Let's break down [[Bayesian statistics]], and then explore its connection to [[Latent Dirichlet Allocation]] ([[LDA]]). **Bayesian Statistics: A Different Approach** - **Key Concept:** Bayesian statistics interprets probability as a degree of belief in an event, which gets updated as more evidence becomes available. This contrasts with traditional (frequentist) statistics, which views probability as the long-term frequency of an event occurring. - **The Bayes Theorem:** The foundation of Bayesian statistics is the Bayes Theorem, which provides a way to update our beliefs about a hypothesis based on new data. Here's the idea in a simplified form: Prior Probability * Likelihood / Evidence = Posterior Probability - **Prior Probability:** Our initial belief about a hypothesis. - **Likelihood:** How well the observed data fits the hypothesis. - **Evidence:** The data you observe. - **Posterior Probability:** Our revised belief about the hypothesis after considering the newly observed data. **Why Bayesian Statistics?** - **Prior Knowledge:** It allows us to incorporate prior knowledge or expert opinion into our analysis. - **Updating Beliefs:** It's a natural way to update our understanding of a problem as more information becomes available. - **Handling Uncertainty:** Bayesian approaches often provide a more intuitive way of representing uncertainty in our conclusions. **Bayesian Statistics and Latent Dirichlet Allocation (LDA)** Bayesian techniques form the backbone of how LDA functions. Here's how they relate: 1. **LDA's Goal:** LDA attempts to uncover the hidden topics within a collection of documents. 2. **Priors:** In LDA, we start with prior distributions over the topic distributions for each document and the word distributions for each topic. These priors represent our initial beliefs before seeing the actual words in the documents. 3. **Inference via Bayes Theorem:** LDA uses Bayesian inference techniques (often involving methods like Gibbs Sampling) to update these prior distributions based on the observed data (the collection of documents). This updating is the core of how LDA infers the latent topic structure. 4. **Posterior:** The outcome of LDA is a posterior distribution over the topic-document and word-topic assignments. This gives us the probability of each topic being in each document, and the probability of each word belonging to each topic. **Key Point:** Without the Bayesian framework, LDA would be extremely difficult to implement computationally. Bayesian inference provides a way to deal with the complex probability calculations and hidden variables involved in modeling topics in documents. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Bayesian Statistics") sort title, authors, modified, desc ```