## Expectation Maximization for MAP estimation “Expectation is the root of a heartache.” – William Shakespeare    Expectation–maximization (EM) is an iterative method that attempts to find the maximum likelihood estimator of a parameter θ of a parametric probability distribution. The algorithm computes maximum likelihood estimates of unknown parameters in probabilistic models involving latent variables. Therefore the EM algorithm is an iterative method that alternates between computing a conditional expectation and solving a maximization problem, hence its name.

## Introduction to Graph Models “Graphical models are a marriage between probability theory and graph theory.” – Michael Jordan, 1998. Probability is very important in modern pattern recognition problems. These problems could be assessed by formulating and  solving difficult probabilistic models, however, using a graphic representation of these probabilistic problems is often highly advantageous for the following reasons: 1) The visualisation of models makes the models themselves easier to understand and handle. They can also help us to distinguish new models or to point out similarities between already existing model structures, that we have not assumed.

## Forecasting recessions with economic indicators

Abstract This study compares three economic indicators often used in forecasting recessions: the Yield Spread, the Chicago Index and the Leading index. We find that the latter two predict recessions well one and two quarters ahead, but fail in forecasting recessions on a longer time period. On the contrary, the Yield Spread performs better when forecasting recessions four and six quarters ahead.