A Markov chain can be used to model a joint probability density of a sequence, $p_{R_1{R}_2...R_N}\left(x_1,x_2,..x_N\right),$ from neighbor pair probability data: $p_{R_n{R}_{n+1}}\left(x_n|x_{n+1}\right)n=1,2,...N-1,$ the ${R_n}^{\prime }s$ specifying the type of random variable, $x_n$. A Maximum Entropy Principle (MEP) is used to show that, with knowledge of only these neighbor pair probabilities, the Markov chain maximizes entropy. To introduce more information, it would be useful to consider triplet probabilities, but data limitations may preclude this approach. Instead, the joint probability density function is modeled with neighbor and next neighbor pair probabilities. Optimized triplet probabilities are obtained from these probabilities, again using a MEP method, and an augmented Markov chain is constructed from them. This joint probability density function is the MEP joint probability density function with known neighbor and next neighbor pair probabilities. Based on this information, we construct various length Markov and augmented Markov chains to produce diverging patterns of chain probabilities.

马尔可夫链可用于对序列的联合概率密度进行建模， $p_{{\mathrm{[R}}_{\mathrm{1个}}{\mathrm{[R}}_2。。。{\mathrm{[R}}_{ñ}}\left(X_{\mathrm{1个}}，X_2，。。X_{ñ}\right)，$ 来自邻居对概率数据： $p_{{\mathrm{[R}}_{ñ}{\mathrm{[R}}_{ñ+\mathrm{1个}}}\left(X_{ñ}|X_{ñ+\mathrm{1个}}\right)ñ=\mathrm{1个}，2，。。。ñ--\mathrm{1个}，$ 的 ${{\mathrm{[R}}_{ñ}}^{\prime }s$ 指定随机变量的类型， $X_{ñ}$。最大熵原理（MEP）用于表明，仅了解这些邻居对的概率，马尔可夫链即可使熵最大化。为了引入更多信息，考虑三重态概率将很有用，但是数据限制可能会阻止这种方法。相反，联合概率密度函数是用邻居和下一个邻居对概率建模的。再次使用MEP方法从这些概率中获得优化的三重态概率，并从它们中构造出增强的马尔可夫链。该联合概率密度函数是具有已知邻居对和下一邻居对概率的MEP联合概率密度函数。基于此信息，我们构建了各种长度的马尔可夫链和增强型马尔可夫链，以产生链概率的不同模式。