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Bayesian hierarchical modeling

Bayesian hierarchical modelling is a statistical model written in multiple levels that estimates the parameters of the posterior distribution using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes’ theorem is used to integrate them with the observed data and account for all the uncertainty that is present. The result of this integration is the posterior distribution, also known as the updated probability estimate, as additional evidence on the prior distribution is acquired.

Forecasting Economic Aggregates Using Dynamic Component Grouping

Marcus P. A. Cobb Forecasting Economic Aggregates Using Dynamic Component Grouping

Abstract:

In terms of aggregate accuracy, whether it is worth the effort of modelling a disaggregate process, instead of forecasting the aggregate directly, depends on the properties of the data. Forecasting the aggregate directly and forecasting each of the components separately, however, are not the only options. This paper develops a framework to forecast an aggregate that dynamically chooses groupings of com- ponents based on the properties of the data to benefit from both the advantages of aggregation and disaggregation. With this objective in mind, the dimension of the problem is reduced by selecting a subset of possible groupings through the use of agglomerative hierarchical clustering. The definitive forecast is then produced based on this subset. The results from an empirical application using CPI data for France, Germany and the UK suggest that the grouping methods can improve both aggregate and disaggregate accuracy.

t-SNE

T-distributed Stochastic Neighbor Embedding (t-SNE) is a machine learning algorithm for visualization. It is a nonlinear dimensionality reduction technique well-suited for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions. Specifically, it models each high-dimensional object by a two- or three-dimensional point in such a way that similar objects are modeled by nearby points and dissimilar objects are modeled by distant points with high probability.

Neural Networks

‘Artificial’ neural network (ANN), is a computing system made up of a number of simple, highly interconnected processing elements, which process information by their dynamic state response to external inputs.

ANNs are processing devices (algorithms or actual hardware) that are loosely modeled after the neuronal structure of the mamalian cerebral cortex but on much smaller scales. A large ANN might have hundreds or thousands of processor units, whereas a mamalian brain has billions of neurons with a corresponding increase in magnitude of their overall interaction and emergent behavior. Although ANN researchers are generally not concerned with whether their networks accurately resemble biological systems, some have.

Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes’ theorem is used to update the probability for an hypothesis as more evidence or information becomes available. Bayesian updating is particularly important in the dynamic analysis of a sequence of data.

Many Bayesian methods required a lot of computation to complete, and most methods that were widely used during the century were based on the frequentist interpretation. However, with the advent of powerful computers and new algorithms like Markov chain Monte Carlo, Bayesian methods have seen increasing use within statistics coming into the 21st century.