Editing Forward algorithm (section)

==Applications==
The forward algorithm is mostly used in applications that need us to determine the probability of being in a specific state when we know about the sequence of observations. The algorithm can be applied wherever we can train a model as we receive data using Baum-Welch<ref>Zhang, Yanxue, Dongmei Zhao, and Jinxing Liu. "The Application of Baum-Welch Algorithm in Multistep Attack." ''The Scientific World Journal'' 2014.</ref> or any general EM algorithm. The Forward algorithm will then tell us about the probability of data with respect to what is expected from our model. One of the applications can be in the domain of Finance, where it can help decide on when to buy or sell tangible assets.
It can have applications in all fields where we apply Hidden Markov Models. The popular ones include Natural language processing domains like tagging part-of-speech and speech recognition.<ref name="speechRecognition"/> Recently it is also being used in the domain of Bioinformatics.
Forward algorithm can also be applied to perform Weather speculations. We can have a HMM describing the weather and its relation to the state of observations for few consecutive days (some examples could be dry, damp, soggy, sunny, cloudy, rainy etc.). We can consider calculating the probability of observing any sequence of observations recursively given the HMM. We can then calculate the probability of reaching an intermediate state as the sum of all possible paths to that state. Thus the partial probabilities for the final observation will hold the probability of reaching those states going through all possible paths.