CONJUGATE PRIORS

This mathlet shows Bayesian updating with simulated data for two different likelihood functions (binomial and geometric) with a conjugate prior distribution (beta).

• The data distribution radio buttons allow the user to choose the probability distribution for the data, i.e. the likelihood function. With each likelihood function there are sliders that can be used to set its parameters.
• The top graphing window shows the probability mass function for the likelihood.
• The $$\boldsymbol{a}$$ and $$\boldsymbol{b}$$ sliders are used to set the parameters of the initial prior distribution $$Beta(a, b)$$ for the $$\theta$$ parameter of the likelihood function. Moving these sliders also resets the data and graphs (see reset button below).
• The $$\boldsymbol{X}$$ slider is used to simulate data. Every time the user clicks on a value the mathlet uses that as data from one trial and updates the prior to a posterior distribution for $$\theta$$. The new posterior is shown in blue below the $$X$$ slider and the previous posterior distribution becomes the new prior distribution.
• The bottom graphing window shows graphs of the sequence of posterior distributions. The current posterior is shown in light blue and the current prior is shown in green. Earlier posteriors/priors are shown in a darker blue.
• The reset button clears the bottom graph and sets the prior distribution to its initial state based on the values of the $$a$$ and $$b$$ sliders.
• The $$\boldsymbol{x}$$ and $$\boldsymbol{y}$$ readouts show the position of the mouse when it is in either graphing window.

© 2014 J. Shen, J. Orloff, J.-M Claus, J. Bloom, H.Miller