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Posted on April 18, 2013 @ 10:15:00 AM by Paul Meagher
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
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This tells us that the probability of getting a good yield from our wheat is fairly high if we get 28 cm or more of rain during the wheat growing season. The probability of getting 28 cm of rain or more is, however, only .21 so we might want to examine other rainfall amounts and yield amounts to see if there is a good yield value for a more probable rain fall amount. This is how a startup farmer might go about making an optimal decision regarding whether to purchase wheat seed for the upcoming growing season. It might be noted that there is a very high correlation between rainfall amounts and wheat yield (correlation coefficient of .95) so of all the variables that a farmer might take into account in making a seed purchase decision, an investigation into rainfall amounts and wheat yields is a particularly important relationship to examine when projecting a probable return on investment. Don't waste your time calculating probabilities based upon factors that don't really matter that much.
There are two ways to make decisions - analytically or non-analytically. Making a decision analytically requires the quantification of the main elements in your decision problem so that you can compute answers. The main reason entrepreneurs might want to bother with analytic decision making is if they can make better decisions by adopting an analytical approach versus a non-analytical approach (perhaps "intuitive" would be a more favorable word to use). In some ways this dichotomy is false because most "analytic" decisions involve a combination of analytic and intuitive problem solving, however, it is worth emphasizing the distinction because the role of analysis in entrepreneurial decision making is not an aspect of entrepreneurship that is discussed much. It is worth examining whether Bayesian inference techniques might be useful for entrepreneurs to learn because they lead to more success. It is difficult to say whether this is true or not because the idea of Bayesian entrepreneurship has not been studied or promoted to date. Maybe this blog will help change this state of affairs by offering some instruction on how Bayesian inference techniques might be applied in entrepreneurial decision making.
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| Top ten wheat producers — 2011 (million metric ton) |
| People's Republic of China |
117 |
| India |
86 |
| Russia |
56 |
| United States |
54 |
| France |
38 |
| Canada |
25 |
| Pakistan |
25 |
| Australia |
24 |
| Germany |
22 |
| Kazakhstan |
22 |
| World total |
469 |
| Source: UN Food & Agriculture Organisation(FAO) |
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