A Tutorial on Bayesian Nonparametric Models

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.Comment: 28 pages, 8 figure

Location Dependent Dirichlet Processes

Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the LDDP in the context of mixture modeling, and develop a mean field variational inference algorithm for this mixture model. The effectiveness of the proposed modeling framework is shown on an image segmentation task

Spatial Econometric Issues for Bio-Economic and Land-Use Modeling

We survey the literature on spatial bio-economic and land-use modelling and review thematic developments. Unobserved site-specific heterogeneity is common in almost all of the surveyed works. Heterogeneity appears also to be a significant catalyst engendering significant methodological innovation. To better equip prototypes to adequately incorporate heterogeneity, we consider a smorgasbord of extensions. We highlight some problems arising with their application; provide Bayesian solutions to some; and conjecture solutions for others.spatial econometrics, bio-economic and land-use modelling, Bayesian solution, Land Economics/Use,

Complexity in forecasting and predictive models

Te challenge of this special issue has been to know the state of the problem related to forecasting modeling and the creation of a model to forecast the future behavior that supports decision making by supporting real-world applications. Tis issue has been highlighted by the quality of its research work on the critical importance of advanced analytical methods, such as neural networks, sof computing, evolutionary algorithms, chaotic models, cellular automata, agent-based models, and fnite mixture minimum squares (FIMIX-PLS).info:eu-repo/semantics/publishedVersio

MDL Denoising Revisited

We refine and extend an earlier MDL denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative and non-informative wavelet coefficients, respectively. This suggests two refinements, adding a code-length for the model index, and extending the model in order to account for subband-dependent coefficient distributions. A third refinement is derivation of soft thresholding inspired by predictive universal coding with weighted mixtures. We propose a practical method incorporating all three refinements, which is shown to achieve good performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200