how to tell whether two different systems are the same how to compare noisy data sequences why is it necessary to measure the state of a discrete process what makes a data sequence unique can you measure a discrete state of a system why is a typical data sequence imperfect what's the difference between a proxy and an idealised sequence? why do we compare noisy data sequences what is the best way to measure the state of a markov chain how do we decompose the problem? how to find the likelihood of the same markov process how to compare two Markov processes to find their exact nature? what is the best way to find the exact state of a process? why is the data sequence a stationary sequence what is the best way to compare data sequences? why is the proxy process imperfect how to find the relationship between two discrete processes in the data? how to find the difference between a continuous markov procedure and a stationary process why is it necessary to compare two independent systems to establish a stationary time sequence? why is a discrete proxy sequence better than a complete proxy