The Price of Wisdom - 高山雪 Snow Hill

Continuing from the previous article < Subjective Probability Estimation >, a nother thing we should deal with caution is other peoples' subjective probability. Clarifying Expert's Estimation As mentioned, we should understand what people mean when they speak "chance" - a descriptive probability.  If an expert or a consultant says his estimation for a possibility of an event happening is "more likely", you have to be very cautious about this word, and should seek further clarification by what does he mean by that. Because you will never know if there is any difference between your understanding about "more likely" and his. If you don't clarify, you'll never know.   You can guide him through the following example conversation. You should start from the average and guide him through by questions: You: Would you say it is 50%? Expert: No, more than that. I said it is more likely. You: 70%? Expert: I would say it is a bit more than 70%. Y

機率分布大致有兩類：離散型 Discrete Distribution，和連續型 Continuous Distribution。離散型分布是指獨立離散的機率，而連續型分布是指機率是無縫緊連地出現。 例如： 離散型分布 ：P(10) = 0.16 連續型分布 ：P(10-20) = 30 離散型分布 ，包括：伯努利分布 Bernoulli Distribution、二項分布 Binomial Distribution、卜瓦松分布 Poisson Distribution。 我會在本篇文章簡述離散型的機率分布。

在不確定情況下，我們可以利用 Principle of Insufficient Reason  來先進行平均機率假設，即：把每個「假說 Hypothesis」 的 Prior Probability 假設為一樣的平均機率，再計算 Posterior Probability (事後機率分佈)。 如有 N 個假說 Hypothesis ，它們各自的 Prior Probability  便假定為 1/N 。 然後把新資訊納入計算，把第一次計算出來，每個 Hypothesis 的 Posterior Probability 變成下次更新的 Prior Probability，再計算每個 Hypothesis 的新的 Posterior Probability。如此類推，一直更新。這就是「 貝氏更新 (Bayesian Updating) 」。

In this article, we will continuously go through Mr K's decision making process in Example 4 in < Decision Tree > by examining his risk tolerance. Risk Tolerance Risk tolerance is the willingness of a person to take risk for better consequences. It means how the person weigh the downside of the consequences as compared to the upside, i.e. how significance of the downside of the consequences he would be impacted?  Most   risk averse people will weigh the downside (loss) heavier than the upside (gains), even the probability for both sides are equal.  Risk tolerance is a crucial factor to determine the diversification of an asset portfolio, which also is an attribute to tradeoff of risk/return. So, understanding the role of risk tolerance  is important not only for making daily decisions but also beneficial for making investment decisions.