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The purpose of this study is to estimate the linear regression parameters using two alternative techniques. First technique is to apply the generalized linear model (GLM) and the second technique is the Markov Chain Monte Carlo (MCMC) method.

In this paper, the authors adopted the incurred claims of Egyptian non-life insurance market as a dependent variable during a 10-year period. MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate the parameters of interest. However, the authors used the R package to estimate the parameters of the linear regression using the above techniques.

These procedures will guide the decision-maker for estimating the reserve and set proper investment strategy.

In this paper, the authors will estimate the parameters of a linear regression model using MCMC method via R package. Furthermore, MCMC uses Gibbs sampling to generate a sample from a posterior distribution of a linear regression to estimate parameters to predict future claims. In the same line, these procedures will guide the decision-maker for estimating the reserve and set proper investment strategy.

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, making simulation methods indispensable in both Bayesian and frequentist estimation and model choice. We review several existing probability estimators and then show that a broader perspective on the simulation problem can be afforded by interpreting the outcome probabilities through Bayes’ theorem, leading to the recognition that estimation can alternatively be handled by methods for marginal likelihood computation based on the output of Markov chain Monte Carlo (MCMC) algorithms. These techniques offer stand-alone approaches to simulated likelihood estimation but can also be integrated with traditional estimators. Building on both branches in the literature, we develop new methods for estimating response probabilities and propose an adaptive sampler for producing high-quality draws from multivariate truncated normal distributions. A simulation study illustrates the practical benefits and costs associated with each approach. The methods are employed to estimate the likelihood function of a correlated random effects panel data model of women's labor force participation.

The purpose of this paper is to establish a cheap but accurate approximation of the forward map in electrical capacitance tomography in order to approach robust real‐time inversion in the framework of Bayesian statistics based on Markov chain Monte Carlo (MCMC) sampling.

Existing formulations and methods to reduce the order of the forward model with focus on electrical tomography are reviewed and compared. In this work, the problem of fast and robust estimation of shape and position of non‐conducting inclusions in an otherwise uniform background is considered. The boundary of the inclusion is represented implicitly using an appropriate interpolation strategy based on radial basis functions. The inverse problem is formulated as Bayesian inference, with MCMC sampling used to efficiently explore the posterior distribution. An affine approximation to the forward map built over the state space is introduced to significantly reduce the reconstruction time, while maintaining spatial accuracy. It is shown that the proposed approximation is unbiased and the variance of the introduced additional model error is even smaller than the measurement error of the tomography instrumentation. Numerical examples are presented, avoiding all inverse crimes.

Provides a consistent formulation of the affine approximation with application to imaging of binary mixtures in electrical tomography using MCMC sampling with Metropolis‐Hastings‐Green dynamics.

The proposed cheap approximation indicates that accurate real‐time inversion of capacitance data using statistical inversion is possible.

The proposed approach demonstrates that a tolerably small increase in posterior uncertainty of relevant parameters, e.g. inclusion area and contour shape, is traded for a huge reduction in computing time without introducing bias in estimates. Furthermore, the proposed framework – approximated forward map combined with statistical inversion – can be applied to all kinds of soft‐field tomography problems.

It is well known that volatility asymmetry exists in financial markets. This paper reviews and investigates recently developed techniques for Bayesian estimation and model selection applied to a large group of modern asymmetric heteroskedastic models. These include the GJR-GARCH, threshold autoregression with GARCH errors, TGARCH, and double threshold heteroskedastic model with auxiliary threshold variables. Further, we briefly review recent methods for Bayesian model selection, such as, reversible-jump Markov chain Monte Carlo, Monte Carlo estimation via independent sampling from each model, and importance sampling methods. Seven heteroskedastic models are then compared, for three long series of daily Asian market returns, in a model selection study illustrating the preferred model selection method. Major evidence of nonlinearity in mean and volatility is found, with the preferred model having a weighted threshold variable of local and international market news.

One of the crucial issues in the contemporary finance is the prediction of the volatility of financial assets. In this paper, the authors are interested in modelling the stochastic volatility of the MAD/EURO and MAD/USD exchange rates.

For this purpose, the authors have adopted Bayesian approach based on the MCMC (Monte Carlo Markov Chain) algorithm which permits to reproduce the main stylized empirical facts of the assets studied. The data used in this study are the daily historical series of MAD/EURO and MAD/USD exchange rates covering the period from February 2, 2000, to March 3, 2017, which represent 4,456 observations.

By the aid of this approach, the authors were able to estimate all the random parameters of the stochastic volatility model which permit the prediction of the future exchange rates. The authors also have simulated the histograms, the posterior densities as well as the cumulative averages of the model parameters. The predictive efficiency of the stochastic volatility model for Morocco is capable to facilitate the management of the exchange rate in more flexible exchange regime to ensure better targeting of monetary and exchange policies.

To the best of the authors’ knowledge, the novelty of the paper lies in the production of a tool for predicting the evolution of the Moroccan exchange rate and also the design of a tool for the monetary authorities who are today in a proactive conception of management of the rate of exchange. Cyclical policies such as monetary policy and exchange rate policy will introduce this type of modelling into the decision-making process to achieve a better stabilization of the macroeconomic and financial framework.

The application of statistical inversion theory provides a powerful approach for solving estimation problems including the ability for uncertainty quantification (UQ) by means of Markov chain Monte Carlo (MCMC) methods and Monte Carlo integration. This paper aims to analyze the application of a state reduction technique within different MCMC techniques to improve the computational efficiency and the tuning process of these algorithms.

A reduced state representation is constructed from a general prior distribution. For sampling the Metropolis Hastings (MH) Algorithm and the Gibbs sampler are used. Efficient proposal generation techniques and techniques for conditional sampling are proposed and evaluated for an exemplary inverse problem.

For the MH-algorithm, high acceptance rates can be obtained with a simple proposal kernel. For the Gibbs sampler, an efficient technique for conditional sampling was found. The state reduction scheme stabilizes the ill-posed inverse problem, allowing a solution without a dedicated prior distribution. The state reduction is suitable to represent general material distributions.

The state reduction scheme and the MCMC techniques can be applied in different imaging problems. The stabilizing nature of the state reduction improves the solution of ill-posed problems. The tuning of the MCMC methods is simplified.

The paper presents a method to improve the solution process of inverse problems within the Bayesian framework. The stabilization of the inverse problem due to the state reduction improves the solution. The approach simplifies the tuning of MCMC methods.

In a Bayesian approach, we compare the forecasting performance of five classes of models: ARCH, GARCH, SV, SV-STAR, and MSSV using daily Tehran Stock Exchange (TSE) market data. To estimate the parameters of the models, Markov chain Monte Carlo (MCMC) methods is applied. The results show that the models in the fourth and the fifth class perform better than the models in the other classes.

This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.

This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS.

In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques.

The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study.

The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature.