Markov Chain Monte Carlo (MCMC) is a mathematical method that draws samples randomly from a black box to approximate the probability distribution of attributes over a range of objects or future states. Or the reading level of children in a school system, where each reading level from 1 through 10 is a state. Instead of attempting to measure the probability of states such as heads or tails, we could try to estimate the distribution of land and water over an unknown earth, where land and water would be states.
Another word for outcomes is states, as in: what is the end state of the coin flip? There are just a few possible outcomes, and we assume H and T are equally likely. So let’s contruct a table that shows the outcomes of two coin tosses as measured by the number of H that result. Flipping it twice can result in either HH, TT, HT or TH. A coin toss has two possible outcomes, heads ( H) or tails ( T).
Distribution (or probability distribution) - You can think of a distribution as table that links outcomes with probabilities.Flipping a coin 100 times would be a sample of the population of all coin tosses and would allow us to reason inductively about all the coin flips we cannot see. So in the name of efficiency, we select subsets of the population and pretend they represent the whole. It’s physically impossible to collect, inefficient to compute, and politically unlikely to be allowed. For example, humans will never have a record of the outcome of all coin flips since the dawn of time. Populations are often too large for us to study them in toto, so we sample. coin flips, whose outcomes we want to predict. Population - The set of all things we want to know about e.g.We’re often stuck behind a veil of ignorance, unable to gauge reality around us with much precision. Also, reusing a small piece of one song in another song, which is not so different from the statistical practice, but is more likely to lead to lawsuits.) Sampling permits us to approximate data without exhaustively analyzing all of it, because some datasets are too large or complex to compute. Sample - A subset of data drawn from a larger population.Markov Chain Monte Carlo is a method to sample from a population with a complicated probability distribution. A Beginner's Guide to Markov Chain Monte Carlo, Machine Learning & Markov Blankets
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