An interactive Shiny app for teaching and exploring variograms and Gaussian random fields. Designed for statistics courses and workshops — no R installation needed for students.
Scan to open on any device |
Live app: https://olatunjijohnson-variogramapp.hf.space Students can open this URL in any browser — phone, tablet, or laptop. No R, no installation, no login required. |
Exponential model: 2D Gaussian random field (top) with 100 random sample locations (dots) and the resulting empirical semivariogram vs. theoretical curve (bottom).
The app lets you simulate a Gaussian random field, draw a sample from it, and see how well the empirical variogram recovers the true covariance structure. It is designed to build intuition about:
- How covariance model parameters (variance, scale, nugget, smoothness) shape the variogram
- How sample size and spatial design affect estimation
- What Monte Carlo permutation envelopes mean in practice
| Feature | Description |
|---|---|
| 12 covariance models | Matérn, Exponential, Gaussian, Spherical, Circular, Cubic, Wave, Power, Powered Exponential, Cauchy, Gneiting, Pure Nugget |
| Live formula display | The mathematical formula updates in real time with MathJax rendering |
| 1D and 2D simulation | 1D produces a time series; 2D produces a spatial raster map |
| Sampling designs | Random sampling or inhibitory (minimum-distance) sampling |
| Empirical semivariogram | Plotted against the true theoretical curve |
| Monte Carlo envelope | Permutation-based 95% significance band (toggle on/off) |
| Bin counts | Number of pairs per bin shown on the plot (toggle on/off) |
| Multiple simulations | Run N realisations and animate through them with a slider |
| Download | Save the variogram plot as a PNG |
| Control | What it does |
|---|---|
| Covariance model | Selects the covariance function used to simulate the field |
| Dimension | 1D (time series) or 2D (spatial map) |
| Domain | Size of the simulation grid |
| Variance σ² | Marginal variance of the process (controls the sill) |
| Scale φ | Range parameter — larger values = stronger spatial correlation over longer distances |
| Nugget τ² | Micro-scale noise added to each observation |
| Smoothness κ | (Matérn / Powered Exponential / Cauchy only) Controls how smooth the field is |
| Sampling design | Random: locations drawn uniformly. Inhibitory: locations kept at least delta apart |
| Min distance | Minimum gap between sample locations in inhibitory sampling |
| Sample locations | Number of points sampled from the simulated field |
| Max variogram distance | Upper limit on the x-axis of the variogram plot |
| Number of bins | How many distance classes the variogram is divided into |
| MC envelope | Toggle a 95% permutation envelope (slower — reduce sample size first) |
| Bin counts | Show the number of pairs contributing to each bin |
| Number of simulations | Simulate multiple realisations; animate with the slider |
Open https://olatunjijohnson-variogramapp.hf.space in any browser. No R required.
# install.packages("remotes")
remotes::install_github("olatunjijohnson/variogramApp")Then launch with:
library(variogramApp)
run_variog_app()Requires R with shiny, geoR, ggplot2, and dplyr installed:
# install.packages(c("shiny", "geoR", "ggplot2", "dplyr"))
shiny::runGitHub(
repo = "variogramApp",
username = "olatunjijohnson",
subdir = "inst/variogramApp"
)The quickest way is to share the URL or display the QR code on a slide:
# install.packages("qrcode")
library(qrcode)
png("variogramApp_qr.png", width = 400, height = 400)
plot(qr_code("https://olatunjijohnson-variogramapp.hf.space"))
dev.off()If you need your own instance (e.g. for a high-traffic class session),
deploy to Hugging Face Spaces for free. All
deployment files are in deploy/huggingface/ in this repository.
Step 1 — Create a free account at huggingface.co, then create a new Space with SDK: Docker and Visibility: Public.
Step 2 — Clone your new Space and copy the deployment files in:
git clone https://huggingface.co/spaces/YOUR_USERNAME/variogramApp
cd variogramApp
# copy deploy/huggingface/* from this repo into the cloned Space folder
git add .
git commit -m "Deploy variogramApp"
git pushStep 3 — Wait ~3 minutes for the build. Your app will be live at
https://YOUR_USERNAME-variogramapp.hf.space.
- Keep Number of sample locations at 100 or below for fast simulations on the hosted server
- The Monte Carlo envelope can take 1–2 minutes with 100 samples — warn students before they enable it, or reduce samples to 50 first
- Use Number of simulations > 1 with the animation slider to show students how the empirical variogram varies across realisations of the same process — this is one of the most effective teaching uses of the app
| Package | Role |
|---|---|
shiny |
Web application framework |
geoR |
Variogram computation and Gaussian random field simulation |
ggplot2 |
All plots |
dplyr |
Data manipulation |
If you use this app in teaching or research, please cite:
Johnson, O. (2021). variogramApp: An interactive Shiny application for exploring variograms and Gaussian random fields (v0.2.0). https://github.com/olatunjijohnson/variogramApp