# Interactive Elements

I create interactive web elements to illustrate my research or support my teaching.

Here are a few examples.

### Analytic Element Model

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

### Change of Variables

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).

### Copula Sandbox

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

### Correlation

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

### Gaussian inference

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

### Gaussian parameters

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

### Graph Elimination

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.

### HTML Quiz Generator

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

### Kalman Filter

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

### Linear Transformation

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

### Particle Filter

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.