Member-only story

Tutorial Introduction to Bayesian Analysis: Unlocking the Power of Uncertainty

Duane Kelly

·16.2k Followers· Follow

Published in Bayes Rule With MatLab: A Tutorial Introduction To Bayesian Analysis

5 min read · 2 weeks before

20 View Claps

4 Respond

Save

Listen

Bayesian analysis is a powerful statistical framework that allows us to quantify and reason about uncertainty. It provides a principled way to combine prior knowledge and data to make inferences about the world. Bayesian methods are widely used in a variety of fields, including machine learning, data science, statistics, and engineering.

This tutorial will provide a gentle to Bayesian analysis. We will cover the basics of Bayesian probability theory, modeling, and inference. By the end of this tutorial, you will have a solid understanding of the key concepts of Bayesian analysis and be able to apply them to your own research and projects.

Bayes' Rule With MatLab: A Tutorial Introduction to Bayesian Analysis

by James V Stone

4.7 out of 5

Language	:	English
File size	:	9918 KB
Screen Reader	:	Supported
Print length	:	190 pages
Lending	:	Enabled

Bayesian Probability Theory

Bayesian probability theory is based on the idea that probability is a measure of our uncertainty about the world. We can express our uncertainty in terms of probability distributions. A probability distribution is a function that assigns probabilities to different possible outcomes of an event.

The most common probability distribution used in Bayesian analysis is the Gaussian distribution. The Gaussian distribution is a bell-shaped curve that describes the probability of observing a particular value of a random variable.

We can use probability distributions to represent our prior knowledge about the world. For example, we might have a prior belief that the mean of a certain distribution is 10. We can represent this prior belief using a Gaussian distribution with a mean of 10.

When we observe new data, we can update our prior belief using Bayes' theorem. Bayes' theorem is a mathematical formula that allows us to calculate the posterior probability distribution of a parameter given the observed data.

The posterior probability distribution is our updated belief about the parameter after taking into account the observed data. We can use the posterior probability distribution to make inferences about the world. For example, we can use the posterior probability distribution to calculate the expected value of a parameter or to determine the probability that a parameter takes on a particular value.

Bayesian Modeling

Bayesian modeling is the process of creating a statistical model that reflects our beliefs about the world. A Bayesian model consists of two parts: a prior distribution and a likelihood function.

The prior distribution represents our prior knowledge about the world. The likelihood function describes the probability of observing the data given the parameters of the model.

We can use Bayes' theorem to calculate the posterior probability distribution of the parameters of a Bayesian model. The posterior probability distribution is our updated belief about the parameters after taking into account the observed data.

We can use the posterior probability distribution to make inferences about the world. For example, we can use the posterior probability distribution to calculate the expected value of a parameter or to determine the probability that a parameter takes on a particular value.

Bayesian Inference

Bayesian inference is the process of drawing s about the world based on our posterior probability distribution. We can use Bayesian inference to make predictions, estimate parameters, and test hypotheses.

Prediction

We can use Bayesian inference to make predictions about future observations. For example, we can use the posterior probability distribution of the mean of a distribution to predict the mean of a future observation.

Parameter Estimation

We can use Bayesian inference to estimate the parameters of a statistical model. For example, we can use the posterior probability distribution of the mean of a distribution to estimate the mean of the distribution.

Hypothesis Testing

We can use Bayesian inference to test hypotheses about the world. For example, we can use the posterior probability distribution of a parameter to test the hypothesis that the parameter is equal to a particular value.

This tutorial has provided a gentle to Bayesian analysis. We have covered the basics of Bayesian probability theory, modeling, and inference. By the end of this tutorial, you should have a solid understanding of the key concepts of Bayesian analysis and be able to apply them to your own research and projects.