How to Live as Bayes' Formula? - Huxiu.com
How to Live as Bayes' Formula?#
This article introduces Bayes' formula and its application in the cognitive world, emphasizing the influence of old knowledge on new knowledge and the Bayesian school's attitude towards the uncertainty of truth. At the same time, the article also mentions the role of Bayes' formula in guiding behavior and the importance of prior probability in investment decision-making.
• Bayes' formula combines old knowledge with new knowledge to explain the origin and development of cognition.
• The Bayesian school emphasizes the uncertainty of truth and constantly seeks to approximate the truth.
• Prior probability plays an important guiding role in investment decision-making, determining the direction of individual investment.
A few days ago, I was a guest on the "Face-to-Face" podcast, trying to explain Bayes' formula with words. I tried a few times, but I felt the effect was mediocre, and in the end, I had to give up completely. After recording the show, I still couldn't let it go and pondered over it. This short article is a summary of my thoughts.
It seems that nowadays it's embarrassing to go out without mentioning "Bayes". Fortunately, I have been using Bayes' formula in my scientific research in recent years, so I haven't been left behind.
"Bayes' formula" was only made public after Bayes passed away.
Nowadays, our research and application of Bayesian thinking are all "fabricated" by later generations. Of course, you can also say it is "developed", just like the interpretation of Dream of the Red Chamber by experts in redology, who knows what Cao Xueqin was thinking.
So, let me talk about my understanding of Bayesian thinking, which is harmless.
Nowadays, what people refer to as Bayesian thinking, Bayesianism, and Bayesian philosophy are all the evolution of mathematical formulas to a higher level, especially in the methodology of cognitive world.
First of all, I summarize Bayes' formula in plain language as follows: Our latest knowledge comes from our past knowledge and the facts we have seen.
In mathematical language, it can be explained as: the posterior probability is proportional to the prior probability multiplied by the likelihood function, like this:
It's too abstract, let me explain: it means that no matter what new knowledge we learn, new phenomena we understand, or new conclusions we draw, these new knowledge not only depend on the new phenomena and new content we see, but also strongly rely on our previous knowledge of this matter.
As the popular book "Money Psychology" says, "What everyone has experienced will greatly influence their thoughts."
The power of old knowledge is great, so there are a thousand Hamlets.
In other words, everyone has their own opinions and perspectives.
Similarly, if your old knowledge is like an ideological imprint that cannot be shaken, no matter how many new facts you see, it will be useless. You will turn a blind eye, which is called stubbornness.
On the other hand, if we only see similar and repetitive new facts, trapped in an information cocoon, it is also difficult to come up with new knowledge.
Stubbornness + information cocoon, naturally makes you think you are the best.
If you have an open mindset and a multi-faceted understanding of "new facts", then you are definitely a master.
As for others' opinions, they may not be suitable for you. Even if you copy someone else's investment strategy, it may not work for you. According to the perspective of Bayes' formula, this is normal - everyone's situation is different, so their prior knowledge is different.
Moreover, Bayes' formula has also given rise to a school of statistics called the "Bayesian school".
Their basic idea is that the answer to a certain problem is not uniquely determined, but has an uncertain "probability distribution". The distribution of truth can be any shape, here are two examples:
In other words, the Bayesian school does not believe that they can grasp the truth, but they will continuously approach the truth through exploration.
Doesn't this align with our actual experience?
In reality, when we judge a problem, such as whether a company's future performance will be good or not, we can at most know what is more probable and what is less probable.
More probable means that if we continue to play this game, our chances of winning will be higher. But we cannot be sure which path is 100% successful and which plan is 100% failure.
Therefore, long-term holding does not guarantee success, and dollar-cost averaging does not guarantee making money.
Any knowledge can find positive examples and counterexamples, all with probabilities.
Pursuing a unique and definitive standard answer is futile.
Similarly, how to become a "smart aleck"?
It is to attack someone's deterministic viewpoint with a low probability event.
Once you understand this, it's not worth it to defend your own expression so desperately.
Just say, "Anything is possible, and no one knows for sure," and that's it!
Using Bayes' formula to explain and guide behavior is another shining aspect.
We have certain prior knowledge, then we discover a new "fact" and form new knowledge based on it. Then we encounter another new fact and update our knowledge again...
Constantly seeking, iterating, and developing.
Similarly, making bold assumptions, being cautious in verification, advancing step by step, and feeling the way forward, this is a typical Bayesian approach.
This tells us, first of all, we must take action!
What is most important when going out? Taking action is the most important!
Secondly, iteration is important.
Failure is not the mother of success, but summarizing is.
In the book "Interpreting Funds", I said, "In our investment, we need to prepare, shoot, aim again, prepare again, shoot again, aim again."
Take action first, then iterate.
I often see people saying, "I will invest when I have money." Actually, if you don't even know how to invest 1,000 yuan, you won't know what to do when you have 1 million.
In different situations, different strategies and different knowledge are reasonable.
Before 2015, I liked actively managed funds, but now I mainly invest in index funds - this is not contradictory, nor is it self-contradictory. I have iterated based on new circumstances.
What are the new circumstances?
Index funds in China are becoming more abundant, with lower fees. I am getting older, with a lower risk appetite, more capital, and less time and energy to spend on investment.
According to Bayes' formula, this change is normal.
Similarly, according to the formula: if you are really a novice with no prior knowledge, then the first investment lesson you encounter is extremely important - this is your prior probability, it determines which school you will most likely become a disciple of.
Think about it carefully, Bayes was originally a theologian who came up with a mathematical formula to verify whether God really exists. But it has evolved into so many applications.
It explains cognitive behavior well, can explain why experts become more and more skilled, can also explain why stubborn people cannot be persuaded, and can guide us on how to move forward. It has even become an important foundation for machine learning. No wonder it is so trendy now!
And so many unrelated things are connected in the end, it is indeed very interesting!