Evaluating Material Flammability in Microgravity and Martian Gravity Compared to the NASA Standard Normal Gravity Test

In statistics, there are various terms that may feel unfamiliar to researcher who is not accustomed to discussing it. However, despite all of many functions and benefits that we can get as researchers to process data, it will later be interpreted into a conclusion. And then researcher can digest and understand the research findings. The distribution of continuous random opportunities illustrates obtaining opportunities with some detection of time, weather, and other data obtained from the field. The standard normal distribution represents a stable curve with zero mean and standard deviation 1, while the t distribution is used as a statistical test in the hypothesis test. Chi square deals with the comparative test on two variables with a nominal data scale, while the f distribution is often used in the ANOVA test and regression analysis.

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A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

Volume 2A: 42nd Design Automation Conference ◽

10.1115/detc2016-59151 ◽

2016 ◽

Author(s):

Po Ting Lin ◽

Wei-Hao Lu ◽

Shu-Ping Lin

Keyword(s):

Design Optimization ◽

Design Space ◽

Optimization Problems ◽

Nonlinear Problems ◽

Kernel Functions ◽

Sensitivity Analyses ◽

Normal Space ◽

Highly Nonlinear ◽

Standard Normal ◽

Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

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An improved exact sampling algorithm for the standard normal distribution

Computational Statistics ◽

10.1007/s00180-021-01136-w ◽

2021 ◽

Author(s):

Yusong Du ◽

Baoying Fan ◽

Baodian Wei

Keyword(s):

Normal Distribution ◽

Standard Normal Distribution ◽

Sampling Algorithm ◽

Exact Sampling ◽

Standard Normal

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Interpretable Variational Graph Autoencoder with Noninformative Prior

Future Internet ◽

10.3390/fi13020051 ◽

2021 ◽

Vol 13 (2) ◽

pp. 51

Author(s):

Lili Sun ◽

Xueyan Liu ◽

Min Zhao ◽

Bo Yang

Keyword(s):

Latent Variables ◽

Latent Variable ◽

Expert Knowledge ◽

Structural Information ◽

Standard Normal Distribution ◽

Noninformative Prior ◽

Latent Space ◽

Distribution Parameters ◽

Standard Normal ◽

Low Dimensional

Variational graph autoencoder, which can encode structural information and attribute information in the graph into low-dimensional representations, has become a powerful method for studying graph-structured data. However, most existing methods based on variational (graph) autoencoder assume that the prior of latent variables obeys the standard normal distribution which encourages all nodes to gather around 0. That leads to the inability to fully utilize the latent space. Therefore, it becomes a challenge on how to choose a suitable prior without incorporating additional expert knowledge. Given this, we propose a novel noninformative prior-based interpretable variational graph autoencoder (NPIVGAE). Specifically, we exploit the noninformative prior as the prior distribution of latent variables. This prior enables the posterior distribution parameters to be almost learned from the sample data. Furthermore, we regard each dimension of a latent variable as the probability that the node belongs to each block, thereby improving the interpretability of the model. The correlation within and between blocks is described by a block–block correlation matrix. We compare our model with state-of-the-art methods on three real datasets, verifying its effectiveness and superiority.

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A Test for Functional Form Against Nonparametric Alternatives

Econometric Theory ◽

10.1017/s0266466600013165 ◽

1992 ◽

Vol 8 (4) ◽

pp. 452-475 ◽

Cited By ~ 72

Author(s):

Jeffrey M. Wooldridge

Keyword(s):

Alternative Model ◽

Regression Models ◽

Functional Form ◽

Parametric Model ◽

Finite Sample ◽

Test Statistic ◽

Sieve Estimation ◽

Finite Sample Properties ◽

Standard Normal ◽

Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

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