In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determi...

In this work we focus on a sentence retrieval task to present a comparison between Language Modeling based on a multi-variate Bernoulli distribution and Language Modeling based on the popular multinomial models. Nowadays, a view on text generation as a multiple Bernoulli process is not predominant in Language Modeling for Information Retrieval but we show how the characteristics of the task are...

there are miscellaneous quality characteristics in healthcare which are interested to be monitored. however, monitoring each characteristic needs a special statistical method. there are some characteristics with very small incidence rates that it’s usually considered not to be necessary to monitoring them, since their incidence rates are so small that p and np charts are not able to monitor the...

The mixture of Bernoulli distributions [6] is a technique that is frequently used for the modeling of binary random vectors. They differ from (restricted) Boltzmann Machines in that they do not model the marginal distribution over the binary data space X as a product of (conditional) Bernoulli distributions, but as a weighted sum of Bernoulli distributions. Despite the non-identifiability of th...

The cumulative sum (CUSUM) chart, well-known to be sensitive in detecting small and moderate parameter changes, is proposed here for monitoring a high yield process. The sensitivities of the CUSUM charts based on geometric, Bernoulli and binomial counts are compared. Based on the comparisons, recommendations for the selection of a chart are provided. Simple procedures are given for optimal desi...

Usually, in monitoring a proportion p < /em>, the binary observations are considered independent; however, in many real cases, there is a continuous stream of autocorrelated binary observations in which a two-state Markov chain model is applied with first-order dependence. On the other hand, the Bernoulli CUSUM control chart which is not robust to autocorrelation can be applied two-sided co...

Usually, in monitoring schemes the nominal value of the process parameter is assumed known. However, this assumption is violated owing to costly sampling and lack of data particularly in healthcare systems. On the other hand, applying a fixed control limit for the risk-adjusted Bernoulli chart causes to a variable in-control average run length performance for patient populations with dissimilar...

A commonly used paradigm in diverse application areas is to assume that an observed set of individual binary features is generated from a Bernoulli distribution with probabilities varying according to a Beta distribution. In this paper, we present our nonparametric variational inference algorithm for the Beta-Bernoulli observation model. Our primary focus is clustering discrete binary data usin...