Questions tagged [circular-statistics]
Directional statistics (also called circular or spherical statistics) is the discipline of statistics that deals with directions (unit vectors in $\mathbb{R}^n$), axes (lines through the origin in $\mathbb{R}^n$) or rotations in $\mathbb{R}^n$.
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Radial axis transformation in polar kernel density estimate
Consider a kernel density estimate of a continuous, non-negative random variable defined over the unit circle with no discontinuity between 360 and 0 degrees.
Unlike in the most common KDE ...
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How to choose priors for bounds on circular truncated distributions?
I am considering choices of priors for truncated distributions on a circle. Let's take the truncated normal distribution on the unit circle as an example. It has parameters $\mu \in [-\pi, \pi]$ and $\...
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Possibility priors in Bayesian analysis?
A couple of trains of thought have come together for a model I am designing. Let's start with the first part: Bayesian inference doesn't update strongly enough.
One of the parameters $\theta$ is an ...
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watson's two sample test with ties - does it exist on R?
I would like to compare two samples with the watson's two sample test in R (circular data). As I have a lot of ties in my samples, I followed the example given in the book from Zar (Biostatistical ...
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How to calculate confidence intervals for circular data?
I managed to convert my data i circular/polar data (angle, r). Now I would like to compare two treatments to see if they are statistically different. I thought to use the Watson's U2 test but ...
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Does it make sense to transform a feature containing hours (24h) into two features with xy-coordinates of each hour in the space? [duplicate]
I have a clustering problem that I might solve with an algorithm based on Euclidean distance (e.g. K-Means).
One potential feature is the "hour" at which each user began an interaction.
As ...
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How do I interpret the sine and cosine terms in a linear-circular regression?
When using a circular variable as a predictor (X) in a linear regression, the consensus seems to be to split the variable into sine and cosine terms.
e.g. Y ~ cos(X) + sin(X) + etc
This creates two ...
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Determining significance for the V test (circular statistics)
I am trying to write some code to determine whether a sample of circular measurements is significantly clustered around a specific angle. I want to use the V test (1) because it seems to be the ...
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Python / R package for multivariate gaussian process regression for circular data?
I have two circular predictor features (two angles between 0 and 360 degrees) and a circular outcome (another angle, between 0 and 360 degrees). I'd like to be able to fit a model and get predictions ...
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Regression of circular variable with scikit-learn
I am trying to use Support Vector Regression on a (neurophysiological) dataset where the position of points on a circular manifold in N dimensions is correlated with a circular variable (phase of an ...
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Clustering and grouping of rhythmic data (acrophases)
I am looking for suggestions towards a clustering method for rhythmic/oscillation data.
We performed cosinor regression (sin(2*pi*time/period)+cos(2*pi*time/period))...
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Calculating the parameters of von Mises distribution
I would like to calculate the values of the concentration ($\kappa$) and mean direction ($\mu$) for a von Mises mixture model from the theta values given by the movMF() function in R. At the bottom of ...
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Within a circle, Find a probability distribution to model a random variable with distance to center and angle information
Within a circle with radius R, a random variable with two types of information as below:
Distance to the circle center. The distance should satisfy uniform distribution~U[a R], where 0<=a<R is ...
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Mahalanobis distance for a vector with (also) angular data
I have a vector of data that is composed of 9 values:
position in 3d
orientation in 3d
size in 3d.
Obviously, angles are "circular" values, that is 359deg is near to 1deg, but $359 - 1 = ...
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Measuring dispersion in circular data
stats noob here.
I have a (circular) dataset with values in [0, 2pi]. I need some kind of a measure of how disperse or diverse the dataset is. I have looked a bit into non circular (regular) data, and ...
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Calculate uncertainty of surface normal based on points uncertainty
How to calculate angular variation of fitted plane from points that has positional uncertainty with normal probability distribution?
For example, I have 4 points
P1 = 102.0000 84.0000 139.5443
P2 = ...
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Is circular correlation maximized by points laying on a square grid on the plane?
Background
Circular correlation is given by:
$$R_{\operatorname{circular}} \triangleq \frac{\sum_{i=1}^m \sin (x_i - \bar x) \sin (y_i - \bar y)}{\sqrt{\sum_{i=1}^m \sin (x_i - \bar x)^2} \sqrt{\sum_{...
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Definition of directional variance
We are currently adding some basic functionality for directional statistics to SciPy. Directional statistics refer to data whose magnitude does not matter such as unit vectors.
While implementing the ...
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Significance of diurnal variation found by c-association, but not LSSA
I have several time series with unevenly (unequally or irregularly) spaced data points. On theoretical grounds, I expect a diurnal (24 h) cycle. I have used two methods to analyse these data:
Least-...
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Running a poisson GLM with cyclical explanatory variable?
Im running a few poisson GLMs looking at count data of bats sightings in relation to lunar cycle.
We specifically want to look at how species are affected leading up to and away from new moon/full ...
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How best to model day time dependet activity?
I aquired the median activity data of animals per hour and wanted to model them dependent on time. Now I have tried different models and came up with the following. (This only includes a small portion ...
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Modeling repeated measures analysis with circular variables
(question cross-posted to stack overflow here:https://stackoverflow.com/questions/72189932/circular-analysis-repeated-measures-design-model-building-evaluation-and-inte?noredirect=1#...
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How to calculate the value (wind direction) of "maximal effect" in a linear-circular correlation?
I am trying to evaluate the effect of wind direction (circular variable) on a dependent linear variable. I have used circular-linear regression to find the correlation coefficient between the two ...
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Which statistical test should I use to see if the month of onset of a disease is random or clusters in the winter?
I have data showing which month a disease started for 119 subjects. The months are represented by 1-12 (Jan - December). We hypothesize the disease more often onsets during winter months. What test ...
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Loss Function for Polar Coordinates Target Variables?
Suppose I want to do regression on targets that are polar coordinates. What loss functions are appropriate? I know I could always use mean squared error, but I'm not sure that's the most appropriate.
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How can I quantify this non-linear relationship where y-values peak within a narrow range of x-values?
I have plotted this data, and to me there appears to be a clear relationship between the variables (sediment accumulates when wind direction is between 150 and 250 degrees). Is there a appropriate ...
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Why doesn't mean square error work in case of angular data?
Suppose, the following are the first few lines from a dataset for solving a regression problem:
...
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Machine learning regressor for cyclic values
I have a question regarding training a Machine Learning regressor for cyclic values. For instance, consider phase values. We cannot use conventional regression methods for this as for example the ...
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Why does the von Mises-Fisher distribution need two parameters?
The von Mises-Fisher distribution has two parameters: the mean $\mu \in \mathbb{R}^p$ and concentration $\kappa \geq 0$, where $\mu$ is constrained to have unit norm.
Why not instead define the ...
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Variance of von Mises-Fisher Distribution
As a follow up to this previous question on the expectation of the von Mises-Fisher distribution, what is the variance of a von-Mises Fisher distribution as a function of the mean direction $\mu$ and ...
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Fitting sine wave with lm in R for circadian activity- frequencies?
I'm trying to fit a sine wave over some activity data, just like this post. I've managed to get a reasonable looking graph for one condition:
However, when I plot the other condition the wave looks ...
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Best distance measure for cluster analysis of time series data with a circular variable
I'm doing hierarchical clustering on a set of time series (say 21 time series of 400 time points), however the variable I want to cluster is a circular variable, i.e. a directional vector between 0 ...
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How to define distance for vector of angles?
I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
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Measure of similarity between two distributions - with variable starting point (wrap-around)
I would like to compute the (dis)similarity between two distributions. The first represents tones sung by an experimental subject during a recording. There are different numbers of tones, each with ...
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use GAMM models for full circular wind direction data
using a GAM modeling approach enables to include circular data as fixed effects. I wish to analyze the effect of wind on the flight behaviour of birds. In order to do so I want to add wind speed and ...
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Skewness of Von mises distribution using two different methods
I want to use skewness of circular data using circ_skewness code in MATLAB. I know there are two methods for this:
Pewsey, Metrika, 2004
Statistical analysis of circular data, Fisher, p. 34
However,...
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Converting a circular outcome variable to a linear one
I have a problem where I want to measure deviations from zero degrees. This outcome variable is a circular measure, since a deviation of -180 degrees is equivalent to 180 degrees.
However, I don't ...
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Skewness and kurtosis of VonMises distribution
I could not find a reference that has mentioned the skewness and kurtosis of a circular data that has Von Mises distribution.
What are the values? and it is great if someone can introduce some ...
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Covariate analysis comparing distributions / means of circular data
Are there publicly available software packages to run an analysis comparing the means or distributions of two samples of circular data with the presence of a covariate? If not, are there ways to ...
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Two sample Kuiper test for checking normality of circular data
I have circular data and want to check whether it is a normal (Von Mises) distribution or not.
I do the following steps:
Create a Von Mises distribution with the same mean and kappa as my main data.
...
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Expected ratio of x'Ax and x'AAx on a unit sphere?
Suppose $A$ is symmetric positive definite matrix. Is there a nice expression for the first moment of the following quantity?
$$\frac{x^TAx}{x^TA^2 x}$$
Where $x$ is distributed as $\text{Normal}(0,...
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Testing for circular uniformity of headings (Rayleigh, v-test)
I have two-dimensional recordings of animal trajectories. The animals exit their nest and I am trying to test whether their headings over a period of time have a distribution different than uniform. ...
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Distribution of $\langle x^2,a\rangle$ where $x$ is is a random direction?
Suppose $x\in R^n$ follows the uniform distribution on the surface of a unit sphere centered at 0 and $a$ is a vector in $R^n$. What can we say about the distribution of the following quantity?
$$\...
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Normality test for circular data
I have some angles and I am wondering how can I test whether the distribution of my data is normal or not. In fact, I want something similar to KS test. Howver, I want to use it for circular data to ...
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What would be a good objective function for a computer vision model that predicts rotation?
Let's say I have to correct images of scenes which can be rotated in the range $[0, 2\pi)$. For my particular application I already know a CNN makes sense. I'd use this to detect the orientation, then ...
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Coefficient of variation of circular data
The definition of coefficient of variation is as follows:
coefficient of variation= standard deviation/mean.
I am using circular (directional) statistics to find the mean and standard deviation. My ...
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Interpreting multiple circular-circular regression output
I'm new to circular stats and have been playing with circglmbayes and bpnreg. I'm not sure how to interpret the output. I have consulted the CrossValidated database, and the papers/tutorials ...
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Is the difference between directional means from two populations significant? (circular data)
I am comparing the orientation of two data sets with geographical lines and have used the processing tool "Linear Directional Mean" (ArcGIS Pro, Spatial Analyst) to calculate the mean of ...
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Circular statistics polar coordinates data in R
I am very much new to dealing with this type of data (polar coordinates!) and it would be great if someone could help me out.
My data come from an experiment in which I had 66 different pairs of ...
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When are circular statistics needed (reference)?
I have a set of data of measurements for the lateral angle of the internal acoustic meatus (it's an angle between the canal of our inner ear and another bone structure in our skull). The measurements ...
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