Bayesian Inference

Each project has a GitHub link provided along with a short desciprtion.

• Bayesian Neural Network Implementation
  • Implementation of Bayesian neural networks using TensorFlow-probability, modelling both epistemic and aleatoric uncertainties. Variational inference with Bayes by Backprop for training.
• Variational Auto-Encoder
  • Generation of new fashion MNIST Data using Variational Auto-Encoders, based on minimising the Kullback-Leibler (KL) diveregence.
• Approximate Integration
  • Integration using Monte-Carlo estimation, comparison with true values, and Gaussian Quadrature methods for calculating entropy of a probability distribution function.
• Bayesian Coin Tossing
  • Bayesian statistics model for a simple coin toss example with PyMC3, using No U-Turn Sampling (NUTS) for posterior approximation.
• Integration involving PDFs
  • Integration of the product of probability distribution functions using Gaussian Quadrature, recovering mean and variance.
• Parameter Estimation using MCMC
  • Parameter estimation for a single-degree-of-freedom structural dynamical system using Markov chain Monte Carlo (MCMC) and state-space modeling.
• Kalman Filter State Estimation
  • State estimation of a single-degree-of-freedom structural dynamical system using Kalman Filter and state-space formulation.
• Probabilistic Kalman Filter
  • Probabilistic form of Kalman Filter simplifying complex integrations for non-Gaussian assumptions.
• Kulback-Lieber Divergence for Approximating PDF
  • Approximation of a probability distribution function by minimizing the KL-divergence.