Bayesian Regression Calculator

Bayesian Regression

Bayesian Regression applies Bayesian inference to linear regression, providing not just point estimates of parameters but full probability distributions. This approach quantifies uncertainty in the model parameters and predictions.

How It Works

Bayesian Regression works by:

1. Specifying prior distributions for model parameters (coefficients)
2. Updating these priors with observed data using Bayes' theorem
3. Obtaining posterior distributions that represent our updated beliefs about the parameters

The key components are:

• Prior Distribution: Initial belief about parameter values before seeing the data
• Likelihood Function: How likely the observed data is given the parameters
• Posterior Distribution: Updated belief about parameters after observing the data

Key hyperparameters include:

• Alpha: Precision of the prior distribution for coefficients
• Beta: Precision of the noise distribution

When to Use Bayesian Regression

Use Bayesian Regression when:

• You want to quantify uncertainty in your model parameters and predictions
• You have prior knowledge that you want to incorporate into the model
• You need to make decisions that account for uncertainty
• You have limited data but still want to make robust inferences
• You want to avoid overfitting through regularization

How to Use This Calculator

Enter your data below as comma-separated x,y pairs (one pair per line) or upload a CSV file. For multiple features, use format x1,x2,...,y with one data point per line. The calculator will perform Bayesian inference and provide posterior distributions for model parameters.