to compute a fixed state path. The process is also called posterior decoding. The algorithm computes probability much more efficiently than the naive approach, which very quickly ends up in a combinatorial explosion. Together, they can provide the probability of a given emission/observation at each position in the sequence of observations. It is from this information that a version of the most likely state path is computed ("posterior decoding"). The algorithm can be applied wherever we can train a model as we receive data using Baum-Welch 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. 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. Variants of the algorithm Hybrid Forward Algorithm: A variant of the Forward Algorithm called Hybrid Forward Algorithm (HFA) can be used for the construction of radial basis function (RBF) neural networks with tunable nodes. The RBF neural network is constructed by the conventional subset selection algorithms. The network structure is determined by combining both the stepwise forward network configuration and the continuous RBF parameter optimization. It is used to efficiently and effectively produce a parsimonious RBF neural network that generalizes well. It is achieved through simultaneous network structure determination and parameter optimization on the continuous parameter space. HFA tackles the mixed integer hard problem using an integrated analytic framework, leading to improved network performance and reduced memory usage for the network construction. Forward Algorithm for Optimal Control