Chapter 94: Statistics, Probability, Randomness, and Accidents

Source: https://www.facebook.com/100063294665283/posts/756957423090740/

[James’ Origin and Today] Chapter 94 - [Statistics, Probability, Randomness and Accident] (12/28/2023)

Understand logical "true" and "false" propositions and investment relationships.

Statistical methods:

Is a mathematical method and scientific field designed to collect, organize, analyze and interpret data. It involves collecting large amounts of data, collating and summarizing this data.

Purpose:

It provides objective and quantitative information through data analysis to help us better understand and explain phenomena and make reasonable decisions and inferences.

Result:

Narrative statistics are used to describe and summarize data, such as calculating means, variances, and percentages. Inferential statistics makes inferences and predictions by drawing conclusions from a sample, such as conducting hypothesis testing and establishing confidence intervals.

Statistics There are two possible outcomes:

1. After analyzing all the data that can be collected in the past, it is found that there is only one result - which is "true" (but it can be falsified in the future. Before it is falsified, we can only believe it to be true). For example: "All humans need oxygen." This is a "true" proposition, but it is possible that if new evidence is discovered, if a person can survive without oxygen, the previous proposition can be falsified.

The basic idea of the "presumption of innocence" is that a defendant is considered innocent in the eyes of the law until proven guilty. This means that the "inference of innocence" is "true." It is the prosecutor's responsibility to provide sufficient evidence to prove the defendant's guilt, rather than the defendant having to prove his or her innocence. You can't prove something that doesn't exist.

So why is there an inference of innocence? Because "not guilty" is a proposition. The prosecutor needs to falsify it and present evidence of guilt to prove guilt, which means proving that "not guilty" is false. If guilt is inferred, it is impossible to prove innocence. It is impossible to prove something that does not exist. No matter how much evidence you add to your innocence, you cannot prove your innocence.

Just like "swans are all white" in Europe a long time ago, this is a proposition. Unless you find a swan that is not white, you can prove that the proposition "swans are all white" is wrong and "false". , which means that true propositions can be falsified. But if no one in the world has ever seen a black swan and says "swans are not only white", then no matter how many white swans you find (because no one has seen a black swan at that time), you cannot prove that "swans are not only white" is "true". This is a false proposition. Therefore, before the discovery of black swans, "all swans are white" is a true proposition, and "swans are not only white" is a false proposition.

So in the stock market we say, "As long as you invest in the U.S. market index for more than 20 years, you will not suffer a loss." This is a true proposition because it can be falsified. This proposition is true until it is proven that there has been a loss by investing in the U.S. market index for more than 20 years. You can look for anyone who has suffered losses by investing in the U.S. market index for more than 20 years. This can be falsified, so "as long as you invest in the U.S. market index for more than 20 years, you will not suffer losses" is a true proposition, and it is "true" so far.

But if someone says, "In the past, but in the future, investing in the U.S. market index may not necessarily make money in 20 years," this is not a true proposition, because you cannot prove a non-existent proposition. Future false propositions are false propositions that cannot be falsified.

Therefore, in the process of mutual discussion, you must have logical thinking. If you do not have logical thinking, you will not be able to explain it clearly no matter how much you talk to him, because many people have no concept of logic and think that they cannot refute it during the discussion. They will mistakenly think that his proposition is true, but it is actually a false proposition. Therefore, during the discussion, you should pay great attention to whether what the other party says is a logical and true proposition. If he only uses false propositions to argue, you can only say that he does not understand logic, and just stay away from such people.

2. Statistically, there is not only one result "true". When there are many possibilities for something to happen, it is a probability distribution. That is, after analyzing all the data that can be collected in the past, if it is found that there are multiple possible distributions - that is a probability distribution.

Probability distribution: Every event that occurs has a probability of occurrence under a specific event.

Purpose, probability is the probability distribution of past occurrences, inferring the possible probability of long-term sampling in the future. The longer the time and the larger the number of samples, the closer it will be to the past statistical probability distribution.

So we say that if you invest in U.S. large-cap index funds for more than 25 years, your annualized return will be 7.94% - 17.24%. This is a probability distribution, that is, if you take any 25-year sample from the past statistics, your annualized return will be between 7.94% - 17.24%. This is the probability distribution of return. We use this statistical probability distribution as the basis for long-term investment.

However, many people only invest for three or five years and expect such a rate of return. If they do not want to suffer losses, they cannot truly realize the rate of return of the 25-year probability distribution. This is a mismatch in construction. If the investment is for five years, the probability distribution of the five-year statistics must be used as the expected value. The probability distribution of the five-year investment is

The probability distribution is between -5.58% and +28.76%. Therefore, if an investment loses money in five years, the expected value of the probability distribution in twenty or twenty-five years cannot be used.

Random: When the number of samples is insufficient (the time is short and the sampling is insufficient), it is a random event. The events and results that occur cannot be determined, and they occur randomly, and there is no predictability of the order of their occurrence. It does not necessarily mean that the one with a high probability will happen first, and it does not necessarily mean that the one with a high probability will always happen, nor does it necessarily happen within the expected range of the probability distribution (the probability distribution has a range and interval. If it is not within this range and interval (too few samples), the expected result cannot be obtained. The probability distribution derived from statistics is a range that has a test and a confidence interval). When sampling is insufficient, what has a high probability may not happen. The probability event with the smallest probability may occur for the first time, which is a random event that is not within the range of establishing a confidence interval. Random events cannot be predicted.

Accident: When a random event is definitely predicted and the event that occurs is beyond the certain prediction, it is called an accident. For example, if it is said that it will definitely rain tomorrow, but it does not rain, it is an accident. The short-term rise and fall of the stock market are random. If it is predicted that the stock market will definitely fall tomorrow, but the result is a rise, it will be an accident. If it is said that there is a 35% chance that it will rain tomorrow, then go back to the probability event above (it may happen, it may not happen. But it cannot be predicted with certainty).

Statistics is a historical trajectory obtained by analyzing all data over a long period of time in the past. The only result is a true proposition, otherwise it is a probability distribution.

Statistics are based on a longer history and more data in the past to obtain a more certain answer. For example, as long as you invest in American index funds, you will not suffer losses for 25 years. This is confirmed by data over the past 100 years. For example, in the United States, the price has increased by 27,000 times over the past two hundred years. This is a statistical result. (If we say this, the U.S. stock market index will rise more than 2,000 times in the next 100 years. This is also a true proposition based on statistical results and can be falsified in the next 100 years). A proposition based on statistical results can be proven (falsified) over time. Propositions based on statistical results are true until falsified!

Probability is the possibility of predicting the future based on what you know now, or what you think. For example, there is a 35% chance of rain tomorrow, which is a probability prediction! Probability is usually just the possibility of an event distribution, but it does not necessarily happen and can be falsified in a short time. But it is certain that the market will rise tomorrow, that the bird will fly up next, or that the bird will jump two steps forward (the bird's movements and the short-term rise and fall of the stock market are random and cannot be predicted), etc... are all overconfident guesses and cannot be accepted. Making certain predictions and placing bets based on the probability distribution results of statistical data is overconfidence. Just listen, don't believe it, let alone use your resources to make bets.

Probability is a mathematical concept used to describe the likelihood of an event occurring. It is a number between 0 and 1 that is used to indicate the likelihood of an event occurring (there is no guarantee of what will happen next time). And it is impossible to determine which specific result is, it is just a probability distribution after statistical analysis.

It should be noted that probability describes the possibility of a random event and does not guarantee that a specific event will definitely occur or not occur. Probability is simply used to evaluate the likelihood of an event occurring. And there's no way to determine which one the specific outcome will be.

Random means unpredictable results, that is, whether it will rain tomorrow is actually close to random. Although the weather forecast says there is a 70% (probability) that it will rain, it is actually not really sure whether it will rain. If it is predicted that it will rain 99% of the time but it does not rain or it will be sunny, then it is a fat-tail event (a random occurrence with low probability) that occurs unexpectedly.

In life, you should never make predictions about random events and get positive, and firmly believe in executing them. That is gambling, which will inevitably lead to disaster and should be avoided. Mark Twain’s famous saying: Man is tired not of what he knows nothing about, but of what he believes deeply).

Random refers to the fact that the outcome of an event or phenomenon cannot be accurately predicted (especially in conditions outside the statistical system. Usually, sampling must be large enough to approach the statistical probability distribution, otherwise it is just random, and predicting events will produce unexpected prediction errors). Randomness has the characteristics of uncertainty. In a random situation, every possible outcome has a chance to occur, and there is no way to determine which outcome it will be.

It should be noted that probability distributions are regular. But the process is an unpredictable and random phenomenon. A probability distribution is a deterministic outcome. Randomness is the uncertainty of outcome. Because randomness is the result of undersampling.

Randomness cannot determine how or when it will occur, and risk control cannot be done because it is impossible to predict what will happen and how it will happen. When you don’t know what will happen or when it will happen, it is impossible to avoid risks and it is impossible to control risks. If you can control risks by predicting random events, it may be overconfidence. When faced with random risks, the best thing to do is not to do it (don’t take chances with bad luck, don’t gamble. Stay away from bad luck, opportunities will come). If someone is pretty sure about how a random event is going to happen, it's usually human overconfidence. For example, the bird will jump down within five seconds, or the bird will jump three steps forward within one second! or I won't be struck by thunder today! Or the market will rise in the next hour, the next K-line will fall, it will rise tomorrow, and it will fall next month. Such statements are all overconfidence! Even if there is a probability distribution to rely on, there is no guarantee of accidents due to insufficient sampling, and we are afraid of accidents (fat tail events).

Just like there are a hundred balls in a bag, only one is a white ball, and the other 99 are red balls. If you pick any ball, the probability of getting a white ball is 1/100. But if you are sure that the ball you take out once must be a red ball! This is overconfidence. Just like speculators will say that it will definitely rise tomorrow! Or the stock will definitely fall! Wait.. That’s also overconfidence. Even if it is said that 70% of the market will rise tomorrow, it is random and cannot be trusted, let alone use your money to bet on random events. Accidents usually happen sooner than luck does.

Accidents occur when humans are overconfident and certain that random events will definitely happen. If the results are not as expected, it becomes an accident. In life, it’s not about focusing on good things happening, let alone saying “sure” to random events, but it’s about avoiding overconfident surprises and having good luck come to you.