We consider estimation of the regression function in a semiparametric logistic regression model using likelihood-ratio based inversion. The dichotomous response variable ∆ is influenced by a set of covariates that can be partitioned as (X,Z) where Z (real valued) is the covariate of primary interest and X (vector valued) denotes a set of control variables. For any fixed X, the conditional proba...

We define a new notion of conditional belief, which plays the same role for Dempster­ Shafer belief functions as conditional probability does for probability functions. Our definition is dif­ ferent from the standard definition given by Demp­ ster, and avoids many of the well-known problems of that definition. Just as the conditional prob­ ability Pr(·IB) is a probability function which is the ...

Probability enjoys a monadic structure (Lawvere 1962; Giry 1981; Ramsey and Pfeffer 2002). A monadic computation represents a probability distribution, and the unit operation return a creates the (Dirac) distribution “certainly a.” The bind operation combines a distribution of type M a and a function of type a -> M b; the function is a probability kernel (Pollard 2002), and it represents the co...

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­‐ additive has conditional probabilities that fail to be conglomerable i...

A fair die is about to be tossed. The probability that it lands with ‘5’ showing up is 1/6; this is an unconditional probability. But the probability that it lands with ‘5’ showing up, given that it lands with an odd number showing up, is 1/3; this is a conditional probability. In general, conditional probability is probability given some body of evidence or information, probability relativised...

A simple model of rational belief holds that: (i) an instantaneous snapshot of an ideally rational belief system corresponds to a probability distribution; and (ii) rational belief change occurs by Bayesian conditionalization. But a priori probability distributions of the Kolmogorov sort cannot distinguish between propositions that are simply true from propositions that are necessarily true. Fu...

Conventional multiclass conditional probability estimation methods, such as Fisher’s discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class pr...

Existence of capacity drop phenomenon, as the difference between pre-queue and queue discharge flow rates, has been one of the controversial concepts of traffic engineering. Several researches have focused on capacity drop existence and also its estimation issues. This paper aims to estimate capacity drop based not only on a comparison between breakdown and queue discharge flow rates, but also ...

We develop an analytical framework to derive the meta distribution and moments of the conditional success probability (CSP), which is defined as success probability for a given realization of the transmitters, in large-scale co-channel uplink and downlink non-orthogonal multiple access (NOMA) networks with one NOMA cluster per cell. The moments of CSP translate to various network performance me...