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Questions tagged [spatial]

The field of study concerning statistical methods that use space and spatial relationships (such as distance, area, volume, length, height, orientation, centrality and/or other spatial characteristics of data) directly in their mathematical computations.

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1answer
7k views

40,000 neuroscience papers might be wrong

I saw this article in the Economist about a seemingly devastating paper [1] casting doubt on "something like 40,000 published [fMRI] studies." The error, they say, is because of "erroneous statistical ...
53
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4answers
14k views

Why does including latitude and longitude in a GAM account for spatial autocorrelation?

I have produced generalized additive models for deforestation. To account for spatial-autocorrelation, I have included latitude and longitude as a smoothed, interaction term (i.e. s(x,y)). I've based ...
35
votes
1answer
8k views

Why is Mantel's test preferred over Moran's I?

Mantel's test is widely used in biological studies to examine the correlation between the spatial distribution of animals (position in space) with, for example, their genetic relatedness, rate of ...
30
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7answers
4k views

Is there an accepted definition for the median of a sample on the plane, or higher ordered spaces?

If so, what? If not, why not? For a sample on the line, the median minimizes the total absolute deviation. It would seem natural to extend the definition to R2, etc., but I've never seen it. But then,...
27
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4answers
18k views

Generating visually appealing density heat maps in R

While I know that there are a series of functions for generating heat maps in R, the problem is that I'm unable to produce visually appealing maps. For example, the images below are good examples of ...
23
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2answers
831 views

What statistical model or algorithm could be used to solve the John Snow Cholera problem?

I'm interested in learning how to develop a geographic approximation of some kind of epicenter based on the data from the John Snow Cholera outbreak. What statistical modeling could be used to solve ...
23
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2answers
11k views

Spatial statistics models: CAR vs SAR

When would one prefer to use a Conditional Autoregressive model over a Simultaneous Autoregressive model when modelling autocorrelated geo-referenced aerial data?
16
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5answers
12k views

2D analog of standard deviation?

Consider the following experiment: a group of people is given a list of cities, and asked to mark the corresponding locations on an (otherwise unlabeled) map of the world. For each city, you will get ...
16
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2answers
5k views

Showing spatial and temporal correlation on maps

I have data for a network of weather stations across the United States. This gives me a data frame that contains date, latitude, longitude, and some measured value. Assume that data are collected once ...
15
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2answers
3k views

What is the rationale of the Matérn covariance function?

The Matérn covariance function is commonly used as kernel function in Gaussian Process. It is defined like this $$ {\displaystyle C_{\nu }(d)=\sigma ^{2}{\frac {2^{1-\nu }}{\Gamma (\nu )}}{\Bigg (}{\...
15
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4answers
13k views

Entropy of an image

What is the most information/physics-theoretical correct way to compute the entropy of an image? I don't care about computational efficiency right now - I want it theoretically as correct as possible. ...
14
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2answers
3k views

Question about logistic regression

I want to run a binary logistic regression to model the presence or absence of conflict (dependent variable) from a set of independent variables over a 10 year period (1997-2006), with each year ...
14
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2answers
1k views

Spatial autocorrelation versus spatial stationarity

Let's assume we have points in two-dimensional space, and we wish to measure the effects of attributes $X$ on attribute $y$. The typical linear regression model is of course $$y= X\beta + \epsilon$$ ...
13
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2answers
430 views

Exploratory analysis of spatio-temporal forecast errors

The data: I have worked recently on analysing the stochastic properties of a spatio-temporal field of wind power production forecast errors. Formally, it can be said to be a process $$ \left (\epsilon^...
13
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2answers
1k views

Model for population density estimation

A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, ...
13
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3answers
6k views

Statistical measure for if an image consists of spatially connected separate regions

Consider these two grayscale images: The first image shows a meandering river pattern. The second image shows random noise. I am looking for a statistical measure that I can use to determine if it ...
12
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1answer
1k views

Statistical significance of difference between distances

I have over 3000 vectors on a two-dimensional grid, with an approximately uniform discrete distribution. Some pairs of vectors fulfil a certain condition. Note: the condition is only applicable to ...
11
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1answer
5k views

Linear Regression and Spatial-Autocorrelation

I want to predict Tree Heights in a certain area using some variables obtained through remote sensing. Like approximate Biomass, etc. I want to first use a linear regression (I know it's not the best ...
11
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3answers
3k views

Finding the average GPS point

I need to write a program to find the average GPS point from a population of points. In practice the following happens: Each month a person records a GPS point of the same static asset. Because of ...
11
votes
2answers
884 views

Why is Moran's I not equal to “-1” in perfectly dispersed point pattern

Is wikipedia wrong...or I don't understand it? Wikipedia: The white and black squares ("chess pattern") are perfectly dispersed so Moran's I would be −1. If the white squares were stacked to one ...
11
votes
3answers
514 views

Estimating parameters for a spatial process

I'm given an $n\times n$ grid of positive integer values. These numbers represent an intensity that should correspond to the strength of belief of a person occupying that grid location (a higher value ...
11
votes
1answer
1k views

What is the proper way of calculating the kernel density estimate from geographical coordinates?

I have to calculate the 2d kernel density estimate (kde) from a list of latitude and longitude coordinates. But one degree in latitude is not the same distance as one degree in longitude, this means ...
11
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1answer
1k views

What causes a U shaped pattern in the spatial correlogram?

I've noticed in my own work this pattern when examining a spatial correlogram at varying distances a U-shaped pattern in the correlations emerges. More specifically, strong positive correlations at ...
11
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2answers
5k views

Clustering spatial data in R

I have a set of sea surface temperature (SST) monthly data and I want to apply some cluster methodology to detect regions with similar SST patterns. I have a set of monthly data files running from ...
10
votes
1answer
4k views

How Does Kriging Interpolation work?

I am working on a problem in which I need to use Kriging to predict the value of some variables based on some surrounding variables. I want to implement its code by myself. So, I've went through too ...
10
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3answers
4k views

Measure the uniformity of distribution of points in a 2D square

I have a 2D square, and I have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out (or more or less uniformly distributed) ...
10
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2answers
3k views

spatial autocorrelation for time series data

I have a 20-yr dataset of an annual count of species abundance for a set of polygons (~200 irregularly shaped, continuous polygons). I have been using regression analysis to infer trends (change in ...
9
votes
3answers
7k views

What is the difference between spatial dependence and spatial heterogeneity?

What is the difference between spatial dependence and spatial heterogeneity? My question is motivated by readings in model specification problems in spatial econometrics, in particular Anselin (2010)....
9
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2answers
2k views

How can I account for spatial covariance in a linear model?

Background I have data from a field study in which there are four treatment levels and six replicates in each of two blocks. (4x6x2=48 observations) The blocks are about 1 mile apart, and within the ...
9
votes
3answers
671 views

How can I simulate census microdata for small areas using a 1% microdata sample at a large scale and aggregate statistics at the small area scale?

I would like to perform an individual-level multivariate analysis at small levels of geographic aggregation (Australian census collection districts). Clearly, the census isn't available at these ...
9
votes
2answers
227 views

Regression on the unit disk starting from “uniformly spaced” samples

I need to solve a complicated regression problem over the unit disk. The original question attracted some interesting comments, but no answers unfortunately. In meantime, I learned something more on ...
9
votes
2answers
6k views

Density-based spatial clustering of applications with noise (DBSCAN) clustering in R

this question started as "Clustering spatial data in R" and now has moved to DBSCAN question. As the responses to the first question suggested I searched information about DBSCAN and read some docs ...
9
votes
1answer
1k views

Modeling a spatial trend by regression with the $(x,y)$ coordinates as predictors

I plan to include coordinates as covariates in the regression equation in order to adjust for the spatial trend that exists in the data. After that, I want to test residuals on spatial autocorrelation ...
9
votes
3answers
354 views

An estimation problem in GPS tracking

Problem: Consider two cars (taken to be point objects), named leader $L$ and follower $F$, both equipped with GPS devices that communicate with each other. The object of $F$ is to follow $L$ as ...
8
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1answer
647 views

Intrinsic spatial stationarity: doesn't it only apply for small lags?

From the definition of Intrinsic stationarity: $E[Z(x)-Z(x-h)] = 0$ This assumption is used for example in ordinary kriging, instead of assuming a constant mean over the entire space, we assume the ...
8
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1answer
759 views

Suggested books on spatial statistics

What are some of the best books for studying i) variability of univariate and multivariate variables (real, count data) across a spatial domain. ii) sampling a univariate or multivariate variable ...
8
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1answer
1k views

Why do you have to provide a variogram model when you are kriging?

I am very new to spatial statistics and watching lots of tutorials, But I don't really get why you have to provide a variogram model when you krige. I am using the gstat package in R, and this is ...
8
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1answer
1k views

Ordinary kriging example step by step?

I have followed tutorials online for spatial kriging with both geoR and gstat (and also ...
8
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2answers
752 views

Why does the first eigenvector in PCA resemble the derivative of an underlying trend?

I am using PCA to analyze several spatially related time series, and it appears that the first eigenvector corresponds to the derivative of the mean trend of the series (example illustrated below). I ...
8
votes
3answers
288 views

Statistical model to predict the next move on network only using movement history

Is it possible to build a statistical model that predicts the next move in a graph solely based on past movements and the structure of the graph? I have made an example to illustrate the problem: ...
8
votes
1answer
1k views

Stationarity - assumptions and examination

I am examining rodent captures on six permanent rodent trapping grids measuring 150 x 150 meters and consisting of 121 trap stations evenly spaced 15 meters apart. There are six such trapping grids ...
8
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1answer
1k views

Should I check the z-score if the p-value of Local Moran's I is significant?

The dataset I'm using contains income data per area. The values are not normally distributed as shown in the following diagram. Global Moran's I indicates significant spatial patterns and Local Moran'...
8
votes
1answer
224 views

Plotting a “posterior median surface”

As part of reproducing a model I described partially in this question on Stack Overflow, I want to obtain a plot of a posterior distribution. The (spatial) model describes the selling price of some ...
8
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0answers
4k views

Specify correlation structure for different groups in mixed-effects model (lme4/nlme)

I am trying to account for spatial autocorrelation in a linear mixed-effects model in R with measurements repeated in time. BodyMass has been collected once per <...
7
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1answer
1k views

Using kriging with very sparse data

I have a very sparse set of measurements of a quantity, around 10 measurements at different locations across a continent. The distributions of locations is highly irregular. I would like to smooth ...
7
votes
2answers
254 views

How to capture competitive spatial interactions between multiple stores and customers

I am estimating sales with data on customer and store locations and attributes using a Huff-style model, where sales decay with drive time and increase with attractiveness of the store. One ...
7
votes
2answers
204 views

Associating a probability to disease propagation in regions of a map

I am trying to model disease propagation. I am considering a map separated into regions. One region is infected. There is data over time, with the number of people travelling into and out of the ...
7
votes
1answer
4k views

Pattern recognition techniques in spatial or spatio-temporal data?

I am working with weather forecasters and have access to historical climatology data. Given current weather conditions in an area of interest (i.e. the current "map"), we want to try to find the most ...
7
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1answer
2k views

In spatial regression, what is a spherical autocorrelation structure?

I have a large gridded dataset for the globe (i.e a spherical, wraparound surface) that I'm applying spatial regression to (using a CAR model). I've been using the default autocorrelation function, ...
7
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1answer
159 views

How to check for bivariate Gaussianity without the use of regression?

What steps could be taken to check for bivariate Gaussianity without using regression based check? Can we somehow employ the use of definition of variogram measure for assessing spatial variability?