اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDesign and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics
368
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Grobner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and non-regular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.
قيم البحث
اقرأ أيضاً
In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by Diaconis and Sturmfels (1998) for conditional
testing problems on contingency tables by Markov chain Monte Carlo methods. In this method, we make use of a connected Markov chain over the given conditional sample space to estimate the P-values numerically for various conditional tests. A Markov basis plays an importance role in this arguments, because it guarantees the connectivity of the chain, which is needed for unbiasedness of the estimate, for arbitrary conditional sample space. As another important point, a Markov basis is characterized as generators of the well-specified toric ideals of polynomial rings. This connection between commutative algebra and statistics is the main result of Diaconis and Sturmfels (1998). After this first paper, a Markov basis is studied intensively by many researchers both in commutative algebra and statistics, which yields an attractive field called computational algebraic statistics. In this paper, we give a review of the Markov chain Monte Carlo methods for contingency tables and Markov bases, with some fundamental examples. We also give some computational examples by algebraic software Macaulay2 and statistical software R. Readers can also find theoretical details of the problems considered in this paper and various results on the structure and examples of Markov bases in Aoki, Hara and Takemura (2012).
The current and upcoming generation of Very Large Volume Neutrino Telescopes---collecting unprecedented quantities of neutrino events---can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the neutrino mass or
dering. The sensitivity of an experiment to these effects can be estimated from Monte Carlo simulations. With the high number of events that will be collected, there is a trade-off between the computational expense of running such simulations and the inherent statistical uncertainty in the determined values. In such a scenario, it becomes impractical to produce and use adequately-sized sets of simulated events with traditional methods, such as Monte Carlo weighting. In this work we present a staged approach to the generation of binned event distributions in order to overcome these challenges. By combining multiple integration and smoothing techniques which address limited statistics from simulation it arrives at reliable analysis results using modest computational resources.
We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expe
ctation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symmetric support, our criteria can be expressed as linear combinations of $B_s(d)$ characteristic, which is used to characterize the generalized minimum aberration. We give some empirical studies for 12-run non-regular designs to evaluate our method.
In repeated measures factorial designs involving clustered units, parametric methods such as linear mixed effects models are used to handle within subject correlations. However, assumptions of these parametric models such as continuity and normality
are usually hard to come by in many cases. The homoscedasticity assumption is rather hard to verify in practice. Furthermore, these assumptions may not even be realistic when data are measured in a non-metric scale as commonly happens, for example, in Quality of Life outcomes. In this article, nonparametric effect-size measures for clustered data in factorial designs with pre-post measurements will be introduced. The effect-size measures provide intuitively-interpretable and informative probabilistic comparisons of treatment and time effects. The dependence among observations within a cluster can be arbitrary across treatment groups. The effect-size estimators along with their asymptotic properties for computing confidence intervals and performing hypothesis tests will be discussed. ANOVA-type statistics with $chi^2$ approximation that retain some of the optimal asymptotic behaviors in small samples are investigated. Within each treatment group, we allow some clusters to involve observations measured on both pre and post intervention periods (referred to as complete clusters), while others to contain observations from either pre or post intervention period only (referred to as incomplete clusters). Our methods are shown to be, particularly effective in the presence of multiple forms of clustering. The developed nonparametric methods are illustrated with data from a three-arm Randomized Trial of Indoor Wood Smoke reduction. The study considered two active treatments to improve asthma symptoms of kids living in homes that use wood stove for heating.
It has been shown in the literature that effective gravitational constants, which are derived from Verlindes formalism, can be used to introduce the Tsallis and Kaniadakis statistics. This method provides a simple alternative to the usual procedure n
ormally used in these non-Gaussian statistics. We have applied our formalism in the Jeans mass criterion of stability and in the free fall time collapsing of a self-gravitating system where new results are obtained. A possible connection between our formalism and deviations of Newtons law of gravitation in a submillimeter range is made.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
