Interval Of Possible Values Research Articles

Nonparametric Maximum Likelihood Estimation from Samples with Irrelevant Data and Verification Bias

Suppose that some measurements come from a distribution F that is of interest and others come from another, irrelevant distribution G. Some measurements from F are verified and known to be from F. The other, unverified measurements may be from F or from G. Not all measurements from F are equally likely to be verified, and no measurement from G is ever verified. This model applies to measurements of low concentrations obtained using gas chromatography/mass spectroscopy, for example, as is shown in this article. How well a feature T(F) of F can be estimated when there are unverified data depends on what can be assumed about F, G, and the conditional probability v(x) of verifying a measurement of x from F. If F, G, and v are unrestricted, then more than one choice of (F, G, v) gives the same distribution p of the observable x, and thus T(F) cannot be uniquely estimated from data. But if the set of values of T(F) that correspond to a distribution p of x is small enough, then it is reasonable to try to estimate that set of T(F) from data. This article shows that the set of possible values of T(F) is a finite interval for some choices of T, such as the mean, and proposes estimators of the interval of possible values. An example using data from a Love Canal study shows that the partially identified set of T(F) can be sufficiently small for estimators of T(F) to be useful.

Interval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control

Usually, expert systems use numbers to describe the experts' degree of belief in their statements. In practice, however, it is difficult to assign an exact numerical value to the expert's degree of belief. At best, we can get an interval of possible values. This fact leads to the use of interval-valued degree of belief. When intervals are used to describe degrees of belief, then computations with intervals must be used to process them. In this paper, we describe applications of such interval computations to expert systems and to intelligent control.

INTERVAL METHODS IN KNOWLEDGE REPRESENTATION

In this issues, we continue to publish abstracts and reviews of recents papers on interval methods in knowledge representation. In knowledge representation, intervals are used for two main purposes: • to describe durations of events; and • to describe uncertainty of measurement results and expert estimates of different quantities; often, we do not know the exact value of a quantity, but we know its lower and upper bounds (e.g., we may not know the exact value of someone's weight, but we may know that this weight is in between 140 and 160 pounds). An important case of this uncertainty occurs in knowledge elicitation, when we ask experts to numerically estimate their degrees of belief in their own statements; in this case, it is often difficult for an expert to estimate this degree of belief precisely, but an expert can often provide us with an interval of possible values. The reviews are collected by Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA, email vladik@cs.utep.edu

Understanding evidential reasoning

We address recent criticisms of evidential reasoning, an approach to the analysis of imprecise and uncertain information that is based on the Dempster-Shafer calculus of evidence. We show that evidential reasoning can be interpreted in terms of classical probability theory and that the Dempster-Shafer calculus of evidence may be considered to be a form of generalized probabilistic reasoning based on the representation of probabilistic ignorance by intervals of possible values. In particular, we emphasize that it is not necessary to resort to nonprobabilistic or subjectivist explanations to justify the validity of the approach. We answer conceptual criticisms of evidential reasoning primarily on the basis of the criticism's confusion between the current state of development of the theory — mainly theoretical limitations in the treatment of conditional information — and its potential usefulness in treating a wide variety of uncertainty analysis problems. Similarly, we indicate that the supposed lack of decision-support schemes of generalized probability approaches is not a theoretical handicap but rather an indication of basic informational shortcomings that is a desirable asset of any formal approximate reasoning approach. We also point to potential shortcomings of the underlying representation scheme to treat probabilistic reasoning problems. We also consider methodological criticisms of the approach, focusing primarily on the alleged counterintuitive nature of Dempster's combination formula, showing that such results are the result of its misapplication. We also address issues of complexity and validity of scope of the calculus of evidence.

INGRID: A graph invariant manipulator

INGRID, a software system for assisting researchers and students of graph theory, is described. It is a partial commutative rule-based system using forward chaining, consists of approximately 1200 production rules, and is written in Berkeley Pascal on a VAX 11/780 under UNIX. INGRID has a data base of 36 graphical invariants and approximately 350 theorems symbolically relating these invariants. A set of one or more user-supplied restrictions upon the values of some invariants is propagated by INGRID, via the theorems, into intervals of possible values for other of the invariants. With the simple user interface provided by INGRID, even a graph theory novice can often discern properties of a graph that might normally require the capabilities of a well-informed expert.

Estimation of dosimetric parameters from inhaled activity distribution in human body.

A method is proposed to estimate parameters for dose calculation from inhaled activity distribution in the human body.Inhalation of 60Co aerosols is simulated by the metabolic model proposed in ICRP Publi-cation 30. The ranges of parameters for dose calculation are as follows : particle size 1 to 20 μm ; inhalation class Y; time after inhalation 1 to 90 d. The ratio of radionuclide retentions in the lower to upper bodies, divided by the diaphragm, is used as the index of activity distribution in the body. The results of computer simulations show that the retained activity ratio is valid to estimate intervals of possible values of particle size and time after inhalation.