ترغب بنشر مسار تعليمي؟ اضغط هنا

On modeling of variability in mixture experiments with noise variables

106   0   0.0 ( 0 )
 نشر من قبل Edmilson Rodrigues Pinto Dr.
 تاريخ النشر 2015
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

In mixture experiments with noise variables or process variables that can not be controlled, investigate and try to control the variability of the response variable is very important for quality improvement in industrial processes. Thus, modeling the variability in mixture experiments with noise variables becomes necessary and has been considered in literature with approaches that require the choice of a quadratic loss function or by using the delta method. In this paper, we make use of the delta method and also propose an alternative approach, which is based on the Joint Modeling of Mean and Dispersion (JMMD). We consider a mixture experiment involving noise variables and we use the techniques of JMMD and of the delta method to get models for both mean and variance of the response variable. Following the Taguchis ideas about robust parameter design we build and solve an optimization problem for minimizing the variance while holding the mean on the target. At the end we provide a discussion about the two methodologies considered.



قيم البحث

اقرأ أيضاً

The ocean is filled with microscopic microalgae called phytoplankton, which together are responsible for as much photosynthesis as all plants on land combined. Our ability to predict their response to the warming ocean relies on understanding how the dynamics of phytoplankton populations is influenced by changes in environmental conditions. One powerful technique to study the dynamics of phytoplankton is flow cytometry, which measures the optical properties of thousands of individual cells per second. Today, oceanographers are able to collect flow cytometry data in real-time onboard a moving ship, providing them with fine-scale resolution of the distribution of phytoplankton across thousands of kilometers. One of the current challenges is to understand how these small and large scale variations relate to environmental conditions, such as nutrient availability, temperature, light and ocean currents. In this paper, we propose a novel sparse mixture of multivariate regressions model to estimate the time-varying phytoplankton subpopulations while simultaneously identifying the specific environmental covariates that are predictive of the observed changes to these subpopulations. We demonstrate the usefulness and interpretability of the approach using both synthetic data and real observations collected on an oceanographic cruise conducted in the north-east Pacific in the spring of 2017.
This paper sets out a forecasting method that employs a mixture of parametric functions to capture the pattern of fertility with respect to age. The overall level of cohort fertility is decomposed over the range of fertile ages using a mixture of par ametric density functions. The level of fertility and the parameters describing the shape of the fertility curve are projected foward using time series methods. The model is estimated within a Bayesian framework, allowing predictive distributions of future fertility rates to be produced that naturally incorporate both time series and parametric uncertainty. A number of choices are possible for the precise form of the functions used in the two-component mixtures. The performance of several model variants is tested on data from four countries; England and Wales, the USA, Sweden and France. The former two countries exhibit multi-modality in their fertility rate curves as a function of age, while the latter two are largely uni-modal. The models are estimated using Hamiltonian Monte Carlo and the `stan` software package on data covering the period up to 2006, with the period 2007-2016 held back for assessment purposes. Forecasting performance is found to be comparable to other models identified as producing accurate fertility forecasts in the literature.
The purpose of an entanglement witness experiment is to certify the creation of an entangled state from a finite number of trials. The statistical confidence of such an experiment is typically expressed as the number of observed standard deviations o f witness violations. This method implicitly assumes that the noise is well-behaved so that the central limit theorem applies. In this work, we propose two methods to analyze witness experiments where the states can be subject to arbitrarily correlated noise. Our first method is a rejection experiment, in which we certify the creation of entanglement by rejecting the hypothesis that the experiment can only produce separable states. We quantify the statistical confidence by a p-value, which can be interpreted as the likelihood that the observed data is consistent with the hypothesis that only separable states can be produced. Hence a small p-value implies large confidence in the witnessed entanglement. The method applies to general witness experiments and can also be used to witness genuine multipartite entanglement. Our second method is an estimation experiment, in which we estimate and construct confidence intervals for the average witness value. This confidence interval is statistically rigorous in the presence of correlated noise. The method applies to general estimation problems, including fidelity estimation. To account for systematic measurement and random setting generation errors, our model takes into account device imperfections and we show how this affects both methods of statistical analysis. Finally, we illustrate the use of our methods with detailed examples based on a simulation of NV centers.
397 - Andrej Srakar 2020
Multiple Indicators Multiple Causes (MIMIC) models are type of structural equation models, a theory-based approach to confirm the influence of a set of exogenous causal variables on the latent variable, and also the effect of the latent variable on o bserved indicator variables. In a common MIMIC model, multiple indicators reflect the underlying latent variables/factors, and the multiple causes (observed predictors) affect latent variables/factors. Basic assumptions of MIMIC are clearly violated in case of a variable being both an indicator and a cause, i.e. in the presence of reverse causality. Furthermore, the model is then unidentified. To resolve the situation, which can arise frequently, and as MIMIC estimation lacks closed form solutions for parameters we utilize a version of Bollens (1996) 2SLS estimator for structural equation models combined with Joreskog (1970)s method of the analysis of covariance structures to derive a new, 2SLS estimator for MIMIC models. Our 2SLS empirical estimation is based on static MIMIC specification but we point also to dynamic/error-correction MIMIC specification and 2SLS solution for it. We derive basic asymptotic theory for static 2SLS-MIMIC, present a simulation study and apply findings to an interesting empirical case of estimating precarious status of older workers (using dataset of Survey of Health, Ageing and Retirement in Europe) which solves an important issue of the definition of precarious work as a multidimensional concept, not modelled adequately so far.
An on-line drilling system, the tutor-web, has been developed and used for teaching mathematics and statistics. The system was used in a basic course in calculus including 182 students. The students were requested to answer quiz questions in the tuto r-web and therefore monitored continuously during the semester. Data available are grades on a status exam conducted in the beginning of the course, a final grade and data gathered in the tutor-web system. A classification of the students is proposed using the data gathered in the system; a Good student should be able to solve a problem quickly and get it right, the diligent hard-working Learner may take longer to get the right answer, a guessing (Poor) student will not take long to get the wrong answer and the remaining (Unclassified) apparent non-learning students take long to get the wrong answer, resulting in a simple classification GLUP. The (Poor) students were found to show the least improvement, defined as the change in grade from the status to the final exams, while the Learners were found to improve the most. The results are used to demonstrate how further experiments are needed and can be designed as well as to indicate how a system needs to be further developed to accommodate such experiments.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا