What is meant by Gibbs sampling?
Gibbs sampling is a Markov Chain Monte Carlo algorithm for generating samples from a joint probability distribution of multiple random variables. It is used to approximate complex distributions by sequentially drawing values for each variable based on the conditional distributions of the other variables.
Typical software functions in the area of "Gibbs Sampling":
- Initialization: Setting starting values for the variables to be sampled.
- Conditional Distribution Calculation: Computing the conditional probability distributions for each variable.
- Sequential Updating: Iteratively updating each variable based on the current values of the other variables.
- Convergence Check: Monitoring the convergence of the Markov chain to the target distribution.
- Visualization: Graphical representation of the sampled values and their distributions.
- Parameter Optimization: Adjusting sampling parameters to improve efficiency.
Examples of "Gibbs Sampling":
- Bayesian Inference: Estimating posterior distributions in complex statistical models.
- Image Reconstruction: Restoring images from noisy or incomplete data.
- Multivariate Distributions: Sampling from high-dimensional probability distributions.
- Missing Data: Imputation of missing values in datasets.
- Mixture Models: Estimating parameters in Gaussian Mixture Models.
- Time Series Analysis: Modeling and forecasting time series data with complex dependencies.