Other Probabilistic Methods
Probabilistic methods extend beyond basic models, offering sophisticated tools for uncertainty quantification across diverse applications. These approaches provide robust frameworks for reasoning under uncertainty, enabling more nuanced and reliable predictions in complex domains.
- Kalman Filters: Recursive estimators that optimally track dynamic systems in the presence of noise. They maintain a probability distribution over the system state and update it with each new measurement, making them essential for navigation systems, financial forecasting, and sensor fusion.
- Particle Filters: Non-parametric implementations of Bayes filters that approximate posterior distributions using random samples (particles). They excel at tracking non-linear, non-Gaussian systems where traditional methods fail, with applications in robotics, computer vision, and target tracking.
- Markov Chain Monte Carlo (MCMC): A family of algorithms that sample from probability distributions by constructing Markov chains with the desired distribution as equilibrium. MCMC methods like Metropolis-Hastings and Gibbs sampling tackle problems too complex for analytical solutions, revolutionizing fields from physics to genomics.