Statistical learning--stochastic process

random process: My understanding is a collection of random variables. For example, X (t) =acos (wt+θ), T>=0,a,w is constant, and θ is a random variable that is evenly distributed on [0,2π]. For a fixed t,x (t) is a random variable, It is the function of theta. Since θ is a random variable, its function is also a random variable. For different t, such as T1,T2. X (T1), X (T2) is two different random variables. So you just need to understand the concept of random variables, the stochastic process is to introduce the concept of time on the basis of random variables, the stochastic process is just a series of random variables in time.

The airport includes two elements: location (site), phase space (phase spaces). When a value of a phase space is randomly assigned to each location in accordance with a distribution, the whole is called the airport. We might as well use farming to make an analogy. "Location" is like an acre of farmland; "Phase space" is like a variety of crops. We can plant different crops in different places, which is like giving each "location" of the airport a different value in the phase space. So, the tacky point is that the airport is where the crops are planted in which field.

Markov processes and Markov chains: on the timeline, from the previous state to the current state, the current state is only related to the previous finite state, the conversion process is called the Markov process, and these states constitute a sequence called Markov chain. If the current state is only related to a previous state, it is called a first-order Markov chain, and if it is N, it is called the N-order Markov chain.

The difference between Gaussian and Gaussian mixtures: The Gaussian process refers to the current state sequence of a high-dimensional Gaussian distribution, the addition of a new state sequence consisting of the next state is a Gaussian distribution, and the Gaussian mixture model is a sequence in which each element conforms to the Gaussian distribution.

Statistical learning--stochastic process