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Applied Univariate Statistics
Published in Nick Zacharov, Sensory Evaluation of Sound, 2018
Per Bruun Brockhoff, Federica Belmonte
Below we will use post hoc multiple mean comparisons within mixed models, and show univariate hypothesis test results collected across multiple attributes. For both types of results it will be important to protect against “significance by chance” during the interpretation of such multiple test results. For post hoc analysis within mixed models, you can use any approach among classical linear models. Thus classical correction methods such as Dunnet’s, Tukey’s, Scheffe and Bonferroni methods also apply similarly for analysing fixed effects within mixed models. We will detail a few of these methods here. They are generally available in R (see R Core Team (2016)) through various post hoc packages, see e.g. Lenth (2016). R is an open source language and environment for statistical computing and graphics. It is the mostly used development language for statistical computing and together with Python® similarly so for machine learning and data science. The number of add-on packages to base R has been increasing exponentially since 2002, and passed 10.000 in the beginning of 2017. It is beyond the scope of this chapter to introduce the basic use of R, and such introductions are numerously found online, e.g. Brockhoff et al. (2015a).
Statistics
Published in Benjamin D. Shaw, Uncertainty Analysis of Experimental Data with R, 2017
You can use the t variable to compare the means of two samples to determine whether they are significantly different at a chosen confidence level P. For example, suppose we measure the lifetimes of birthday candles (in minutes). The data set x1 is a set of lifetimes measured during someone’s birthday party and x2 is a set of lifetimes measured during another birthday party: There is a built-in R function, t.test(), that can do this test: What is relevant here is the p-value. A typical criterion to apply is the following: If the p-value is greater than 1 − P (= 0.05 here), then the sample means are not significantly different in a statistical sense. In the present case, the means differ by about 1 minute, but this difference is not statistically significant. A conclusion you would reach is that all of the birthday candles were likely to have come from the same population. This example actually corresponds to a hypothesis test, which is an interesting subject in itself.
Major Histocompatibility Complex Binding and Various Health Parameters Analysis
Published in Adwitiya Sinha, Megha Rathi, Smart Healthcare Systems, 2019
Abhinav Gautam, Arjun Singh Chauhan, Ayush Srivastava, Chetan Jadon, Megha Rathi
R is a language and environment for statistical computing and graphics. It is a GNU project that is similar to the S language and environment, which was developed at Bell Laboratories. It is being collaboratively developed by various developers from across the globe. The R project was first started in 1997 by Robert Gentleman and R Ihaka, both professors of the University of Auckland. As of today, R is one of the most powerful machine learning languages that is being used by industry giants and is even being provided by clouds-based programs to developers—International Business Machines Corporation (IBM) Watson being one of them.
Efficient computation of derivatives for solving optimization problems in R and Python using SWIG-generated interfaces to ADOL-C†
Published in Optimization Methods and Software, 2018
K. Kulshreshtha, S.H.K. Narayanan, J. Bessac, K. MacIntyre
R is a language and environment for statistical computing and graphics [32]. It is widely used in statistics and data mining. To obtain derivatives in R, one can use several non-native approaches, including the Template Model Builder system [1] and Ryacas [14]. However, none of these options support the differentiation of functions expressed as R programs, as would an AD tool for R. Attempts to develop such a tool include radx [3]. This tool can compute first- and second-order forward-mode derivatives of univariate functions, but it is no longer actively developed. Natively, inside R, the numDeriv package provides methods for calculating (usually) accurate numerical first- and second-order derivatives [25]. Accurate calculations are done by using Richardson's extrapolation, or when applicable, a complex step derivative is available; a simple difference method is also provided. The deriv function from the stats package computes derivatives of simple expressions symbolically [31]. A package named madness [26] was released recently on CRAN. This package performs automatic differentiation for R via forward accumulation. However this package does not allow operations between variables of differing dimensions, such as scalar–vector multiplication, which is critical in a lot of modelling situations. Since numerical finite differences are not reliably accurate and cannot compute adjoints (see [15]), there is a need to provide derivatives within R using AD tools.
Multivariate Poisson-lognormal model for analysis of crashes on urban signalized intersections approach
Published in Journal of Transportation Safety & Security, 2018
Mo Zhao, Chenhui Liu, Wei Li, Anuj Sharma
As is shown in Equations 1–3, because it is very difficult to directly derive the marginal distribution of crash counts by numerical computation due to the existence of the unrestricted covariance matrix, , the likelihood-based methods cannot be used for estimation here. Thus, the Bayesian method with the MCMC simulation is employed to estimate parameters (El-Basyouny et al., 2014; Ma et al., 2008; Park & Lord, 2007). The Just Another Gibbs Sampler (JAGS) software is a program for analyzing Bayesian hierarchical models using MCMC simulation (Plummer, 2003). In JAGS, when conjugate priors are available, the Gibbs sampling is used. Otherwise, slicing sampling is used. R is a programming language and software environment for statistical computing and graphics (R Core Team, 2016). Package “rjags” is an interface program to run JAGS from R (Plummer, 2015) and is used to estimate the parameters of the proposed MVPLN model in this study.
Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis
Published in Science and Technology of Advanced Materials, 2019
Tarojiro Matsumura, Naoka Nagamura, Shotaro Akaho, Kenji Nagata, Yasunobu Ando
Calculation was conducted by using our own source code developed in R (http://cran.r-project.org/). R is an open-source programming language and software environment for statistical analysis and graphics. The reason for using our own code is that major R packages for the calculation of the EM algorithm [e.g. 28] cannot deal with the weight at each data point. The computer carrying out the calculations had an Intel(R) Core(TM) i7 CPU with four cores at 2.9 GHz with 16 GB memory.