First, classical learning algorithms, as PC or K2 are reviewed. The use of graphical probabilistic models in the field of education has been considered for this research. Negligible bias is involved using the estimated inclusion probabilities instead of the true ones, along with gains in efficiency relative to the use of familiar designs. In order to check the validity of this strategy, a simulation study was performed. As the number of simulated samples increases, the empirical HT estimator has the same performance of the HT estimator which would be obtained using the true inclusion probabilities. Accordingly, the inclusion probabilities may be estimated by simulation using an appropriate number of replications of the sampling scheme as suggested by Fattorini (2006, 2009). While the sampling scheme is easy to implement, the Horvitz-Thompson (HT) estimator is inapplicable even for moderate values of and, because the computation of inclusion probabilities involves enumerating all the possible samples and all the orderings in which the units enter the sample. Fattorini (2006) suggest modifying the simple random sampling without replacement in such a way that, at each drawing, the probabilities of selecting those units that are adjacent to the previously selected ones are reduced or increased according to a prefixed factor. Indeed, adjacent units are often more alike than units that are far apart, thus giving a poor contribution to the sample information. The purpose of this paper is to investigate the use of a complex spatial schemes proposed by Fattorini (2006) to account for the presence of spatial autocorrelation among the units. Usually, the scheme adopted to select units are familiar schemes such as stratified sampling or cluster sampling. Then, a sample of units is selected, aerial photos of the sampled units are provided and visually interpreted to determine the forest cover within. Forest cover is usually estimated at large scale by spatial sampling strategies, in which the study region is partitioned into polygons of equal size (e.g.
In this framework the monitoring of forest cover at large scale by statistically sound methodologies is a key pre-requisite. Pagliarella (2013) A post-Kyoto protocol, the Reduction of Emissions from Deforestation and forest Degradation (REDD) project was proposed and initiated in 2005. Finally, the results of the application of the model in two real data sets are shown.Īuthors: L.Fattorini, M.C. A simulation study is presented which includes a variety of scenarios in order to test the reliability of the proposed model. Model-fitting is performed using the expectation–maximization (EM) algorithm, and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. This is extended and establishes likelihood-based multivariate methods for a data matrix with ordinal data which applies fuzzy clustering via finite mixtures to the ordered stereotype model. Recently a group of likelihood-based finite mixture models for a data matrix with binary or count data, using basic Bernoulli or Poisson building blocks has been developed. a b s t r a c t Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. Reviews and compares the performance several model choice measures.Illustrates this new approach with two examples.Tests the reliability of this methodology through a simulation study.Establishes likelihood-based methods via finite mixtures with the stereotype model.New methodology for clustering rows and columns from a matrix of ordinal data.
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