Category: Bayesian Inference

Bayesian Inference VII – Bayesian Updating Continuous Priors and Data

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

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

Bayesian Inference II – Bayesian Updating Discrete Priors

We get closer and closer to the exciting, interesting parts of data science. Bayesian Inference or more precisely Bayesian updating is one part of that. It is used in some machine learning algorithms and allows us to update probabilities when we get new data. Bayesian Updating Discrete Priors We will today just look at discrete … Continue reading Bayesian Inference II – Bayesian Updating Discrete Priors

Bayesian Inference I – Maximum Likelihood Estimate

There are times when we don't know the values of parameters. The maximum likelihood estimate and following methods will enable us the estimate the values of parameters. Maximum Likelihood Estimate (MLE) What is the maximum likelihood estimate? The maximum likelihood estimate gives us the biggest probability for an experiment it tells us therefore for which … Continue reading Bayesian Inference I – Maximum Likelihood Estimate