Probabilistic Measurement Model Research Articles

A Self-Calibrating Probabilistic Framework for 3D Environment Perception Using Monocular Vision.

Cameras are sensors that are available anywhere and to everyone, and can be placed easily inside vehicles. While stereovision setups of two or more synchronized cameras have the advantage of directly extracting 3D information, a single camera can be easily set up behind the windshield (like a dashcam), or above the dashboard, usually as an internal camera of a mobile phone placed there for navigation assistance. This paper presents a framework for extracting and tracking obstacle 3D data from the surrounding environment of a vehicle in traffic, using as a sensor a generic camera. The system combines the strength of Convolutional Neural Network (CNN)-based segmentation with a generic probabilistic model of the environment, the dynamic occupancy grid. The main contributions presented in this paper are the following: A method for generating the probabilistic measurement model from monocular images, based on CNN segmentation, which takes into account the particularities, uncertainties, and limitations of monocular vision; a method for automatic calibration of the extrinsic and intrinsic parameters of the camera, without the need of user assistance; the integration of automatic calibration and measurement model generation into a scene tracking system that is able to work with any camera to perceive the obstacles in real traffic. The presented system can be easily fitted to any vehicle, working standalone or together with other sensors, to enhance the environment perception capabilities and improve the traffic safety.

Exemplifying natural science measurement in the social sciences with Rasch measurement theory

This paper presents a social science example of measurement in which the integer count from a convenient origin is shown to be in equal units. This feature is identical to direct measurement in the natural sciences. The example rests on applying the probabilistic Rasch measurement model to two assessments of the same persons which (i) realises measurement as a real valued comparison between persons invariant with respect to instruments; (ii) characterises random variation of replicated measurements by the Gaussian distribution; (iii) shows that the variance of the replications is the inverse of the size of the unit.

Assessment of cognitive ability at conscription for the Danish army: Is a single total score sufficient?

Børge Priens Prøve (BPP) was developed for the Danish Army by psychologist Børge Prien in the 1950s, as a test of general cognitive ability for use at conscription for the Danish armed forces. The final BPP (1957) had four subtests; a Raven-like matrix subtest, and three subtests measuring verbal, numerical, and visuospatial ability. The BPP is a speeded test counting the number of correct responses within 45minutes. Thus, we consider the BPP as a measure of "cognitive efficiency" rather than a pure measure of cognitive ability. The BPP is still in use.Using techniques available in 1960, Rasch concluded that the matrices and numerical tests appeared to satisfy the requirements of the Rasch (Probabilistic models for some intelligence and attainment tests, Danish Institute for Educational Research, Copenhagen; 1960) model, while the verbal and visuospatial tests did not. Since then, there have been, to our knowledge, no published studies of the psychometric scaling properties of the BPP, partly because the practice of the Danish draft board has been to record only the total score. We examine these properties by analysis of data from two cohorts (n=9,491), using the Leunbach (A probabilistic measurement model for assessing whether two tests measure the same personal factor. The Danish Institute of Educational, Copenhagen, Denmark; 1976) model to assess whether the sum of the four subtests provides a statistically sufficient measure of a common latent trait. Since we found only weak evidence against fit to the Leunbach model, we claim that this warrants the use of a summarized total BPP score. We examined whether BPP subscales suffered from differential test functioning (DTF) relative to samples. Weak, and for practical purposes too weak, DTF was suggested for one subscale.

On a law of ordinal error

When no systematic factor disturbs replicated measurements of the same entity with the same instrument, the observed or inferred distribution is expected to satisfy the Gaussian law of measurement error. A characteristic of this distribution, which ensures it is unimodal with a smooth transition between adjacent probabilities, is that it is strictly log-concave. Many assessments in the social sciences begin by analogy to measurements in that an idealised linear continuum is partitioned by successive thresholds into contiguous, ordered categories. However, the distances between successive thresholds, generally finite, are not equal and assessments remain ordinal. The paper establishes that if the thresholds in the probabilistic Rasch measurement model used to transform ordinal assessments into measurements are in their natural order, then the distribution is also strictly log-concave. Therefore it is proposed that the Rasch model with ordered thresholds be referred to as the law of ordinal error. Accordingly, by analogy to the expectation that the distribution of replicated measurements satisfy the law of measurement error, it is proposed that the observed or inferred distribution of replicated ordinal assessments be expected to satisfy the proposed law of ordinal error.

A comparative analysis of reduction quality for probabilistic and possibilistic measurement models

In this article, several known and new methods of solving the measurement data interpretation problem for probabilistic and possibilistic measurement models are compared and the dependency of their quality on the completeness and accuracy of the measurement model is analyzed. It is shown that optimal use of a researcher’s prior information about the measurement model allows one to significantly increase the accuracy of the interpretation of measurements. In some cases the error of possibilistic interpretation was less than that of probabilistic one, even though possibilistic interpretation minimizes the necessity of the error, rather than the mean squared error. This is due to the fact that prior information may be sufficient to model the input signal using a fuzzy vector, but insufficient to model it using a random vector.

Real-Time Simultaneous Pose and Shape Estimation for Articulated Objects Using a Single Depth Camera.

In this paper we present a novel real-time algorithm for simultaneous pose and shape estimation for articulated objects, such as human beings and animals. The key of our pose estimation component is to embed the articulated deformation model with exponential-maps-based parametrization into a Gaussian Mixture Model. Benefiting from this probabilistic measurement model, our algorithm requires no explicit point correspondences as opposed to most existing methods. Consequently, our approach is less sensitive to local minimum and handles fast and complex motions well. Moreover, our novel shape adaptation algorithm based on the same probabilistic model automatically captures the shape of the subjects during the dynamic pose estimation process. The personalized shape model in turn improves the tracking accuracy. Furthermore, we propose novel approaches to use either a mesh model or a sphere-set model as the template for both pose and shape estimation under this unified framework. Extensive evaluations on publicly available data sets demonstrate that our method outperforms most state-of-the-art pose estimation algorithms with large margin, especially in the case of challenging motions. Furthermore, our shape estimation method achieves comparable accuracy with state of the arts, yet requires neither statistical shape model nor extra calibration procedure. Our algorithm is not only accurate but also fast, we have implemented the entire processing pipeline on GPU. It can achieve up to 60 frames per second on a middle-range graphics card.

Sonar Sensor Models and Their Application to Mobile Robot Localization

This paper presents a novel approach to mobile robot localization using sonar sensors. This approach is based on the use of particle filters. Each particle is augmented with local environment information which is updated during the mission execution. An experimental characterization of the sonar sensors used is provided in the paper. A probabilistic measurement model that takes into account the sonar uncertainties is defined according to the experimental characterization. The experimental results quantitatively evaluate the presented approach and provide a comparison with other localization strategies based on both the sonar and the laser. Some qualitative results are also provided for visual inspection.

Triadic judgment models and Weber's law

Let a, b, c, with a ⩾ b ⩾ c , be positive real numbers indicating the intensities of physical stimuli in a psychophysical experiment; let P abc be the probability that b is judged to be more similar to a (“closer to”) a than to c. This paper investigates the following representation and its subcases for triadic judgments P abc = F [ u ( a ) - u ( b ) , u ( b ) - u ( c ) ] , where u is a real-valued, strictly increasing, continuous function and F is continuous, strictly decreasing in the first variable, and strictly increasing in the second variable. In addition to elucidating the connections between the representation and models of discrimination and bisection paradigms, this paper examines the mathematical consequences of Weber's law on subcases of the representation, demonstrating that the resulting analytic forms of these triadic models are very limited. The results constitute partial solutions to questions raised in Falmagne [(1985). Elements of psychophysical theory. New York: Oxford University Press] concerning the impact of Weber's law on probabilistic measurement models for triadic judgments.

Note Technique: Invariance et Modèles de Mesure dans les Sciences Sociales, Introduction à l'œuvre de Georg Rasch

This technical note deals with a class of probabilistic measurement models identified by the Danish mathematician Georg Rasch (1901-80). Models of this class have been used to construct and test questionnaires in the various social sciences. This is a remarkable class of models because the defining conception of measurement is similar to that of the natural sciences. In particular, the criterion of invariance with respect to a frame of reference is central. These models are capable of advancing our conceptions of both the social sciences and the natural sciences.

Rehabits: A common language of functional assessment

Probabilistic measurement models offered by Rasch and others can be used to link different functional assessment instruments into a single measurement system. This study assessed 54 subjects (diagnoses: 8 brain injuries, 7 neuromuscular, 22 musculoskeletal, 7 spinal cord, 10 stroke) admitted to a free-standing rehabilitation hospital at admission and discharge using both the Functional Independence Measure (FIM) and the Patient Evaluation and Conference System (PECS). Thirteen FIM and 22 PECS motor skills items were scaled together into a 35-item instrument, providing scale values for all items in the same unit of measurement. Separate FIM and PECS measures produced for each subject correlate .94 and .91( p < .0001), respectively, with the cocalibration measures, and 0.91 ( p < .0001) with each other. Either instrument's ratings are easily and quickly converted into the other's using the common unit of measurement, the rehabit (rehabilitation measuring unit). This article argues that the stability of the PECS and FIM item difficulty estimates over thousands of subjects, dozens of hospitals, hundreds of raters, and years of assessment is convincing evidence in support of the widespread use of their cocalibrated, common scale values as a functionometric ruler.

Educational applications of probabilistic conjoint measurement models

This chapter is a survey of four different applications of probabilistic models to problems in educational measurement. The first, by Esdaille, is an analysis of the Bermuda Educational Assessment Programme's Primary 5 Mathematics Component. The second, by Shaw, presents a detailed comparison of two South African tests, one multiple choice and the other short response direct questions, and suggests that the medium correlation coefficient usually obtained in comparisons between scores obtained from multiple-choice items and direct questions can in part be attributed to design errors in some multiple choice items. The third study tests the assertions of some linguists and literary critics that it may not be possible to expect or derive normative understandings of irony. Smith's analysis of over 250 U.S. students' interpretations of ironic poetry shows otherwise. Finally, Valgeirsdóttir describes how a probabilistic model informed the iterative construction of a pencil and paper adaptive aptitude test in Iceland.

Psychiatric, business, and psychological applications of fundamental measurement models

This chapter is a collection of four studies applying probabilistic models to problems outside of education. Denmark's Allerup, Bech, and Loldrup present the calibration of the Visual Analogue Scale, used for measuring pain, and the use of this scale for measuring the reductions in pain brought about via the administration of three different treatments. Alvarez and Bañegil's study is a calibration of the criteria by which implementation of Just In Time and Total Quality Management techniques are recognized in Spain. Styles tests the assertion of sociologist O.D. Duncan that the reason for low correlations between measures of attitude and behaviour may be because these variables may not involve separate constructs but simply differing amounts of the same construct. Her conjoint measurement study of data from an Australian survey shows just how much harder it is to do than to say. Finally, from Israel, Tenenbaum presents the results of two studies involving the relationship of anxiety to performance among athletes, showing that commonly used instruments do not produce data of the consistency needed for fit to probabilistic conjoint measurement models in these applications.

Goodness of fit tests for probabilistic measurement models

General goodness of fit tests for probabilistic response models are developed. The tests are applicable in psychophysics, in the theory of choice behavior and in mathematical learning theories. The necessary and sufficient constraints that a measurement model puts on the response probabilities are used for testing this model. In addition, representation theorems for some models are proved and the goodness of fit to experimental data is considered.

The separation of individual- and system- influences on behavior in social contexts

Social behavior, i.e. interactive processes, commonly are said to depend on individual behavior traits and on interindividual relationship parameters simultaneously. By observational methods it is impossible to determine for a given social act to which amount it depends on properties of the individuals or relationships (group or social system) involved. A hierarchy of probabilistic measurement models is derived, which lead to measurements of individual traits which are independent from the social system in which the interaction takes place. Interindividual relationship intensities on the other hand likewise can be measured without being distorted by individual behavior traits. The measurement of an individual's social activity e.g. can be achieved in such a way that it does not depend on how socially attractive his companions are. At the same time this measurement does not depend on interindividual relationships either. Such measurements are called ‘samplefree’ or ‘specifically objective’ in the terminology of G. Rasch.