σ 2 )f(σ 2 ) dengan βj ∼ N(µβj , σ2 ) dan σ 2 ∼ IG(a, b). Distribusi prior konjugat tersebut kemudian dikalikan dengan fungsi likelihood L(β, σ2 ) sehingga membentuk distribusi posterior f(β|σ 2 ). Distribusi posterior inilah yang digunakan untuk mengestimasi parameter model melalui proses Markov Chain Monte Carlo (MCMC). Algoritma MCMC yang digunakan adalah algoritma Gibbs Sampler. Model regresi linear berganda yang diperoleh dengan metode maximum likelihood adalahyˆ = −27, 8210000 + 0, 0307430X1 + 0, 0039211X2 + 0, 0034631X3 + 0, 6537000X4dengan kecocokan modelnya adalah sebesar 95,7 %. Sedangkan model regresi linear berganda yang diperoleh dengan metode Bayes adalahyˆ = −26, 620000 + 0, 029380X1 + 0, 004204X2 + 0, 003321X3 + 0, 656200X4dengan kecocokan modelnya adalah sebesar 99,99 %. Dengan demikian dapat disimpulkan bahwa metode Bayes lebih baik dari pada metode maximum likelihood.Kata Kunci: Model Regresi Linear Berganda, metode Maximum Likelihood, dan metode Bayes

scholarly journals Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

2020 ◽  
Vol 68 (6) ◽  
pp. 1896-1912
Author(s):  
Yijie Peng ◽  
Michael C. Fu ◽  
Bernd Heidergott ◽  
Henry Lam
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Modeling ◽  
Stochastic Models ◽  
Likelihood Estimation ◽  
Data Driven ◽  
Simulation Based

A Simulation-Based Approach for Calibrating Stochastic Models

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