I have to do a project in which i have to analyze a data-set with a Bayesian approach,i have to decide which one now despite the course is started few months ago. I searched a lot of data-set on kaggle but i'm afraid to take something that cannot be analyzed in a Bayesian way. I found a big data-set on US election in 2012 and 2016, is this a good "setting" for a Bayesian analysis?
Yes, a dataset with polling data for an election could be a good candidate for an elementary Bayesian analysis project.
Based on past history and opinions about the current political climate, suppose a political consultant has the prior distribution $Beta(330, 270)$ for the probability $\theta$ that Candidate A will win in a certain congressional district (or state). This prior has $P(\theta > .52) \approx 0.93.$ In R statistical software:
1 - pbeta(.52, 330, 270) ## 0.9298421
Then polling early data can provide a binomial likelihood, and Bayes' Theorem can provide a posterior distribution, from which one can find $P(\theta > .52).$
If there is subsequent polling, then this posterior distribution can become the new prior to get an updated posterior, and so on.
Using beta prior distributions 'conjugate' with binomial likelihoods makes it easy to find beta posterior distributions.
Bayesian analysis is just a way of estimating parameters in a model of data, so any model with parameters can (in principle) be estimated using Bayesian methods.
A popular way to get a handle on the posterior distribution created by a Bayesian analysis is by using Markov chain Monte Carlo (MCMC). MCMC is computationally expensive and works best with small to moderate size data sets. MCMC is not great for "Big Data" (hundreds of thousands of points or more) unless you have Big Computing.
For an intro to Bayesian analysis, see this book chapter.