Probability: Signals or Subjective
Probability is a measure defined to add to a whole across all the event space. The basic premise of probability is that of the distribution. We see that certain variables have certain distributions be it Normal, Poisson, or Gamma. These distributions define a range of outcomes and the probabilities that each outcome would be reached. There may be a hazard rate which defines the possibility an event could happen as time goes forward. The higher the rate, the more likely an event would occur at all. Probability can be conditional: given something happens, we may expect something else to happen on a range of outcomes and probabilities, so given something happens, the probability distribution for something else may change.
At the heart of the notion of probability is actually fairness as probability derives from gambling games where the fair value to be paid for a game in the long run is the expectation value of the game. In the short run we can see all types of proportions arise from a bet, but in the long run, you will see a convergence to probability by the law of large numbers.
I talk relatively loosely about these terms because a lot of probability is intuition and not heavy calculation. Looking at the problem the right way easily gets us to the answer while crunching away is likely to result in a very non intuitive answer. This is because probability contrary to common sense is not a judgment. Making a lot of errors on a probability exam does not mean you have poor judgment. Probability is a perception. There are people who say you shouldn’t act on a perception. They are saying you shouldn’t act on a probability. Now is that reasonable? We can always objectify life and calculate probabilities of success for everything but in the end we are rewarded for the right answers and not for choosing the answers with highest probability. I think it is perfectly reasonable to act on a perception if this perception updated your prior beliefs on what subjectively was your choice. Especially because the alternative of acting like a more objective Frequentist rather than a subjective Bayesian statistician would also have you “act upon a perception,” you just would hold your prior beliefs and act upon the new information by itself. The difference between these two schools of thought is that the Bayesian if he hears a phone ringing upstairs will go downstairs to get his cellphone while the Frequentist will always go upstairs. The Frequentist does not keep a prior belief that his phone is really downstairs. In politics, we would say the Bayesian keeps his beliefs and is like an average voter while the Frequentist is reactive and we would call the Frequentist somewhat of a reactionary.
I think it is plainly obvious that the subjective Bayesian statistics school is closer to real human behavior and the reactive objective Frequentist school is inflexible and serves only to reward insight for not being an independent enough thinker to go downstairs for where you thought your phone was.
Objective views I thus argue lead to right wing politics eventually while subjective views can accommodate the left wing. To act upon a perception instead of the truth is to exercise your judgment in the space of probabilities while those who act only upon the truth are fundamentally reactive. Exercising your judgment necessarily involves your subjective beliefs.
Probability in other words is a way of viewing the world like literature. Is real life really that exciting without writers making up stories for us? Similarly we can ask would the stock market produce so much wealth without traders calculating odds for us in terms of valuing stocks? Just like the ultimate combination of judgment and perception would be a serious air, let’s call it Gravitas, an ultimate combination of judgment and probability would be objective and subjective, and we would probably call it rationality. At the end of the day, mankind is drawn to rationality more than it is drawn to religion, and that is because religion as I’ve said is happiness, but rationality is the beginning of love, as crazy love is not crazy, it was only the end of a past crazy relationship expressed in a new beginning. Generally when we do something we don’t need to ask ourselves what the probabilities are of various outcomes, but if we are asked about something unknown we should be wise to calculate probability and not bet on a sure thing as there are none. This is because when we do something it is reflective of our subjective beliefs so probabilities are already incorporated in the updating of our beliefs, but if we are asked about the unknown, we have to remain objective lest we begin to think we can bet a lot of money on sure things, or in other words, be someone we are not as just as we are not American because we’ve made up some traditions which exclude other Americans, we do not know sure things just because we seem to be able to predict them, as a sure thing is a statement about probability not about history or memory, and someone who has a track record of predicting the future nonetheless cannot claim he predicted sure things but only he predicted some things which had probable outcomes over a distribution.
That is the heart of probability: it challenges the hubris of man who would claim he has mastered nature because he has not even mastered his own; he cannot identify what is a sure thing or not, and never will be able to, because his luck lies in his ability to forecast and predict and not to explain cause and effect which would be necessary to demonstrate he has the ability to forecast probabilities of events before they happen and that he could truly identify sure things. Causality is not statistics however it is closer to history. But we don’t see historians making the most money on Wall Street and that is because a lot of the odds that are made are made by people good at forecasting the future but who may not be good at explaining anything. They are good signalers that’s all. Just like the best people in a dating scene are the ones who signal exactly what they are rapidly and how they can solve the problem for their desired mate. Now some people pride themselves on signaling themselves better than what the truly are or being better at reading signals. Both of those are less important as in the long run, you are what you produce and reading signals is a form of trade not a form of production in my view.
Reading signals is useful but in the long run, it is your own ability to signal which reaps rewards. As to what signaling is and how to get better at it, the first thing to do is to realize when you signal, you let other people give you signals that are easy to read and you can thus get a track record of reading the future. But woe be to your partners of signaling is you countersignal, for example, by appearing really poor when you really are not out of the game, as the people who were letting you predict the future would suddenly misread and miscalculate your signals, and you would disrupt the game entirely. But after a move like that you will be sure the future you read is the right future and not a parlay game set up on you by the men who rule the world. As I for example don’t really like being ruled, and can tell you all there is to trading is probability and if you get things more than fifty percent right you will have edge.
That edge is not analytical or informational it comes from the mistakes of other people like in chess or like in poker from their emotions. So look to games and games of chance for answers, and not to people skills which aren’t valued in trading because no one is smart enough to outsmart what a person is, which is a rational actor some of the time. As they say, French are nice to some of the people all of the time, British are nice to all of the people some of the time, Canadians are nice to all of the people all of the time. It is okay to be crazy to some of the people all of the time: I believe that is known as acting on probability and also known as acting on a perception because it changes our views on probability. Some people notice this and will say you are quantitative.
I agree but what is then qualitative? I believe qualitative is acting with a lot of information on hand, so a qualitative person dwells completely in the world of probability. A quantitative person dwells in probability and games of chance. Games of chance have little ambiguity. So at the end of the day, ambiguity is desirable if you wish to convert from quantitative to qualitative and that probably is what attracts quantitative people to the most unlikely mates. I am qualitative and I act crazy to some of the people all of the time because I act on perceptions because I think fortune favors the bold and I think if we don’t act on perceptions all we can act on is what other people convince us of, and that is usually their perceptions and my prejudices. The best plan is no plan, and you swim best when you aren’t so nervous. Act on perceptions and live on probabilities. Then when it’s all done, come home to start again.
I believe the American band Goo Goo Dolls wrote: “they painted all your secrets with the lies they told to you, and the least they ever gave you was the most you ever had. And you wonder where these dreams go when the world gets in your way, what’s the use in all this screaming, no one’s listening anyway.” You can’t tell if someone is lying. You can’t decide when you don’t have the chance to decide. But you can live in a world of probabilities rather than a world of perceptions and that is by acting reasonable to all of the people all of the time.
Because when we trust in reason we are trusting in the probabilities that define what is reasonable, and as such the best way to be reasonable is to recognize nothing is certain but odds can be placed on everything, only these odds are reflecting fairness and if you don’t value fairness, I suppose you can ignore probability altogether like a social construct. I know I for one value hope more than fairness. Hope requires a spring eternal, while fairness requires solvency. Yet the only way to be solvent is to have hope as after love it is hope that carries us forward which is as self evident as that probability is as much a social construct as race and money, there is no way we can persuade someone else that he shouldn’t act on low probability events, just like there is no way to erase the memory that motivates his behavior thereof. Now maybe with electric shock therapy and strong medication we can make him forget but that would only set him on a different course.
No, I think it is wise to regret nothing and to understand probability matters but you are not wrong probabilistically if you are right on the guess. I wouldn’t listen to odds makers and look for errors in their patterns to make money, which is the basis of statistical arbitrage, but would rather get to understand what stock is going to go up or down and make bets on whatever odds on those stocks. As such, I can bet my beliefs. Bayesian statistics is how children learn: they bet on themselves.