We finally got to the part of Bayesian Updating when both data and prior are continuous. It is, like always, not very different from Bayesian Updating with discrete data and priors except of that we use the PDFs and not the PMFs. Continuous Data, Continuous Prior When we use probability density functions we have to … Continue reading Bayesian Inference VII – Bayesian Updating Continuous Priors and Data

Tag: Bayesian

# Bayesian Inference VI – Beta Distribution

We’ve seen last time how Bayesian Updating with continuous priors works. As mentioned back then, it isn’t always easy to calculate the total probability of X (p(x)). Today I will introduce the Beta Distribution which makes these calculations easier. Beta Distribution The beta(a,b) distribution is a two parameter distribution on range [0,1] and is therefore … Continue reading Bayesian Inference VI – Beta Distribution

# Bayesian Inference V – Bayesian Updating Continuous Priors

We already know how to do Bayesian Updating with discrete priors. Today we will learn how to do Bayesian Updating with continuous priors. Continous Priors To do Bayesian Updating with continuous priors but with discrete data - we will look at the case that both is discrete next time - we just change sums to … Continue reading Bayesian Inference V – Bayesian Updating Continuous Priors

# Bayesian Inference IV – Odds

“The odds are good for my favourite team.”, might somebody say but what do they mean with odds? Odds We will talk today about odds. Not just because to understand the language of sports betters but also because they are quite important for Bayesian updating. Odds can reduce our calculations and therefore our computation if … Continue reading Bayesian Inference IV – Odds

# Bayesian Inference III – Probabilistic Predictions

We are sometimes more interested in the probability that an outcome occurs than in the probability of the hypotheses. We then talk about probabilistic predictions. Probabilistic Predictions Probabilistic predictions are when we talk about things like: “It will rain tomorrow with a probability of 60%, and not rain with a probability of 40%” We often use … Continue reading Bayesian Inference III – Probabilistic Predictions

# Experiment – Monty Hall Problem

After I'd covered the Monty Hall Problem in the last blog-post, I wrote an experiment in python, which shows that when the number of doors increases but the rules of the game stay the say, our probability of winning given that we switched converges to 1. The probability of winning given we stayed converges to … Continue reading Experiment – Monty Hall Problem

# Monty Hall Problem

The Monty Hall Problem is a great example to demonstrate Bayesian Updating with Discrete Priors. Monty Hall Problem The monty hall problem is based on a TV show in which one could either win a car or nothing. The participant was presented three doors. Behind one was a car, behind the others were goats. After … Continue reading Monty Hall Problem