Evaluating Wine-Tasting Results and Randomness with a Mixture of Rank Preference Models

2015 ◽  
Vol 10 (1) ◽  
pp. 31-46 ◽  
Author(s):  
Jeffrey C. Bodington
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Mixture Model ◽  
Expectation Maximization Algorithm ◽  
Mixture Distribution ◽  
Type I ◽  
Type I Errors ◽  
Random Expectation ◽  
Probability Mass ◽  
Mass Functions

AbstractEvaluating observed wine-tasting results as a mixture distribution, using linear regression on a transformation of observed results, has been described in the wine-tasting literature. This article advances the use of mixture models by considering that existing work, examining five analyses of ranking and mixture model applications to non-wine food tastings and then deriving a mixture model with specific application to observed wine-tasting results. The mixture model is specified with Plackett-Luce probability mass functions, solved with the expectation maximization algorithm that is standard in the literature, tested on a hypothetical set of wine ranks, tested with a random-ranking Monte Carlo simulation, and then employed to evaluate the results of a blind tasting of Pinot Gris by experienced tasters. The test on a hypothetical set of wine ranks shows that a mixture model is an accurate predictor of observed rank densities. The Monte Carlo simulation yields confirmatory results and an estimate of potential Type I errors (the probability that tasters appear to agree although ranks are actually random). Application of the mixture model to the tasting of Pinot Gris, with over a 95% level of confidence based on the likelihood ratio and t statistics, shows that agreement among tasters exceeds the random expectation of illusory agreement. (JEL Classifications: A10, C10, C00, C12, D12)

Reliability Analysis for Masked Data under Type-II Generalized Progressively Hybrid Censored Scheme

2014 ◽  
Vol 687-691 ◽  
pp. 1198-1201
Author(s):  
Bin Liu ◽  
Yi Min Shi ◽  
Jing Cai ◽  
Mo Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Type Ii ◽  
Distribution Parameters ◽  
System Lifetime Data ◽  
Quasi Newton

The Type-II generalized progressively hybrid censored scheme with masked data is presented. Based on masked system lifetime data, using the expectation maximization algorithm and the Quasi-Newton method, we obtain the Maximum Likelihood Estimation (MLE) of the components distribution parameters in the Weibull case. Finally, Monte Carlo simulation is presented to illustrate the effect.

scholarly journals Statistical Tests for the Reciprocal of a Normal Mean with a Known Coefficient of Variation

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Wararit Panichkitkosolkul
Keyword(s):  
Monte Carlo Simulation ◽  
Coefficient Of Variation ◽  
Statistical Tests ◽  
Taylor Series Expansion ◽  
Type I ◽  
Type I Errors ◽  
Monte Carlo Simulation Study ◽  
Asymptotic Test ◽  
Normal Mean ◽  
Simulation Results

An asymptotic test and an approximate test for the reciprocal of a normal mean with a known coefficient of variation were proposed in this paper. The asymptotic test was based on the expectation and variance of the estimator of the reciprocal of a normal mean. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and power. Nevertheless, the approximate test was easier to compute than the asymptotic test.

scholarly journals Control charts for skewed distributions

2012 ◽  
Vol 9 (2) ◽  
Author(s):  
Derya Karagöz ◽  
Canan Hamurkaroğlu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Control Charts ◽  
Type I ◽  
Skewed Distributions ◽  
Simulation Results ◽  
Standard Deviations ◽  
Control Limits

In this paper the control limits of \(\bar{X}\) and \(R\) control charts for skewed distributions are obtained by considering the classic, the weighted variance (\(\mathit{WV}\)), the weighted standard deviations (\(\mathit{WSD}\)) and the skewness correction (\(\mathit{SC}\)) methods. These methods are compared by using Monte Carlo simulation. Type I risk probabilities of these control charts are compared with respect to different subgroup sizes for skewed distributions which are Weibull, gamma and lognormal. Simulation results show that Type I risk of \(\mathit{SC}\) method is less than that of other methods. When the distribution is approximately symmetric, then the Type I risks of Shewhart, \(\mathit{WV}\) , \(\mathit{WSD}\), and \(\mathit{SC}\) \(\bar{X}\) charts are comparable, while the \(\mathit{SC}\) \(R\) chart has a noticeable smaller Type I risk.

Using Monte Carlo Software to Teach Abstract Statistical Concepts: A Case Study

2005 ◽  
Vol 32 (3) ◽  
pp. 193-195 ◽  
Author(s):  
Holly Raffle ◽  
Gordon P. Brooks
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Type I Error ◽  
Computer Software ◽  
Course Evaluation ◽  
Error Rates ◽  
Type I ◽  
Statistics Course ◽  
Instructor's Manual

Violations of assumptions, inflated Type I error rates, and robustness are important concepts for students to learn in an introductory statistics course. However, these abstract ideas can be difficult for students to understand. Monte Carlo simulation methods can provide a concrete way for students to learn abstract statistical concepts. This article describes the MC4G computer software (Brooks, 2004) and the accompanying instructor's manual (Raffle, 2004). It also provides a case study that includes both assessment and course evaluation data supporting the effectiveness of Monte Carlo simulation exercises in a graduate-level statistics course.

scholarly journals Adsorption and diffusion of H2 and CO on UiO-66: A Monte Carlo simulation study

2020 ◽  
Vol 11 (3) ◽  
pp. 217-222
Author(s):  
Negin Davoodian ◽  
Zahra Khoshbin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Guest Molecule ◽  
Isosteric Heat ◽  
Simulation Method ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
Guest Molecules ◽  
Metal Organic ◽  
And Diffusion

Metal-organic frameworks (MOFs) are a new class of nanoporous materials that have attracted much attention for the adsorption of small molecules, due to the large size of the cavities. In this study, we investigate the adsorption and diffusion of hydrogen (H2) and carbon monoxide (CO) guest molecules to the UiO-66 framework, as one of the most widely used MOFs, by using Monte Carlo simulation method. The results prove that an increment in the temperature decreases the amount of the adsorbed H2 and CO on the UiO-66 framework. While an enhancement of the pressure increases the amount of the adsorbed H2 and CO on the UiO-66 framework. Besides, the adsorption of H2 and CO on UiO-66 is the type I isotherm. The calculated isosteric heat for CO/UiO-66 is slightly higher than that of H2/UiO-66. The means of square displacement (MSD) value is less for CO molecule; hence, the movement of the guest molecule within the host cavity slows down and the guest molecule travels a shorter distance over a period of time. The guest molecule with higher molecular mass possesses less mobility, and therefore, it will have less permeability.

Sign in / Sign up

Export Citation Format

Share Document