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# Interactive Bayesian Inference Explorer

An interactive Shiny web application for exploring fundamental concepts in Bayesian statistics. This app is designed to build intuition for how prior beliefs combine with observed data to form a posterior distribution.

I am developing this project as part of the 'Introduction to Bayesian Modelling' module for my MSc in Health Data Science. It serves as a practical portfolio piece to demonstrate my growing skills in R, Shiny, and applied Bayesian methods on my journey to becoming a health data scientist.


## 🎯 Features

This application allows you to interactively explore several common Bayesian models.

### Current Features

  * **Binomial Model (Discrete Prior):**
      * Interactively set the number of trials ($n$) and successes ($x$) from observed binomial data.
      * Define a **discrete prior distribution** by specifying possible values for the proportion ($\theta$) and their associated probabilities.
      * Instantly view the resulting Prior, Likelihood, and Posterior distributions in a clear table.
      * Visualize the prior and posterior distributions to see the "Bayesian update" in action, powered by the `TeachBayes` package.



  * **Binomial Model (Conjugate Prior):**

      * Implement the **Beta-Binomial** model.
      * Allow users to set prior beliefs using the Beta($\alpha$, $\beta$) distribution's parameters.
      * Visualize the continuous prior, likelihood, and posterior distributions on a single plot.
      (Left with point estimates and simulations)


  * **Poisson Model (Conjugate Prior):**


  * **Normal Model (Conjugate Priors):**


  * **MCMC Integration:**

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## 🛠️ Technical Stack

  * **Language:** R
  * **Framework:** [Shiny](https://shiny.posit.co/)
  * **Bayesian Core:** [TeachBayes](https://bayesball.github.io/TeachBayes/) (for discrete Bayesian tabulation and plotting functions)
  * **Plotting:** [ggplot2](https://ggplot2.tidyverse.org/) (via `TeachBayes`) & [plotly](https://plotly.com/r/)
  * **Data Manipulation:** [dplyr](https://dplyr.tidyverse.org/) (implied by `magrittr` pipe `%>%`)

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## 🧑‍💻 About Me

My name is Godwill Zulu, and I am a candidate for the MSc in Health Data Science with the University of Galway (Ireland). I'm passionate about leveraging statistical modeling and machine learning to derive actionable insights from complex health data. This project is one step in my journey to build a robust skill set for a career that bridges the gap between data science and healthcare.

Connect with me on [**LinkedIn**] ( https://linkedin.com/in/godwill-zulu/ )\!

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