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I have spent about more than a year in python, but I come from biology background. I should say I have got some understanding of for-loop and nested-for-loop to workout the solution to the problem I have had. But, I suppose that there are better and comprehensive way of solving problem. Below is the codeRead more

I am interested in finding the distribution “$ p^*$ ” closest to an empirical distribution $ \hat{p}$ where $ p^*$ is a mixture of first and zeroth order Markov models. That is, I want to find $ $ p^* = \arg\min_p \sum_{i,j} D\left(\,\hat{p}(j|i)\, \| \, p(j|i) \,\right) $ $ subject to the following constraints $Read more

i have proof question that i cant seem to understand why it is true, it goes like this: For a finite ergodic markov chain Xn with J states (1,2,..,J) and transition matrix P. show that if we find vector (X1,X2,..,XJ) such that SUM(Xi)=1 and XiPij=XjPji for every i,j then (X1,X2,..,XJ) is the stationary distribution. now,Read more

Assume sequence $ (X_1,X_2, X_3, \ldots)$ is Markov sequence of real random variables where $ X_i \in \mathcal{X}$ for some alphabet $ \mathcal{X}$ of finite size $ k$ . Define random variable $ Y_i = (X_{i-1},X_i)$ for $ i \geq 2$ . Is $ Y_2, Y_3, \ldots$ a Markov sequnece? In general, can we sayRead more

I already asked this question in StackExchange, but found little attention. So I’m just going to copy-paste my original question here. Let $ P$ be a stochastic matrix (of an irreducible Markov Chain) with stationary distribution $ \pi^T$ (i.e. $ \pi^T P = \pi^T$ ) and let further $ E$ be the matrix of allRead more