Probabilistic Thinking : Tackling Uncertainty

In today’s fast-paced and ever-changing world, uncertainty is an inevitable part of our lives. Whether we are making a decision about our career, investing in the stock market, or simply predicting the weather, we are constantly faced with the challenge of dealing with incomplete information and making decisions under uncertainty. This is where probabilistic thinking comes in – an effective tool for improving the accuracy of our decisions in a world where countless complex factors shape each moment. By assessing the probability of various outcomes, we can identify the most likely ones and make more precise and effective decisions based on that knowledge.

Probabilistic thinking is the ability to think in terms of probabilities and understand the inherent uncertainty of any given situation. Instead of looking for definite answers, probabilistic thinking acknowledges the presence of uncertainty and assigns probabilities to different outcomes. By doing so, we can make informed decisions that take into account the potential risks and rewards of different courses of action.

There are three underlying concepts we need to discuss about to understand probabilistic thinking in a better manner. They are :

1. Bayesian Thinking: The Power of Updating Your Beliefs

Bayesian thinking is a specific approach to probabilistic thinking that takes into account new information and updates your beliefs accordingly. Bayes’s Theorem explores how we can adjust probabilities when new data becomes available. But the essence of Bayesian thinking, or Bayesian updating, is that when we have limited but useful information about the world and are constantly encountering new information, we should take into account everything we already know as much as possible. This approach allows us to incorporate all relevant prior information into our decision-making process, including base rates or outside information about past situations similar to the one we are currently facing, as statisticians might put it.

For example, let’s say you are a doctor trying to diagnose a patient. You start with an initial diagnosis based on your prior knowledge and experience. As you gather more information, such as lab results and other diagnostic tests, you update your diagnosis based on the new information. By continually updating your diagnosis, you can arrive at a more accurate diagnosis and provide better treatment for your patient. At the same time, lets say you find out that the patient’s sugar levels have almost doubled since last year. This piece of news might sound alarming to the patient unless you also mention the base rate, which is the patient’s sugar levels last year. If the patient’s sugar levels were really healthy last year and after doubling this year, it’s still marginally above average for people who’re the same age as the patient’s, then its really not a critical position and easily handled by taking precautions. 

2. Fat-Tailed Curves: Understanding the Power of Rare Events

Fat-tailed curves are a statistical concept that describes the occurrence of rare events that have a significant impact on the outcome. These events are often overlooked in traditional probabilistic models, which assume a normal distribution of events. However, in many cases, rare events can have a much larger impact than expected, making them a crucial consideration when making decisions under uncertainty. Figuring out which events constitute a fat tailed curve is key. For example, heights of men or women will fall under a normal distribution with very rare exception of a very tall (ten times) or a really short fellow, however wealth contitutes a fat tailed curve. Its fairly common to run into people who are 10 times or 100 times wealthier than you. 

For example, consider the impact of a major weather event on an insurance company. Weather events constitutes a fat tailed curve. If the company only takes into account the normal distribution of weather patterns, it may underestimate the risk of a rare event like a hurricane or tornado. By understanding the power of fat-tailed curves and accounting for the potential impact of rare events, the insurance company can make better decisions about the risks it is willing to take on and the premiums it charges.

3. Asymmetries: Understanding the Power of Risk and Reward

Asymmetries are another important concept in probabilistic thinking, referring to the uneven distribution of risk and reward in different situations. A typical example of asymmetry pertains to people’s ability to predict the effect of traffic on travel time. How often do you depart at the scheduled time and arrive earlier than expected? Hardly ever, right? And how often do you depart on time and arrive later than planned? Most of the time, isn’t it? This shows that our estimation errors are often asymmetric, with a bias in a single direction. This is also true for probabilistic decision-making.

The majority of probability estimates tend to be overly optimistic, rather than under-optimistic. It’s rare to come across an investor who aimed for a 30% annual return rate and actually achieved a 40% return over an extended period of time. If you pick up the Wall Street Journal and randomly select names of investors who aim for 20% return rates with each investment, you’ll find that most of them end up with a return rate closer to 10%.

Conclusion