1 Sum of Bernoulli Distributions Here are some basic statistical concepts needed to perform statistical analysis on binary images. Given a sample space S, a random variable X is a rule that assigns a number to each element of S. X is a function that maps element s ∈ S to a real number, i.e. X : S → R. Bernoulli random variable X takes values only 0 or 1. The probability distribution P of a rand...

The Bernoulli spatial scan statistic is used to detect localised clusters in binary labelled point data, such as that used in spatial or spatio-temporal case/control studies. We test the inferential capability of a recently developed beta-Bernoulli spatial scan statistic, which adds a beta prior to the original statistic. This pilot study, which includes two test scenarios with 6,000 data sets ...

Recent approaches to text classification have used two different first-order probabilistic models for classification, both of which make the naive Bayes assumption. Some use a multi-variate Bernoulli model, that is, a Bayesian Network with no dependencies between words and binary word features (e.g. Larkey and Croft 1996; Koller and Sahami 1997). Others use a multinomial model, that is, a uni-g...

The average height of a digital me has been recently investigated in many papers [2]-[8]. In most works on binary digital tries, a Bernoulli model and independent keys are assumed. We relax these assumptions in that V-ary asymmetric tries. Bernoulli and Poisson models. and dependent keys are considered. We show that the average height of the trie is asymptotically equal to 2 19u n (for the Bern...

The beta-Bernoulli process provides a Bayesian nonparametric prior for models involving collections of binary-valued features. A draw from the beta process yields an infinite collection of probabilities in the unit interval, and a draw from the Bernoulli process turns these into binaryvalued features. Recent work has provided stick-breaking representations for the beta process analogous to the ...

Recent approaches to text classi cation have used two di erent rst order probabilistic models for classi ca tion both of which make the naive Bayes assumption Some use a multi variate Bernoulli model that is a Bayesian Network with no dependencies between words and binary word features e g Larkey and Croft Koller and Sahami Others use a multinomial model that is a uni gram language model with i...

Abstract In this paper, we have derived a set of sufficient conditions for reliable clustering of data produced by Bernoulli Mixture Models (BMM), when the number of clusters is unknown. A BMM refers to a random binary vector whose components are independent Bernoulli trials with clusterspecific frequencies. The problem of clustering BMM data arises in many real-world applications, most notably...

Consider a binary tree, to the vertices of which are assigned independent Bernoulli random variables with mean p ≤ 1/2. How many of these Bernoullis one must look at in order to find a path of length n from the root which maximizes, up to a factor of 1− , the sum of the Bernoullis along the path? In the case, p = 1/2 (the critical value for nontriviality), it is shown to take Θ( −1n) steps. In ...

The Bernoulli shift is a fundamental theoretic model of a sequence of independent and identically distributed(i.i.d.) binary random variables in probability theory, ergodic theory, information theory, and so on. We give a simple sufficient condition for a class of ergodic maps with some symmetric properties to produce a chaotic sequence of i.i.d. binary random variables. This condition is expre...

Here we discuss the “shifted” equivalence class of binary matrices first proposed by Ding et al. (2010). For a given N ×K binary matrix Z, the equivalence class for this binary matrix [Z] is obtained by shifting allzero columns to the right of the non-zero columns while maintaining the non-zero column orderings, see Figure 1. Placing independent Beta( α K , 1) priors on the Bernoulli entries of...