**Bayesian analysis**

The statistics you took in college probably went something like this: You looked at some numerical data. You then calculated some statistics on the data, such as mean and standard deviation. From this you might have gone on to make forecasts of future data points.

Bayesian statistics work quite differently. You start by giving your best guess of data important to you. For example, you might make a forecast of the price of GLD (the gold exchange-traded fund) in two months at 170. (Incidentally, GLD is 165 as this article is being written.) How you come about the forecast isn’t important. It does not have to be mathematically derived. Instead, it simply can be your intuitive trading feel for the market.

Also, you do not just forecast a point. Instead, you allow for your uncertainty by forecasting a probability distribution. So, you might say that your expectation of the price of gold in two months would be distributed in a bell curve with a mean of 170 and a 50% probability of being between 163 and 177 (a standard deviation of about 10 points). Bayesians call this a “prior probability distribution” because it is made before any new market data are generated.

Now the second step. What if GLD goes down to 150 in the month? Would you still be willing to say that it is likely to go to 170 the month after? If you are a trader who listens to the market, you probably wouldn’t be as sure.

Bayesian analysis takes this into account by updating your prior distribution based on the likelihood of the new data point. In this case, because your old forecast pointed to a small likelihood of gold going down, your new forecast distribution of gold prices should be lower. This is called the “posterior distribution” by Bayesians because it is made after the arrival of new data.

“Shifting distributions” (below) shows the two distributions in the GLD example. Note that the middle of the range of the posterior is slightly lower than that of the prior, and that the probability of the upside has been reduced significantly.

Some traders have shied away from Bayesian techniques because of their complexity. If you want to delve further into this, and know college math, the Wikipedia article on “Bayesian Inference” is a good place to start. Otherwise, just keep reading; the spreadsheet will do the math for you.

One more thing: In actual trading, you may find that the simple practice of putting a prior distribution on paper will improve your results. By making your views explicit, you may find it easier to overcome some behavioral biases.