Interactive Elements

This element demonstrates how a flow field changes in the presence of an impermeable wall, an injection and extraction well, and variable regional flow.

This interactive element shows how a function can transform a random variable x associated with a pdf p(x) into another random variable y associated with a pushforward pdf p(y).

This sandbox illustrates several bivariate copulas (Gaussian, Clayton, Gumbel, Frank, and T), and shows how changing their parameters affects their shape.

A very simple element that illustrates the effect of different correlation values on a bivariate Gaussian distribution, or a cloud of scattered Gaussian samples.

Explore the relationship between a probability density function (pdf) and its corresponding cumulative density function (cdf).

A small element that illustrates the connection between entries of a transformation matrix and the corresponding linear transformation.

This small element shows how the posterior changes for a Gaussian system when the prior, observation error, and observation value change.

This toolbox demonstrates how the variable elimination ordering affects the sparsity of a triangular transport map. Try finding an order that reduces fill-in edges.

This simple GUI lets you create the HTML code for interactive student quizzes, then copies the code into your clipboard. 

Explore how we can approximate one probability distribution from another through importance sampling.

This element extends the importance sampling sandbox, illustrating how resampling can be used to generate samples from the targeted distribution.

This sandbox demonstrates the influence of forecast and observation errors on the state estimates for a satellite in orbit obtained through a Kalman filter.

Experiment with different assimilation frequencies, models, model errors, and observation errors. Observe how they affect filter performance.

Experiment with different models, ensemble sizes, assimilation frequencies, model errors, and observation errors. 

A sandbox to experiment with the Ensemble Rauch-Tung-Strievel Smoother, an extension of the EnKF.

Experiment with different models, ensemble sizes, assimilation frequencies, model errors, and observation errors. 

This element illustrates linear regression, and how it minimizes the residual errors while balancing positive and negative residual errors.

A small element that illustrates the connection between entries of a transformation matrix and the corresponding linear transformation.

This illustrates the influence of mean, standard deviations, and correlation on the covariance matrix and shape of a bivariate Gaussian distribution.

This page includes a brief, informal description of how a particle filter can be used to correct the predictions and even parameters of a flawed model. 

This element illustrates the effect of multinomial resampling and stochastic universal resampling, as well as rejuvenation.