Visualizing Bayesian Updating

September 10, 2011
By

(This article was first published on bayesianbiologist » Rstats, and kindly contributed to R-bloggers)

One of the most straightforward examples of how we use Bayes to update our beliefs as we acquire more information can be seen with a simple Bernoulli process. That is, a process which has only two  possible outcomes.

Probably the most commonly thought of example is that of a coin toss. The outcome of tossing a coin can only be either heads, or tails (barring the case that the coin lands perfectly on edge), but there are many other real world examples of Bernoulli processes. In manufacturing, a widget may come off of the production line either working, or faulty.  We may wish to know the probability that a given widget will be faulty.  We can solve this using Bayesian updating.

I’ve put together this little piece of R code to help visualize how our beliefs about the probability of success (heads, functioning widget, etc) are updated as we observe more and more outcomes.


## Simulate Bayesian Binomial updating

sim_bayes<-function(p=0.5,N=10,y_lim=15)
{
  success<-0
  curve(dbeta(x,1,1),xlim=c(0,1),ylim=c(0,y_lim),xlab='p',ylab='Posterior Density',lty=2)
  legend('topright',legend=c('Prior','Updated Posteriors','Final Posterior'),lty=c(2,1,1),col=c('black','black','red'))
  for(i in 1:N)
  {
    if(runif(1,0,1)<=p)
        success<-success+1

    curve(dbeta(x,success+1,(i-success)+1),add=TRUE)
    print(paste(success,"successes and ",i-success," failures"))
  }
  curve(dbeta(x,success+1,(i-success)+1),add=TRUE,col='red',lwd=1.5)
}

sim_bayes(p=0.6,N=90)

The result is a plot of posterior (which become the new prior) distributions as we make more and more observations from a Bernoulli process.

With each new observation, the posterior distribution is updated according to Bayes rule. You can change p to see how belief changes for low, or high probability outcomes, and N for to see how belief about p asymptotes to the true value after many observations.

To leave a comment for the author, please follow the link and comment on their blog: bayesianbiologist » Rstats.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , , ,

Comments are closed.

Sponsors

Mango solutions



plotly webpage

dominolab webpage



Zero Inflated Models and Generalized Linear Mixed Models with R

Quantide: statistical consulting and training

datasociety

http://www.eoda.de





ODSC

ODSC

CRC R books series





Six Sigma Online Training









Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)