# Forecasting with the Baum-Welch Algorithm and Hidden Markov Models Leonard Baum and Lloyd Welch designed a probabilistic modelling algorithm to detect patterns in Hidden Markov Processes. They built upon the theory of probabilistic functions of a Markov Chain and the Expectation–Maximization (EM) Algorithm - an iterative method for finding maximum likelihood or maximum a-posteriori estimates of parameters in statistical models, where the model depends on
unobserved latent variables.

The Baum–Welch Algorithm initially proved to be a remarkable code-breaking and speech recognition tool but also has applications for business, finance, sciences and others. The algorithm finds unknown parameters of a Hidden Markov Model: the maximum likelihood estimate of the parameters of a Hidden Markov Model given a set of observed feature vectors.

Two step process:

1. computing a-posteriori probabilities for a given model; and
2. re-estimation of the model parameters.

A Markov process models a sequence of events that have no direct relationship. A Hidden Markov Model is a probabilistic model of the joint probability of a collection of random variables. Hidden Markov
Models provide a simple and eﬀective frame-work for modelling time-varying spectral vector sequences.

A Hidden Markov Process models a system that depends on an underlying Markov process with unknown parameters. This provides useful information about a random sequence of events.

The Baum–Welch Algorithm and and Hidden Markov Models are used successfully for financial trading systems, predicting market trends, workforce planning, fraud detection, supply chain optimization, forecasting supply and demand, financial time series prediction and anomaly detection in network traﬃc activity.

With enough data and compute power, the Baum–Welch Algorithm and Hidden Markov Models can provide probabilities about a process and predict future events.