A bit of housekeeping first. To keep track of my discussion of topics related to Bayesian Inference, I have created a blog category called "Bayesian Inference". You can click on the category link Bayesian Inference to see how my earlier blogs prepare the groundwork for my later blogs on Bayesian inference. If you are new to this topic, I recommend reading my oldest Bayesian inference blog first and then reading each one up to my most recent Bayesian inference blog. Later blogs build on earlier blogs.

To date I have focused on Bayesian Angel Investing and have offered up some ideas and code as to how Bayesian inference might be applied to angel investing. After introducing the idea of Bayesian Angel Investing I then offered a classification framework for Bayesian Angel Investing. This was followed by a blog on measuring classification accuracy. I then introduced some foundational concepts in Bayesian inference such as conditional probability, prior probability, Bayes Theorem, and the concept and calculation of likelihoods. My last blog discussed a Bayes Wizard application that computes conditional probabilities of startup success and failure according to Bayes Theorem. It was meant to tie some of these foundational concepts together into a simple and useful web application.

Bayes inference techniques are not limited to helping angel investors optimize their investment decision, they can also be used by entrepreneurs to optimize their startup decision making. For example, entrepreneurs must make decisions about how they should invest their startup capital in order to maximize their return on investment. Imagine that you are a new farmer and must make a decision about whether to invest in buying wheat seed for the upcoming growing season. To make an optimal decision here you might begin by estimating the joint probability of getting 28 cm or more of rain during the wheat growing season AND that your wheat yield will be 7800 kg/ha or more. You might estimate this value by tallying the number of instances of (rain >= 28 cm and wheat yield >= 7800 kg/ha) and dividing this by the total number of observations you have on rain amount and wheat yield. Lets assume the P(R>=28 cm & Y>=7800 kg/ha) = .18. From historical records you might also estimate that the probability of getting a rain amount >= 28 cm to be .21. Now using our definition of conditional probability P(H|E)=P(H&E)/P(E), we calculate P(Y>=7800 kg | R >= 28 cm) as follows:

P(Y>=7800 kg | R >= 28 cm) = P(R>=28 cm & Y>=7800 kg/ha) / P(R>=28cm) = .18/.21 = .86