Bayesian Model Comparison Understanding Marginal Likelihoods and Bayes Factors

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Bayesian Model Comparison: Understanding Marginal Likelihoods and Bayes Factors • 💥💥 GET FULL SOURCE CODE AT THIS LINK 👇👇 • 👉 https://xbe.at/index.php?filename=Mar... • Bayesian model comparison is a statistical method used to determine which model out of multiple competing models best fits the data. In this explanation, we will focus on two common methods for model comparison: Marginal Likelihoods and Bayes Factors. • First, let’s discuss the concept of a marginal likelihood. The marginal likelihood, also known as the model evidence, is the likelihood of observing the data given a particular model. In other words, it’s the probability of generating the observed data if the model is true. The marginal likelihood allows us to compare models directly, even if they have different parameters. • Now, let’s introduce Bayes Factors. The Bayes factor is a measure of the strength of evidence for a hypothesis or a model. It compares the likelihood of the data under two different hypotheses or models and can be used to compute the Bayes factor for model comparison. Specifically, a Bayes factor less than 1 indicates that the alternative model is less likely given the data, while a Bayes factor greater than 1 suggests the alternative hypothesis or model is preferred. • To compare models using the Bayes factor, we calculate the ratio of the marginal likelihoods or posteriors of these models. A log-transformed Bayes factor gives us a convenient standardized measure that simplifies the comparison. • It's worth noting that computing marginal likelihoods can be computationally intensive, especially for complex models, and various approximate methods are frequently used. Some of these methods include Markov Chain Monte Carlo (MCMC) and Variational Inference. In practice, Bayes factors are often obtained using these methods due to their computational efficiency. • When it comes to model comparison, keep in mind that a larger Bayes factor indicates stronger evidence in favor of the model with the higher Bayes factor. Additionally, it’s important to remember that lower Bayes factors suggest that less evidence is available to distinguish between models. • If you want to learn more about Bayesian model comparison, you can further explore resources such as: • 1. Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B. (1996). Bayesian Data Analysis (second ed.). New York: Chapman Hall. • #STEM #Programming #Technology #Tutorial #bayesian #model #comparison #understanding #marginal #likelihoods #bayes #factors • Find this and all other slideshows for free on our website: • https://xbe.at/index.php?filename=Mar...

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