# Monte Carlo Method

I have been working lately with my son to get his Chevy Monte Carlo roadworthy and it reminded me of the Monte Carlo method. There are two reasons for this and neither of them is related to the name of the car. The first is the fact that this car has a seemingly random problem created by an electrical system malfunction. The second is the only way it seems possible to fix this issue is to repair random electrical systems. If you don’t know anything about Monte Carlo methods, then you are probably beginning to wonder what in the world I am thinking.

A Monte Carlo method is a class of computational algorithms that rely on random sampling to obtain the numerical result. Sometimes we know the final expected answer of the problem and are using the method to speed up the calculation, and other times there is a completely unknown outcome of the problem. For example, the Monte Carlo method can be used to calculate physical constants, like pi. We know the value of pi to an extremely precise value, but rapidly calculating the value in great precision can be extremely time consuming, so one way of doing this is to use random numbers to generate an estimate to the value of pi. The exact method is to randomly generate the coordinates of a point in an xy-plane within a range from -1 to 1 and count the number of points that land within a circle at the origin with a radius of one. As it turns out, the value of pi can be estimated very precisely with this method, given enough sample points.

The estimation of known physical constants is really just a good exercise to demonstrate the methods. The real usefulness of the Monte Carlo method comes from the ability to compute things that are unknown and overly complex. One of my favorites is in weather forecasting. There are too many variables involved in the forecasting of weather to compute an exact outcome in the time period required to make the forecast useful. It is possible to calculate weather models based on the historical weather events in great detail; when given enough random inputs the existing forecast models have been nearly 100 percent accurate, but in order to have enough random inputs requires more time to compute the model than we have. For example, if we use historic storms and the data from 10 days prior, we can compute the exact path of the storm in 15 days. In other words we can exactly model our weather, but get the results five days after the event. Monte Carlo methods allow us to estimate the weather much faster, but with less accuracy, allowing us to predict severe storms days before they occur; of course as we are all aware, many times the forecast is not accurate.

The same thing happens when utilizing Monte Carlo methods to estimate physical constants; every calculation results in a different result for the constant depending on the random distribution of inputs. In the estimation of pi example it is possible, though only about 33 percent likely, that every random point in the estimation lands within the circle, and we would get an answer that pi is equal to four, instead of 3.14. The same thing happens with weather models as the random sampling used to estimate the weather can give incorrect results.

In the repair of the Monte Carlo we have not had good results with attempting to repair the random electrical failures, as each repair seems to cause a new issue, and this is a common problem with Monte Carlo methods, they are not consistent at giving a correct result.

Until next week, stay safe and learn something new.

*Scott Hamilton is an Expert in Emerging Technologies at ATOS and can be reached with questions and comments via email to
sh*******@te**********.org
or through his website at https://www.techshepherd.org.*