The Kaplan-Meier and closely related Lynden-Bell estimators are used to provide nonparametric estimation of the distribution of a left-truncated random variable. These estimators assume that the left-truncation variable is independent of the time-to-event. This paper proposes a semiparametric method for estimating the marginal distribution of the time-to-event that does not require independence...

In this paper, a one-sample point predictor of the random variable X is studied. X is the occurrence of an event in any successive visits $L_i$ and $R_i$ :i=1,2…,n (interval censoring). Our proposed method is based on finding the expected value of the conditional distribution of X given $L_i$ and $R_i$ (i=1,2…,n). To make the desired prediction, our approach is on the basis of approximating the...

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a ran...

A basic property of the entropy of a discrete random variable x is that: 0 ≤ H(x) ≤ log |X | In fact, the entropy is maximal for the discrete uniform distribution. That is, (∀x ∈ X ) p(x) = 1/|X |, in which case H(x) = log |X |. Definition 3.2 (Conditional entropy). The conditional entropy of y given x is defined as: H(y|x) = ∑ v∈X px(v)H(y|x = v) = − ∑ v∈X px(v) ∑ y∈Y py|x(y|v) log py|x(y|v) =...

We study the operator-valued free Fisher information of random matrices in an operator-valued noncommutative probability space. We obtain a formula for Φ M2(B) (A,A,M2(B), η), where A ∈ M2(B) is a 2 × 2 operator matrix on B, and η is linear operators on M2(B). Then we consider a special setting: A is an operator-valued semicircular matrix with conditional expectation covariance, and find that Φ...

We introduce Multi-Conditional Learning, a framework for optimizing graphical models based not on joint likelihood, or on conditional likelihood, but based on a product of several marginal conditional likelihoods each relying on common sets of parameters from an underlying joint model and predicting different subsets of variables conditioned on other subsets. When applied to undirected models w...

Let {Xi}i=1 be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable Sn,m to be the maximum number of 1s within any m consecutive trials in {Xi}i=1. The random variable Sn,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {Xi}i=1 consists of exchange...

This paper presents some refinements of a rare event simulation algorithm developped in [1] for estimating the probability of connection of two nodes s and t in an undirected graph G representing a communication network where nodes are perfect but links can fail. The method proposed in [1] makes use of disjoint paths (that is, with no common link) and samples a geometric variable representing t...