Stochastic Processes

Assignments

• Stationary Stochastic Process
• LTI & Ergodicity
• Point Process & Gaussian Process
• Estimation Theory
• Markov Chain

Implementations of Stochastic Processes

Link to notebook

This notebook includes implementations to generate stochastic processes:

Example:

• A very pretty gaussian distribution:

• Gaussian process with RBF kernel:

• Brownian motion:

• Poisson process:

• Hawkes process:

Markov Chain

Part 1

Link to notebook

"Baum-Welch" algorithm is implemented to train a Hidden Markov Model parameters from sequences of observed data.

Part 2

Link to notebook

Hidden Markov Model parameters is trained using counting from sequence of observed data and states. "Viterbi" algorithm is implemented to find the most probable sequence of states from observations

Gibbs Sampling

Link to notebook

Implemented Gibbs sampling to denoise an image.

Example: