scholarly journals The multivariate analysis of variance as a powerful approach for circular data

2021 ◽  
Author(s):  
Lukas Landler ◽  
Graeme D. Ruxton ◽  
E. Pascal Malkemper
Keyword(s):  
Statistical Testing ◽  
Circular Data ◽  
Circular Statistics ◽  
Bayesian Approaches ◽  
Explanatory Factors ◽  
Powerful Approach ◽  
Conventional Tests ◽  
Linear Modelling ◽  
Recent Developments ◽  
Scientific Questions

Abstract A broad range of scientific studies involve taking measurements on a circular rather than linear scale (often times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. However, most statistical testing of circular statistics is much simpler: often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported. Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as effective as the most-commonly used tests in these simple situations, while additionally it offers extension to multi-factorial modelling that these conventional tests do not. This, in combination with recent developments in Bayesian approaches, offers a substantial broadening of the scientific questions that can be addressed statistically with circular data.

scholarly journals Dynamics & Spectroscopy with Neutrons—Recent Developments & Emerging Opportunities

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1440
Author(s):  
Kacper Drużbicki ◽  
Mattia Gaboardi ◽  
Felix Fernandez-Alonso
Keyword(s):  
Dynamical Behavior ◽  
Disordered Materials ◽  
Spectroscopic Techniques ◽  
Computational Tools ◽  
Soft Solids ◽  
Sustainable Technologies ◽  
Energy Transfers ◽  
Recent Developments ◽  
Scientific Questions ◽  
Nuclear Quantum Effects

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

scholarly journals Circular Statistics Applied to the Study of the Solar Radiation Potential of Rooftops in a Medium-Sized City

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2813 ◽  
Author(s):  
María-Eugenia Polo ◽  
Mar Pozo ◽  
Elia Quirós
Keyword(s):  
Climate Change ◽  
Alternative Energy ◽  
Urban Morphology ◽  
Circular Data ◽  
Circular Statistics ◽  
Sustainable Cities ◽  
Residential Areas ◽  
City Center ◽  
Alternative Energy Sources ◽  
The City

Solar energy constitutes one of the most effective alternative energy sources for combating climate change. However, the solar potential in a city can vary depending on the urban morphology. The purpose of this paper is to perform a directional statistical analysis of the distribution of the monthly solar potential of rooftops in the city of Cáceres, Spain, in relation to the orientations and slopes of the rooftops. Two residential areas, one in the city center and one on the outskirts of the city, and an industrial zone, all of which exhibit different urban morphologies, have been evaluated. Statistics have been assessed in consideration of the orientation and slope values of the rooftops as circular data, and the radiation values as linear data. The three dissimilar urban morphologies result in different solar potential values, and the monthly disaggregation of the data enables the ability to detect the differences existing in the solar potential between each zone, during each month. The proposed analysis could also be extrapolated to urban planning for the design of more sustainable cities to face the challenges associated with climate change.

scholarly journals Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis

2006 ◽  
Vol 14 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Patrick T. Brandt ◽  
John R. Freeman
Keyword(s):  
Time Series ◽  
Policy Analysis ◽  
Theory Testing ◽  
Multiple Time ◽  
Shape Error ◽  
Time Series Modeling ◽  
International Conflicts ◽  
Bayesian Approaches ◽  
Recent Developments ◽  
Bayesian Time Series

Bayesian approaches to the study of politics are increasingly popular. But Bayesian approaches to modeling multiple time series have not been critically evaluated. This is in spite of the potential value of these models in international relations, political economy, and other fields of our discipline. We review recent developments in Bayesian multi-equation time series modeling in theory testing, forecasting, and policy analysis. Methods for constructing Bayesian measures of uncertainty of impulse responses (Bayesian shape error bands) are explained. A reference prior for these models that has proven useful in short- and medium-term forecasting in macroeconomics is described. Once modified to incorporate our experience analyzing political data and our theories, this prior can enhance our ability to forecast over the short and medium terms complex political dynamics like those exhibited by certain international conflicts. In addition, we explain how contingent Bayesian forecasts can be constructed, contingent Bayesian forecasts that embody policy counterfactuals. The value of these new Bayesian methods is illustrated in a reanalysis of the Israeli-Palestinian conflict of the 1980s.

Applying Circular Statistics to the Analysis of Monitoring Data

2007 ◽  
Vol 23 (4) ◽  
pp. 227-237 ◽  
Author(s):  
Thomas Kubiak ◽  
Cornelia Jonas
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Ambulatory Monitoring ◽  
Circular Data ◽  
Circular Statistics ◽  
Series Data ◽  
Cross Sectional ◽  
Psychological Variables ◽  
Wide Range ◽  
Time Series Approach

Abstract. Patterns of psychological variables in time have been of interest to research from the beginning. This is particularly true for ambulatory monitoring research, where large (cross-sectional) time-series datasets are often the matter of investigation. Common methods for identifying cyclic variations include spectral analyses of time-series data or time-domain based strategies, which also allow for modeling cyclic components. Though the prerequisites of these sophisticated procedures, such as interval-scaled time-series variables, are seldom met, their usage is common. In contrast to the time-series approach, methods from a different field of statistics, directional or circular statistics, offer another opportunity for the detection of patterns in time, where fewer prerequisites have to be met. These approaches are commonly used in biology or geostatistics. They offer a wide range of analytical strategies to examine “circular data,” i.e., data where period of measurement is rotationally invariant (e.g., directions on the compass or daily hours ranging from 0 to 24, 24 being the same as 0). In psychology, however, circular statistics are hardly known at all. In the present paper, we intend to give a succinct introduction into the rationale of circular statistics and describe how this approach can be used for the detection of patterns in time, contrasting it with time-series analysis. We report data from a monitoring study, where mood and social interactions were assessed for 4 weeks in order to illustrate the use of circular statistics. Both the results of periodogram analyses and circular statistics-based results are reported. Advantages and possible pitfalls of the circular statistics approach are highlighted concluding that ambulatory assessment research can benefit from strategies borrowed from circular statistics.

scholarly journals Model selection versus traditional hypothesis testing in circular statistics: a simulation study

Biology Open ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. bio049866
Author(s):  
Lukas Landler ◽  
Graeme D. Ruxton ◽  
E. Pascal Malkemper
Keyword(s):  
Type I Error ◽  
Statistical Treatment ◽  
Model Fitting ◽  
Standard Technique ◽  
Circular Data ◽  
Circular Statistics ◽  
Distribution Model ◽  
Type I ◽  
Rayleigh Test ◽  
Made In

ABSTRACTMany studies in biology involve data measured on a circular scale. Such data require different statistical treatment from those measured on linear scales. The most common statistical exploration of circular data involves testing the null hypothesis that the data show no aggregation and are instead uniformly distributed over the whole circle. The most common means of performing this type of investigation is with a Rayleigh test. An alternative might be to compare the fit of the uniform distribution model to alternative models. Such model-fitting approaches have become a standard technique with linear data, and their greater application to circular data has been recently advocated. Here we present simulation data that demonstrate that such model-based inference can offer very similar performance to the best traditional tests, but only if adjustment is made in order to control type I error rate.

scholarly journals The Rise of Markov Chain Monte Carlo Estimation for Psychometric Modeling

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Roy Levy
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Approaches ◽  
Mcmc Estimation ◽  
Powerful Approach ◽  
Psychometric Modeling ◽  
Psychometric Models ◽  
Monte Carlo Estimation

Markov chain Monte Carlo (MCMC) estimation strategies represent a powerful approach to estimation in psychometric models. Popular MCMC samplers and their alignment with Bayesian approaches to modeling are discussed. Key historical and current developments of MCMC are surveyed, emphasizing how MCMC allows the researcher to overcome the limitations of other estimation paradigms, facilitates the estimation of models that might otherwise be intractable, and frees the researcher from certain possible misconceptions about the models.

Comparisons of Segment Coordination: An Investigation of Vector Coding

2018 ◽  
Vol 34 (3) ◽  
pp. 226-231 ◽  
Author(s):  
Julia Freedman Silvernail ◽  
Richard E.A. van Emmerik ◽  
Katherine Boyer ◽  
Michael A. Busa ◽  
Joseph Hamill
Keyword(s):  
Linear Analysis ◽  
Circular Data ◽  
Circular Statistics ◽  
Coordination Pattern ◽  
Movement Coordination ◽  
Vector Coding ◽  
Movement Organization ◽  
Coordination Patterns ◽  
Compressed Data ◽  
Group Comparisons

The development of a methodology to assess movement coordination has provided gait researchers a tool to assess movement organization. A challenge in analyzing movement coordination using vector coding lies within the inherent circularity of data garnered from this technique. Therefore, the purpose of this investigation was to determine if accurate group comparisons can be made with varying techniques of vector coding analyses. Thigh–shank coordination was analyzed using a modified vector coding technique on data from 2 groups of runners. Movement coordination was compared between groups using 3 techniques: (1) linear average completed with compressed data (0°–180°) and noncompressed data (0°–360°), (2) coordination phase binning analysis; and (3) a circular statistics analysis. Circular statistics (inferential) analysis provided a rigorous comparison of average movement coordination between groups. In addition, the binning analysis provided a metric for detecting even small differences in the time spent with a particular coordination pattern between groups. However, the linear analysis provided erroneous group comparisons. Furthermore, with compressed data, linear analysis led to misclassification of coordination patterns. While data compression may be attractive as a means of simplifying statistical analysis of inherently circular data, recommendations are to use circular statistics and binning methods on noncompressed data.

scholarly journals Descriptive analysis of circular data with outliers using Python programming language

2020 ◽  
Vol 1 (01) ◽  
pp. 31-36
Author(s):  
N.S. Zulkipli ◽  
S.Z. Satari ◽  
W.N.S. Wan Yusoff
Keyword(s):  
Programming Language ◽  
Descriptive Analysis ◽  
Descriptive Statistics ◽  
Circular Data ◽  
Circular Statistics ◽  
Statistical Software ◽  
R Programming Language ◽  
R Programming ◽  
Basic Features ◽  
Python Programming

Descriptive statistics are commonly used in data analysis to describe the basic features of raw data. Descriptive summaries enable us to present the data in a more simple and meaningful way so that the interpretation will be easier to understand. The descriptive analysis of circular data with outliers is discussed in this study. Circular data is different from linear data in many aspects such as statistical modeling, descriptive statistics and etc. Hence, unlike linear data, the availability of statistical software specialises in analysing circular data is very limited. Python is a programming language which frequently used by data analysts nowadays. However, the package for circular statistics is not fully developed and it is not ready to use like in Splus or R programming language. In this study, the descriptive analysis of circular data is performed using the in-demand programming language, Python. Descriptive statistics of the circular data especially with the existence of outliers are discussed and the proposed Python code is available to use.

A Practical Introduction to Landmark-Based Geometric Morphometrics

2010 ◽  
Vol 16 ◽  
pp. 163-188 ◽  
Author(s):  
Mark Webster ◽  
H. David Sheets
Keyword(s):  
Geometric Morphometrics ◽  
A Priori ◽  
Comparative Morphology ◽  
Statistical Testing ◽  
Shape Variation ◽  
Sample Mean ◽  
Procrustes Distance ◽  
Powerful Approach ◽  
Canonical Variates ◽  
Biological Shape

Landmark-based geometric morphometrics is a powerful approach to quantifying biological shape, shape variation, and covariation of shape with other biotic or abiotic variables or factors. The resulting graphical representations of shape differences are visually appealing and intuitive. This paper serves as an introduction to common exploratory and confirmatory techniques in landmark-based geometric morphometrics. The issues most frequently faced by (paleo)biologists conducting studies of comparative morphology are covered. Acquisition of landmark and semilandmark data is discussed. There are several methods for superimposing landmark configurations, differing in how and in the degree to which among-configuration differences in location, scale, and size are removed. Partial Procrustes superimposition is the most widely used superimposition method and forms the basis for many subsequent operations in geometric morphometrics. Shape variation among superimposed configurations can be visualized as a scatter plot of landmark coordinates, as vectors of landmark displacement, as a thin-plate spline deformation grid, or through a principal components analysis of landmark coordinates or warp scores. The amount of difference in shape between two configurations can be quantified as the partial Procrustes distance; and shape variation within a sample can be quantified as the average partial Procrustes distance from the sample mean. Statistical testing of difference in mean shape between samples using warp scores as variables can be achieved through a standard Hotelling's T2 test, MANOVA, or canonical variates analysis (CVA). A nonparametric equivalent to MANOVA or Goodall's F-test can be used in analysis of Procrustes coordinates or Procrustes distance, respectively. CVA can also be used to determine the confidence with which a priori specimen classification is supported by shape data, and to assign unclassified specimens to pre-defined groups (assuming that the specimen actually belongs in one of the pre-defined groups).Examples involving Cambrian olenelloid trilobites are used to illustrate how the various techniques work and their practical application to data. Mathematical details of the techniques are provided as supplemental online material. A guide to conducting the analyses in the free Integrated Morphometrics Package software is provided in the appendix.

scholarly journals Microbial Contributions for Rice Production: From Conventional Crop Management to the Use of ‘Omics’ Technologies

2022 ◽  
Vol 23 (2) ◽  
pp. 737
Author(s):  
Febri Doni ◽  
Nurul Shamsinah Mohd Suhaimi ◽  
Muhamad Shakirin Mispan ◽  
F Fathurrahman ◽  
Betty Mayawatie Marzuki ◽  
...  
Keyword(s):  
Cost Effective ◽  
Rice Production ◽  
Multiple Roles ◽  
Molecular Signaling ◽  
Omics Technologies ◽  
Rice Plants ◽  
Plant Associations ◽  
Recent Developments ◽  
Growth Production ◽  
Scientific Questions

Rice, the main staple food for about half of the world’s population, has had the growth of its production stagnate in the last two decades. One of the ways to further improve rice production is to enhance the associations between rice plants and the microbiome that exists around, on, and inside the plant. This article reviews recent developments in understanding how microorganisms exert positive influences on plant growth, production, and health, focusing particularly on rice. A variety of microbial species and taxa reside in the rhizosphere and the phyllosphere of plants and also have multiple roles as symbiotic endophytes while living within plant tissues and even cells. They alter the morphology of host plants, enhance their growth, health, and yield, and reduce their vulnerability to biotic and abiotic stresses. The findings of both agronomic and molecular analysis show ways in which microorganisms regulate the growth, physiological traits, and molecular signaling within rice plants. However, many significant scientific questions remain to be resolved. Advancements in high-throughput multi-omics technologies can be used to elucidate mechanisms involved in microbial–rice plant associations. Prospectively, the use of microbial inoculants and associated approaches offers some new, cost-effective, and more eco-friendly practices for increasing rice production.

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