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1994 Applied Stochastic Models and Data Analysis
Knowledge discovery aims at extracting new knowledge from potentially large databases; this may be in the form of interesting statements about the data. Two interrelated classes of problem arise that are treated here: to put the subjective notion of ‘interesting’ into concrete terms and to deal with large numbers of statements that are related to one another (one rendering the other redundant or at least less interesting). Four increasingly subjective facets of ‘interestingness’ are identified: the subject field under consideration, the conspicuousness of a finding, its novelty, and its deviation from prior knowledge. A procedure is proposed, and tried out on two quite different data sets, that allows for specifying interestingness by various means and that ranks the results in a way that takes interestingness (relevance, evidence) as well as mutual relatedness (similarity, affinity) into account—manifestations of the second and third facets of interestingness in the given data environment.
Jain, Dipak C.; Vilcassim, Naufel J.
1994 Applied Stochastic Models and Data Analysis
Understanding the purchase rates of households for frequently purchased packaged goods is an important element in developing effective marketing strategies. Previous researchers have attempted to estimate these rates by assuming that the time between purchases is a random variable that follows some common parametric probability distribution such as the exponential or Weibull distribution. Recent research has shown that for many frequently purchased packaged goods, the interpurchase times cannot be adequately described by these commonly used probability distributions. In this study we demonstrate how household purchase rates can be estimated in a robust manner using a generalized semiparametric approach that obviates the need for specifying a parametric form for the distribution of interpurchase times. The motivation being that often there is no theory of household purchase behaviour that specifies a priori the probability distribution underlying the interpurchase times. Our empirical results indicate that, for the data analysed, the household purchase rates exhibit a regular pattern that cannot be recovered by probability distributions often used in previous research. Further, marketing actions taken by sellers do indeed influence household purchase behaviour.
1994 Applied Stochastic Models and Data Analysis
Prediction of customer choice behaviour has been a big challenge for marketing researchers. They have adopted various models to represent customers purchase patterns. Some researchers considered simple zero–order models. Others proposed higher–order models to represent explicitly customers tendency to seek [variety] or [reinforcement] as they make repetitive choices. Nevertheless, the question [Which model has the highest probability of representing some future data?] still prevails. The objective of this paper is to address this question. We assess the predictive effectiveness of the well–known customer choice models. In particular, we compare the predictive ability of the [dynamic attribute satiation] (DAS) model due to McAlister (Journal of Consumer Research, 91, pp. 141–150, 1982) with that of the well–known stochastic variety seeking and reinforcement behaviour models. We found that the stochastic [beta binomial] model has the best predictive effectiveness on both simulated and real purchase data. Using simulations, we also assessed the effectiveness of the stochastic models in representing various complex choice processes generated by the DAS. The beta binomial model mimicked the DAS processes the best. In this research we also propose, for the first time, a stochastic choice rule for the DAS model.
Murthy, D. N. P.; Wilson, R. J.
1994 Applied Stochastic Models and Data Analysis
In multi–component systems, failure of a component often affects one or more of the remaining components of the system. This type of interaction between components is called ‘failure interaction’. In this paper we consider two failure interaction models and study the problem of estimating the parameters of these models.
Smith, Charles E.; Lánský, Petr
1994 Applied Stochastic Models and Data Analysis
A mixture of inverse Gaussian distributions (IGDs) is examined as a model for the lifetime of components. The components differ in one of three ways: in their initial quality, rate of wear, or variability of wear. These three cases are well represented by the parameters of the IGD model. The mechanistic interpretation of the IGD as the first passage time of Brownian motion with positive drift is adopted. The parameters considered are either dichotomous or continuous random variables. Parameter estimation is also examined for these two cases. The model seems to be most appropriate when the single IGD model fails due to heterogeneity of the initial component quality.
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