scholarly journals On Bayesian approach to composite Pareto models

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257762
Author(s):  
Muhammad Hilmi Abdul Majid ◽  
Kamarulzaman Ibrahim
Keyword(s):  
Bayesian Approach ◽  
Simulation Study ◽  
Prior Distribution ◽  
Pareto Distribution ◽  
Threshold Value ◽  
Parameter Estimates ◽  
Data Modelling ◽  
Type Distribution ◽  
Point Estimates ◽  
Income Data

In data modelling using the composite Pareto distribution, any observations above a particular threshold value are assumed to follow Pareto type distribution, whereas the rest of the observations are assumed to follow a different distribution. This paper proposes on the use of Bayesian approach to the composite Pareto models involving specification of the prior distribution on the proportion of data coming from the Pareto distribution, instead of assuming the prior distribution on the threshold, as often done in the literature. Based on a simulation study, it is found that the parameter estimates determined when using uniform prior on the proportion is less biased as compared to the point estimates determined when using uniform prior on the threshold. Applications on income data and finance are included for illustrative examples.

scholarly journals A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model using Markov Chain Monte Carlo

2021 ◽  
Author(s):  
Oliver Lüdtke ◽  
Alexander Robitzsch ◽  
Esther Ulitzsch
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reciprocal Effects ◽  
Ml Estimation ◽  
Model Parameterization ◽  
Lagged Effects ◽  
The Bayesian Approach ◽  
Over Time

The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model provides a general approach for estimating reciprocal effects between constructs over time. However, previous research has shown that this model is difficult to estimate using the maximum likelihood (ML) method (e.g., nonconvergence). In this article, we introduce a Bayesian approach for estimating the bivariate STARTS model and implement it in the software Stan. We discuss issues of model parameterization and show how appropriate prior distributions for model parameters can be selected. Specifically, we propose the four-parameter beta distribution as a flexible prior distribution for the autoregressive and cross-lagged effects. Using a simulation study, we show that the proposed Bayesian approach provides more accurate estimates than ML estimation in challenging data constellations. An example is presented to illustrate how the Bayesian approach can be used to stabilize the parameter estimates of the bivariate STARTS model.

scholarly journals Trade-Off between Operating Time and Energy Consumption in Pulsed Electric Field Electrodialysis: A Comprehensive Simulation Study

Membranes ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 43
Author(s):  
Manuel César Martí-Calatayud ◽  
Mario Sancho-Cirer Poczatek ◽  
Valentín Pérez-Herranz
Keyword(s):  
Energy Consumption ◽  
Electric Field ◽  
Simulation Study ◽  
Specific Energy ◽  
Operating Time ◽  
Specific Energy Consumption ◽  
Threshold Value ◽  
Pulsed Electric Field ◽  
Pulse Frequency ◽  
Time And Energy

Electrodialysis (ED) has been recently introduced in a variety of processes where the recovery of valuable resources is needed; thus, enabling sustainable production routes for a circular economy. However, new applications of ED require optimized operating modes ensuring low energy consumptions. The application of pulsed electric field (PEF) electrodialysis has been demonstrated to be an effective option to modulate concentration polarization and reduce energy consumption in ED systems, but the savings in energy are usually attained by extending the operating time. In the present work, we conduct a comprehensive simulation study about the effects of PEF signal parameters on the time and energy consumption associated with ED processes. Ion transport of NaCl solutions through homogeneous cation-exchange membranes is simulated using a 1-D model solved by a finite-difference method. Increasing the pulse frequency up to a threshold value is effective in reducing the specific energy consumption, with threshold frequencies increasing with the applied current density. Varying the duty cycle causes opposed effects in the time and energy usage needed for a given ED operation. More interestingly, a new mode of PEF functions with the application of low values of current during the relaxation phases has been investigated. This novel PEF strategy has been demonstrated to simultaneously improve the time and the specific energy consumption of ED processes.

scholarly journals Simulation Studies as a Tool to Understand Bayes Factors

2021 ◽  
Vol 4 (1) ◽  
pp. 251524592097262
Author(s):  
Don van Ravenzwaaij ◽  
Alexander Etz
Keyword(s):  
Simulation Study ◽  
Prior Distribution ◽  
Bayes Factor ◽  
R Package ◽  
Bayes Factors ◽  
Simulation Studies ◽  
Social Scientists ◽  
Simple Simulation ◽  
Set Up

When social scientists wish to learn about an empirical phenomenon, they perform an experiment. When they wish to learn about a complex numerical phenomenon, they can perform a simulation study. The goal of this Tutorial is twofold. First, it introduces how to set up a simulation study using the relatively simple example of simulating from the prior. Second, it demonstrates how simulation can be used to learn about the Jeffreys-Zellner-Siow (JZS) Bayes factor, a currently popular implementation of the Bayes factor employed in the BayesFactor R package and freeware program JASP. Many technical expositions on Bayes factors exist, but these may be somewhat inaccessible to researchers who are not specialized in statistics. In a step-by-step approach, this Tutorial shows how a simple simulation script can be used to approximate the calculation of the Bayes factor. We explain how a researcher can write such a sampler to approximate Bayes factors in a few lines of code, what the logic is behind the Savage-Dickey method used to visualize Bayes factors, and what the practical differences are for different choices of the prior distribution used to calculate Bayes factors.

On modeling the maximum duration of dry spells: a simulation study under a Bayesian approach

2018 ◽  
Vol 137 (1-2) ◽  
pp. 1337-1346
Author(s):  
Davi Butturi-Gomes ◽  
Luiz Alberto Beijo ◽  
Fabricio Goecking Avelar
Keyword(s):  
Bayesian Approach ◽  
Simulation Study ◽  
Maximum Duration ◽  
Dry Spells

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

scholarly journals Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

A regional meta-model for stock–recruitment analysis using an empirical Bayesian approach

2002 ◽  
Vol 59 (9) ◽  
pp. 1503-1514 ◽  
Author(s):  
D G Chen ◽  
L Blair Holtby
Keyword(s):  
Bayesian Approach ◽  
Prior Distribution ◽  
Coho Salmon ◽  
Population Diversity ◽  
Empirical Bayesian ◽  
Meta Model ◽  
Resource Managers ◽  
Stock Recruitment ◽  
Two Parameters ◽  
Empirical Bayesian Approach

A regional stock–recruitment meta-model is developed using a hierarchical Bayesian framework to combine information from multiple fish populations. The use of the meta-model is illustrated through analysis of the regional stock–recruitment parameters of the coho salmon (Oncorhynchus kisutch) within two large fisheries management units in southern and northern British Columbia. We construct our regional prior distribution from an analysis of all stock-recruitment data rather than by the more usual approach of assuming a prior distribution. That preliminary analysis indicated that the regional prior distribution for the two parameters of the Ricker model was bivariate normal–lognormal (NLN) with a high degree of correlation between the two Ricker parameters. Because this distribution had not been fully developed, we formulated the density function for the NLN distribution and proved some of its important properties. An empirical Bayesian approach was then used to estimate the regional distributions of the Ricker parameters and derived management parameters. Characterization of the distributional properties of productivity within management regions is a necessary step for resource managers seeking to prosecute mixed-stock fisheries while conserving population diversity.

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