This paper presents a comparison between the naive Bayesian classifier and a flexible Bayesian classifier (FLEXIBLE BAYES) in terms of their ability to estimate continuous probability distributions. The naive Bayesian classifier assumes that numeric attributes are generated by a single Gaussian distribution, while FLEXIBLE BAYES uses kernel density estimation to approximate more complex distributions. The paper evaluates both methods on a variety of natural and artificial domains, finding that FLEXIBLE BAYES often performs better, particularly in cases where the normality assumption does not hold. The paper also discusses the theoretical properties of FLEXIBLE BAYES, showing that it is strongly consistent in estimating probability densities. Experimental results show that FLEXIBLE BAYES outperforms the naive Bayesian classifier in several domains, although it may not always be superior. The paper also explores the implications of using kernel estimation in Bayesian classifiers and suggests that further research is needed to improve the performance of FLEXIBLE BAYES, particularly in setting the kernel width adaptively. The paper concludes that FLEXIBLE BAYES is a promising addition to the repertoire of probabilistic induction algorithms.This paper presents a comparison between the naive Bayesian classifier and a flexible Bayesian classifier (FLEXIBLE BAYES) in terms of their ability to estimate continuous probability distributions. The naive Bayesian classifier assumes that numeric attributes are generated by a single Gaussian distribution, while FLEXIBLE BAYES uses kernel density estimation to approximate more complex distributions. The paper evaluates both methods on a variety of natural and artificial domains, finding that FLEXIBLE BAYES often performs better, particularly in cases where the normality assumption does not hold. The paper also discusses the theoretical properties of FLEXIBLE BAYES, showing that it is strongly consistent in estimating probability densities. Experimental results show that FLEXIBLE BAYES outperforms the naive Bayesian classifier in several domains, although it may not always be superior. The paper also explores the implications of using kernel estimation in Bayesian classifiers and suggests that further research is needed to improve the performance of FLEXIBLE BAYES, particularly in setting the kernel width adaptively. The paper concludes that FLEXIBLE BAYES is a promising addition to the repertoire of probabilistic induction algorithms.