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Naïve Bayes
This chapter introduces the Naïve Bayes algorithm, a predictive model based on Bayesian analysis. The chapter starts with a thought problem involving...
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Calibrated Bayes factors under flexible priors
This article develops and explores a robust Bayes factor derived from a calibration technique that makes it particularly compatible with elicited...
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Bayes factor for single-case ABAB design data
The ABAB design is frequently used among single-case experimental designs (SCED). Bayesian methods have recently received increasing attention for...
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Iterative threshold-based Naïve bayes classifier
The iterative Threshold-based Naïve Bayes (iTb-NB) classifier is introduced as a (simple) improved version of the previously introduced non-iterative...
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Postrior Distribution and Bayes’ Theorem
We prepare some important distributions that are necessary for deriving Bayes’ theorem.
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Threshold-based Naïve Bayes classifier
The Threshold-based Naïve Bayes (Tb-NB) classifier is introduced as a (simple) improved version of the original Naïve Bayes classifier. Tb-NB...
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The Naive Bayes Classifier
The Naive Bayes Classifier makes a so-called conditional independence assumption that is almost always wrong. This incorrect assumption earns the...
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Bayes factors for peri-null hypotheses
A perennial objection against Bayes factor point-null hypothesis tests is that the point-null hypothesis is known to be false from the outset. We...
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A Bivariate Teissier Distribution: Properties, Bayes Estimation and Application
This article presents a bivariate extension of the Teissier distribution, whose univariate marginal distributions belong to the exponentiated...
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On priors which give Bayes minimax estimators of Baranchik’s form
We study the construction of prior distributions which give Bayes minimax estimators of a normal mean vector. Particular attention is paid to priors...
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Generalized Bayes Minimax Estimators of the Variance of a Multivariate Normal Distribution
The problem of estimating the variance of a multivariate normal distribution is considered under quadratic loss. A large class of generalized Bayes...
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Alleviating conditional independence assumption of naive Bayes
In this paper, we consider the problem of how to alleviate the conditional independence assumption of naive Bayes. We try to find an equivalent set...
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The “neglecting the vectorization" error in Stan: erroneous coding practices for computing marginal likelihood and Bayes factors in models with vectorized truncated distributions
The methods for statistical analysis continue to advance; however, they remain susceptible to coding errors. This paper highlights the “neglecting...
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Analysis of estimating the Bayes rule for Gaussian mixture models with a specified missing-data mechanism
Semi-supervised learning approaches have been successfully applied in a wide range of engineering and scientific fields. This paper investigates the...
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Bivariate densities in Bayes spaces: orthogonal decomposition and spline representation
A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows representing a density into...
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A Variational Bayes Approach to Factor Analysis
Factor analysis models are useful dimensionality-reduction techniques for the covariance of observed data. A Bayesian approach to inference for these...
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Introduction to Bayes’ Theorem
This segment begins by deriving Bayes’ Theorem in the simplest scenario from the conditional probability formula we saw earlier in this series. We...
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The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem
Testing a precise hypothesis can lead to substantially different results in the frequentist and Bayesian approach, a situation which is highlighted...
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Bayes’ Theorem Example: False Positive
In this segment we explore the idea of false positives and use Bayes’ Theorem to estimate the probability someone has a disease given that they have...
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Bayes Factors for Forensic Decision Analyses with R
Bayes Factors for Forensic Decision Analyses with Rprovides a self-contained introduction to computational Bayesian statistics using R. With its...
