Not all data you collect in market surveys will consist of exact numbers. Not every opinion will be final. People will have doubts, you have doubts, and there will be a lot of vague talk around you. You can interview different experts and get different opinions, and even worse, similar opinions with discrepancies in details. ‘Maybe yes, maybe no, maybe I don’t know, plus or minus, most likely’ … you’ll hear these kinds of answers all the time. As you talk to people to collect data for your new vision, you may end up lost in a mist of uncertainty. The good news is that uncertainty and probability go hand in hand. The theory of probability is a known thing you can use to blow away the smog and derive crisp answers to your questions.
Don’t fear probability. It’s cool. Most business people are sick of hearing the word ‘statistics’, and tend to shrink from bell curves and strange terms like ‘normal distribution’ (“Why call it ‘normal’?” they ask themselves). Surprisingly, the same business managers make serious faces when they hear talks about game theory and sports team management, probably because Hollywood produces movies like a ‘Beautiful Mind’ and ‘Moneyball’ to spread the word that statistics can do a lot for your business.
As before, I will not go into details, as this is not the purpose of this book. But I will give you an idea how to build cognitive maps and derive data in times of uncertainty. Causal loops in system dynamics need exact numbers, although you can build a hypothesis around the causal map structure and play what-if scenarios with it. For vague diagrams and uncertain data, you have to use Bayesian networks instead of causal loops. You may never build a Bayesian network by yourself but believe me, it’s worth learning a bit about the world of Bayesian inference. After all, this algorithm describes how our brain processes information.
We are all biased towards our personal preferences. And when we collect data, interview people, or read books, we usually have our own opinion about the situation and we change, or update that opinion as new data arrives. Amazingly, the process of updating our beliefs can be formalized using the Bayes rule and expressing it in terms of conditional probability: for any two events, A and B, p(B|A) = p(A|B) x p(B) / p(A), where p(A) is the probability of A, and p(A|B) is the probability of A, given that B has occurred. To make it simple, the Bayes rule can be described in one sentence: by updating our initial beliefs with objective new information, we get a new and improved belief. In the charming book ‘The Theory That Would Not Die’, McGrayne gives plenty of examples of the Bayes rule in action, from modern spam filters to breast-cancer studies.
In Bayesian networks, fragmented knowledge from subject-matter experts is linked using Bayes rule. The Bayesian network is a map with nodes and links; formally, the network is called a ‘directed acyclic graph’ in which nodes represent variables, while links, or edges, represent direct causal influences among these variables. Each variable has a set of possible values called its ‘state space’ that consists of mutually exclusive and exhaustive values of the variable. Examples of variable states can include ‘high’ and ‘low’, ‘yes’ and ‘no’, ‘good’ and ‘bad’, etc. The beauty is that the variable value can be distributed between states. For example, if, during an interview, the oil price analyst says ‘Well, if the oil prices are high, then particular customers will refuse to buy oil from this vendor’ then you can link the node ‘price of oil’ to ‘buy/not buy’ node and set probability values (such as, if price is $10 per barrel, then there is a 90% chance the customers will buy the oil from this vendor). Continuing the interview, you can build and populate the Bayesian network with conditional probability values. Eventually, the network will be able to extrapolate and give you answers for questions you didn’t ask the analyst or ones he didn’t know the answer to. With that, you create an expert system, almost an artificial intellect that can generate answers to your questions by extrapolating the knowledge gleaned from experts and historical data. This is not science fiction. Such systems are already used to diagnose patients. Once you record the knowledge of a doctor, through a series of interviews you can input disease symptoms. The expert system will diagnose the disease and recommend a treatment. It’s a helpful tool if you’re in the medical business – or any other business.
With a Bayesian network, you can answer questions that experts can’t. The algorithm extrapolates between the conditional probability values and can solve a problem, even if it is new to you. When the crisis is far away and you start collecting a substantial amount of data, you can use the data to train your network, much like the black boxes in predictive analytics. Actually, the Bayesian network is a part of the predictive analytics toolbox. The difference between this and other methods such as neural networks is that we can record and input expert knowledge into it – the prior knowledge on the subject, without solid historical data. This is the power of probability theory.
During the data elicitation process (the interviews), your respondents may use different numbers to answer the same question. You can use all this information without even bothering with causal maps, diagrams, and Bayes. A method named ‘Monte Carlo’ is a workhorse of analysis in Excel. For example, in your crisis, a flood destroyed your business, so you decide to start an oil and gas company. Increasing oil prices convinced you that this was the right choice of business. Now you’re working on a business plan, and you only have a vague idea of transportation costs. You watched a few TV shows where financial analyst mentioned different numbers for a similar environment, but you have to pick a number to place in the Excel table cell. Relax – just approximate the numbers using a distribution that fits the best, or the distribution you like the most (usually a normal distribution – the ‘bell curve’.) Excel can do that. Then pick a random number out of this distribution using Excel, repeat the sampling process over and over, and your spreadsheet will be populated with outcomes covering different scenarios.
Do not afraid of vague information. Use it. There is a whole suite of analytic tools and methods ready-made for it.