Search results for "Bayes' theorem"
showing 10 items of 43 documents
Efficient remote sensing image classification with Gaussian processes and Fourier features
2017
This paper presents an efficient methodology for approximating kernel functions in Gaussian process classification (GPC). Two models are introduced. We first include the standard random Fourier features (RFF) approximation into GPC, which largely improves the computational efficiency and permits large scale remote sensing data classification. In addition, we develop a novel approach which avoids randomly sampling a number of Fourier frequencies, and alternatively learns the optimal ones using a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery.
Empirical Bayes improves assessments of diversity and similarity when overdispersion prevails in taxonomic counts with no covariates
2019
Abstract The assessment of diversity and similarity is relevant in monitoring the status of ecosystems. The respective indicators are based on the taxonomic composition of biological communities of interest, currently estimated through the proportions computed from sampling multivariate counts. In this work we present a novel method to estimate the taxonomic composition able to work even with a single sample and no covariates, when data are affected by overdispersion. The presence of overdispersion in taxonomic counts may be the result of significant environmental factors which are often unobservable but influence communities. Following the empirical Bayes approach, we combine a Bayesian mo…
A Novel Border Identification Algorithm Based on an “Anti-Bayesian” Paradigm
2013
Published version of a chapter in the book: Computer Analysis of Images and Patterns. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-40261-6_23 Border Identification (BI) algorithms, a subset of Prototype Reduction Schemes (PRS) aim to reduce the number of training vectors so that the reduced set (the border set) contains only those patterns which lie near the border of the classes, and have sufficient information to perform a meaningful classification. However, one can see that the true border patterns (“near” border) are not able to perform the task independently as they are not able to always distinguish the testing samples. Thus, researchers have worked on thi…
Integration of animal health and public health surveillance sources to exhaustively inform the risk of zoonosis: An application to echinococcosis in …
2020
The analysis of zoonotic disease risk requires the consideration of both human and animal geo-referenced disease incidence data. Here we show an application of joint Bayesian analyses to the study of echinococcosis granulosus (EG) in the province of Rio Negro, Argentina. We focus on merging passive and active surveillance data sources of animal and human EG cases using joint Bayesian spatial and spatio-temporal models. While similar spatial clustering and temporal trending was apparent, there appears to be limited lagged dependence between animal and human outcomes. Beyond the data quality issues relating to missingness at different times, we were able to identify relations between dog and …
Bayesian Methodology in Statistics
2009
Bayesian methods provide a complete paradigm for statistical inference under uncertainty. These may be derived from an axiomatic system and provide a coherent methodology which makes it possible to incorporate relevant initial information, and which solves many of the difficulties that frequentist methods are known to face. If no prior information is to be assumed, the more frequent situation met in scientific reporting, a formal initial prior function, the reference prior, mathematically derived from the assumed model, is used; this leads to objective Bayesian methods, objective in the precise sense that their results, like frequentist results, only depend on the assumed model and the data…
A computer program suitable for analysis of choice of categories in biomedical data recognition problems.
1980
The optimum choice of categories in problems of medical data recognition is governed by the choice of categories, the selection of appropriate features, and by the choice of a loss function. Under these circumstances it is often difficult to find out the suitable classification scheme. The computer program described here serves for the design of the optimum recognition procedure. The Bayes rule is used as decision rule. A criterion for the comparison of different choice of categories is given. The program can be performed after estimation of the underlying prior probabilities and the conditional densities obtained from a training set, and before testing the decision rule with real data.
Monotonicity of Bayes estimators
2013
Let X = (X1; : : : ;Xn) be a sample from a distribution with density (x;θ), θ∈Θ⊂R. In this article the Bayesian estimation of the parameter is considered.We examine whether the Bayes estimators of are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.
Bayesian hypothesis testing: A reference approach
2002
Summary For any probability model M={p(x|θ, ω), θeΘ, ωeΩ} assumed to describe the probabilistic behaviour of data xeX, it is argued that testing whether or not the available data are compatible with the hypothesis H0={θ=θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a0), the simpler probability model (or null model) M0={p(x|θ0, ω), ωeΩ}, where the loss difference L(a0, θ, ω) –L(a0, θ, ω) is proportional to the amount of information δ(θ0, ω), which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 wh…
A Comparative Study to Analyze the Performance of Advanced Pattern Recognition Algorithms for Multi-Class Classification
2021
This study aims to implement the following four advanced pattern recognition algorithms, such as “optimal Bayesian classifier,” “anti-Bayesian classifier,” “decision trees (DTs),” and “dependence trees (DepTs)” on both artificial and real datasets for multi-class classification. Then, we calculated the performance of individual algorithms on both real and artificial data for comparison. In Sect. 1, a brief introduction is given about the study. In the second section, the different types of datasets used in this study are discussed. In the third section, we compared the classification accuracies of Bayesian and anti-Bayesian methods for both the artificial and real-life datasets. In the four…
Statistical classification and proportion estimation - an application to a macroinvertebrate image database
2010
We apply and compare a random Bayes forest classifier and three traditional classification methods to a dataset of complex benthic macroinvertebrate images of known taxonomical identity. Since in biomonitoring changes in benthic macroinvertebrate taxa proportions correspond to changes in water quality, their correct estimation is pivotal. As classification errors are passed on to the allocated proportions, we explore a correction method known as a confusion matrix correction. Classification methods were compared using the misclassification error and the χ2 distance measures of the true proportions to the allocated and to the corrected proportions. Using low misclassification error and small…