Probabilistic Thinking - Mental Models Series -6
“If we do everything right, if we do it with absolute certainty, there’s still a 30 percent chance we’re going to get it wrong.” — Joe Biden, Former Vice President,US
Do you want to improve the accuracy of your thinking? Probabilistic thinking is for you.
Remember the classic question- " Are you with us /against us?". Most of you want to distance yourself from binary conclusions and tribes, individualize your opinion, and leave open the possibility that your sliding scale of probability can change with more information,correct? . Then Probabilistic thinking is for you.
Let us follow the following example to understand better -
Teacher : So let’s try an example. Suppose there’s a five percent chance per month your bike breaks down. In that case…
Student: Whoa. Hold on here. That’s not the chance my bike will break down.
Teacher: No? Well, what do you think the chance is?
Student: Who knows? It might happen, or it might not.
Julia: Right, but can you turn that into a number?
Student: No. I have no idea whether my bike will break down. I’d be making the number up.
Julia: Well, in a sense, yes. But you’d be communicating some information. A 1% chance your bike will break down is very different from a 99% chance.
Student: I don’t know the future. Why do you want to me to pretend I do?
The explanation that the teacher tried to give the student was that imperfect information still beats zero information. Even if the number “five percent” was made up (suppose that this is a new kind of bike being used in a new way that cannot be easily compared to longevity data for previous bikes) it encodes our knowledge that bike are unlikely to break in any given month. Even if we are wrong by a very large amount (let’s say we’re off by a factor of four and the real number is 20%), if the insight we encoded into the number is sane we’re still doing better than giving no information at all.
So,what is probabilistic thinking?
A willingness to always ask questions like
“What else might happen?”,
“What if we’re wrong?”,
“What could happen next?”,
and to look at the full range of situations that might come to pass — and at their costs and benefits — rather than to assume that things will go as planned or as the fashionable ideology or favorite administration model would have predicted.
Why is it so important that we learn to reason probabilistically and statistically?
There are two main reasons.
First, we obviously base our plans for and investments in the future around our predictions of what the future will be like. But the future cannot be known with absolute certainty, so we need to make rational decisions around a probable distribution of outcomes.
Thesecond, more fundamental reason for why we need to get better at probabilistic prediction is that offering and then testing predictions is the basis of scientific progress.
To succeed in life we need to predict the future, and in many ways we’re already good at it. For example, as you’re reading this, try to predict the word at the end of this sentence. Did you do it? Our basic intuition is often pretty good at seeing what’s going to happen, and you don’t need any math to use that. But science has shown that there are areas where our intuitions are flawed, and we can do much better by using statistics and other mental tools.
There are three important aspects of probability that we need to explain so you can integrate them into your thinking to get into the ballpark and improve your chances of catching the ball:
1. Bayesian thinking
First of all,We should also refrain from claiming to have absolute certainty when it comes prediction. Even the smallest amount of skepticism is necessary; it’s okay to say that something is incredibly, incredibly, probable — but not that it is 100% certain.
Bayes’s Rule is a theorem in probability theory that answers the question, "When you encounter new information, how much should it change your confidence in a belief?" It’s essentially about making decisions under uncertainty, and how we should update or revise our theories as new evidence emerges.
Imagine that one morning, during a rainy season, you’re wondering whether to take an umbrella with you before you leave your house. You look outside your window to see that the weather is currently sunny. So, your first thought is that rain is unlikely.
However, upon a second glance, you notice some scary-looking dark clouds on the horizon and you decide to take your umbrella after all.
You didn’t have to stop there, of course. You could improve your guess even more by checking the weather forecast on your favorite weather website. What’s important is that your decision is based on your estimate of the probability that it will rain. So, you used information about the current weather conditions (and possibly from other sources) to update your estimate of this probability.
Let’s continue with the weather example. You can ask the question: “What is the probability that it will rain, given that the weather is windy and there are dark clouds in the sky?” Here you aren’t simply interested in the general probability that it will rain. You want to know the probability of rain after taking into account a particular piece of new information (the current weather conditions). In probability theory, such probabilities are called conditional and the notation used for them is:
P(Event-1 | Event-2).
Conditional probabilities expresses the probability that Event-1 will occur when you assume (or know) that Event-2 has already occurred. With this notation, you can write “the probability that it will rain, given that the weather is currently windy and cloudy, is equal to 0.85″ as:
P("Rain" |"windy&Cloudy") = 0.85
In summary ,Bayes’ theorem is the excellent mathematical device you can use for updating probabilities in light of new knowledge. No other method is better at this job.
for more understanding , visit here https://www.probabilisticworld.com/what-is-bayes-theorem/
2. Fat-tailed curves
No one can explain better than Nassim Taleb when it comes to fat tails.
Let’s start with the notion of fat tails. A fat tail is a situation in which a small number of observations create the largest effect. When you have a lot of data, and the event is explained by the smallest number of observations. In finance, almost everything is fat tails. A small number of companies represent most of the sales; in pharmaceuticals, a small number of drugs represent almost all the sales. The law of large numbers: the outlier determines outcomes. In wealth, if you sample the top 1% of wealthy people you get half the wealth. In violence – a few conflicts (e.g. World Wars I and II) represent most of the deaths in combat: that is a super fat tail.- N Taleb
3. Asymmetries
Finally, you need to think about something we might call “meta probability” —the probability that your probability estimates themselves are any good.
Case 1.Pull a penny out of your pocket. If you flip it, what’s the probability it will come up heads? 0.5. Are you sure? Pretty darn sure.
Case 2 .What’s the probability that my local high school football team will win its next game? I haven’t a ghost of a clue. I don’t know anything even about school football, and certainly nothing about “my” team. In a match between two teams, I’d have to say the probability is 0.5.
Case 3 My wife asked me today: “Do you think Angpo will have corn floor?” Angpo is our local supermarket. “I don’t know,” I said. “I guess it’s about 50/50.” But unlike school football, I know something about supermarkets. A Fairprice supermarket is very likely to have dolmades; a 7-11 almost certainly won’t; Angpo is somewhere in between.
How can we model these three cases? One way is by assigning probabilities to each possible probability between 0 and 1. In the case of a coin flip, 0.5 is much more probable than any other probability. in the case of football team,I have no clue what the odds are. They might be anything between 0 to 1.In Angpo's case, I have some knowledge, and extremely high and extremely low probabilities seem unlikely.
Each of these curves averages to a probability of 0.5, but they express different degrees of confidence in that probability.
I hope you got the concept
Final word
Probabilistic thinking can only get you in the ballpark. It doesn’t guarantee 100% success. However ,w
e can act with a higher level of certainty in complex, unpredictable situations
Footnote -
What are Mental Models ?
“It’s your mind’s toolbox for making decisions. The more tools you have, the more equipped you are to make good decisions. “
A mental model is an explanation of how something works. It is a concept, framework, or worldview that you carry around in your mind to help you interpret the world and understand the relationship between things. Mental models are deeply held beliefs about how the world works.
For More , read https://jamesclear.com/feynman-mental-models
