# Visualization of Deductive Reasoning for Joint Distribution Probability in Simple Topic Model

### Abstract

Bayesian inference is widely used in various application field such as data engineering. When we derive the posterior, we have to combine many theorems or rules such as the Bayes’ theorem. The derivation of the posterior expression is quite difficult, even if we use the probabilistic graphical model. So we propose a deductive reasoning based approach for that. The concrete deductive diagram for a simple topic model is presented in the paper. The deductive reasoning diagram

clarifies which theorems and how they are used in the deduction. In addition, the three conditional independence pattern rules which are used frequently in the posterior derivation are explained visually.

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