You might saw the awareness test in youtube. I like this video and honestly I didn't see the bear in the first time! Right now in my research I'm using MCMC (Markov chain Monte Carlo) method, which is a sampling method and is the family of random walk and the goal is to get the target distribution by sampling. The idea of this method is very simple and first developed by people in Sandia national laboratories.
You probably used monte carlo method for calculating the integral, now we are sampling the probability distribution (using monte carlo) based on constructing a Markov chain and in the Markov chain the current state is just dependent on previous state. Thats it! easy!
For sure there are many details included when you want to implement the algorithm but in this post I just would like to talk about the process of our mind which is very close to Monte Carlo method. The way we are seeing the world is base of how we are sampling our surroundings. Actually we are sampling our environment and because of different backgrounds and mind states, people can see different thing when you show them a certain picture! We see things which are more important for us and we fill the rest of the picture by our mind. This ability of our mind helps us to fill the gaps. This is happening in our dreams too when we are asleep, usually we see the story and when we are part of the dream, usually we don't see ourselves, for example you don't see your arms, you are just your eyes and you see the whole thing but not your body (this is true about me ans some of my friends which I had this discussion with them, so its not general!). I'm not sure how our brain works but I just know its completing the portion we don't pay attention. The other example could be this, imaging you are in a meeting with one of your colleagues, you are sitting around a table in a coffee place and waiting for him/her, he/she comes from the front door and he/she joins you and you start talking about his/her weekend, where his/her went, how was it, how much fun he/she had, does his/her want to try these new things this time and so on;
after the meeting if I ask you some questions you can answer them more correctly, for example: who was his/her weekend? Where did he/she go? or, what kind of coffee he/she had?
But if I ask you what was the color of his/her shoes, you probably cant answer this question, you saw him/her walking to your table and you definitely saw his/her shoes and you are sure he/she didnt come there with barefoot but this information is not important for your mind and when you are sampling the environment you are sampling thing which are more important and you mind fills the other portions, you may say, OK, so what we are seeing is illusion! I'm not sure about that but as far as I know, YES! But its very high quality illusion! ;)
But if I ask you what was the color of his/her shoes, you probably cant answer this question, you saw him/her walking to your table and you definitely saw his/her shoes and you are sure he/she didnt come there with barefoot but this information is not important for your mind and when you are sampling the environment you are sampling thing which are more important and you mind fills the other portions, you may say, OK, so what we are seeing is illusion! I'm not sure about that but as far as I know, YES! But its very high quality illusion! ;)
There is a term in psychology called Change Blindness. We don't pay attention to changes which are not important for us and fill the rest by our mind (some people learned to improve the data they are capturing in one shot, if you watch some action movies you see spies have this character). There is a good example video here for change blindness.
Ok, lets back to the MCMC, how does this things even related to MCMC? So far we know that we are sampling our environment and we are sampling thing which are more important for us, the MCMC method has the same spirit, we are trying to sample the probability distribution which are more important for us. We want to construct the target distribution with less number of samples and ignore the other part of the sample space. We would like to have the best desired distribution with the perfect number of samples and use that target distribution for further analyze. Sampling methods are very good when the decision space is very big and we are limited by some constraint to see the whole picture. Ill try to have another post about different types of sampling and also different types of MCMC.
Happy sampling! :)
Ok, lets back to the MCMC, how does this things even related to MCMC? So far we know that we are sampling our environment and we are sampling thing which are more important for us, the MCMC method has the same spirit, we are trying to sample the probability distribution which are more important for us. We want to construct the target distribution with less number of samples and ignore the other part of the sample space. We would like to have the best desired distribution with the perfect number of samples and use that target distribution for further analyze. Sampling methods are very good when the decision space is very big and we are limited by some constraint to see the whole picture. Ill try to have another post about different types of sampling and also different types of MCMC.
Happy sampling! :)
