Objective Probability Research Articles

Classification Based on Invariants of the Data Matrix

The paper proposes a solution to the problem classification by calculating the sequence of matrices of feature indices that approximate invariants of the data matrix. Here the feature index is the index of interval for feature values, and the number of intervals is a parameter. Objects with the equal indices form granules, including information granules, which correspond to the objects of the training sample of a certain class. From the ratios of the information granules lengths, we obtain the frequency intervals of any feature that are the same for the appropriate objects of the control sample. Then, for an arbitrary object, we find object probability estimation in each class and then the class of object that corresponds to the maximum probability. For a sequence of the parameter values, we find a converging sequence of error rates. An additional effect is created by the parameters aimed at increasing the data variety and compressing rare data. The high accuracy and stability of the results obtained using this method have been confirmed for nine data set from the UCI repository. The proposed method has obvious advantages over existing ones due to the algorithm’s simplicity and universality, as well as the accuracy of the solutions.

CONCEPTUAL APPROACHES TO APPLICATION OF QUANTITATIVE AND QUALITATIVE METHODS OF ASSESSMENT OF ACCOUNTING AND AUDIT RISKS AMOUNT

Introduction. The auditor, when assessing and calculating the level of components of audit risk, often encounters the factors or events. The objective probability of occurrence of these factors or events can not be determined on the basis of statistical observations. Purpose. The article aims to consider the problem of audit risk determination, to indicate the main causes of its occurrence. It is necessary to emphasize the relationship of audit risk and risk to the accounting system and the problems of not only minimizing them, but also transferring users to this information. Quantitative and qualitative methods for determining and assessing audit risk should be analysed. Their advantages and disadvantages must be indicated. Results. For maximum objectivity, it has been proposed to combine quantitative methods for assessing audit risk with qualitative ones on the basis of subjective assessments. A conceptual model for its assessment has been developed in order to carry out the effective audit risk management. His model is based on an optimal combination of quantitative and qualitative methods for evaluating factors that may directly or indirectly influence the size of the audit risk.

Assessment of service quality for complex technical devices based on the Jaynes’ information principle

Arkadiy I. Maron - Associate Professor, Department of Business Analytics, National Research University Higher School of EconomicsAddress: 20, Myasnitskaya Street, Moscow, 101000, Russian FederationE-mail: amaron@hse.ru The Jaynes’ information principle (formalism) advanced for the solution of problems of statistical thermodynamics is applied to the solution of a task of assessing the fairness of a contractor who carries out restoration work on a technical system by the method of replacing elements. The task is the following. The customer possesses a fleet of similar technical devices (for example, cars) certain elements of which are subject to planned replacement. According to the contract, such replacements are carried out by a contractor. Spare elements of three types can be used: new original, new non-original and restored elements. The contract specifies what percentage of spare elements of each type may be used. It is difficult for the customer to check what type of element has been applied. However, for an element of each type it is possible to calculate the average time before the next replacement will be required. The actual average time between requirements for replacement is fixed by the customer. Based on these data and with the help of Jaynes’ information principle, it is possible to find the most objective probabilities of using elements of the various types. Having compared these probabilities with restrictions specified in the contract, the customer draws a conclusion about the fairness of the contractor and, if necessary, takes appropriate action. According to Jaynes’ principle, the most objective are probabilities for which entropy according to Shannon reaches a maximum under the set of restrictions. Respectively, the problem of finding their probabilities is simplified to a problem of finding the maximum nonlinear function under the set of restrictions. In this article, the task is formulated mathematically and solved for a case of three variables using the Lagrange method. Calculations for a real situation from the author’s practice are given.

Objective chance: not propensity, maybe determinism

One currently popular view about the nature of objective probabilities, or objective chances, is that they – or some of them, at least – are primitive features of the physical world, not reducible to anything else nor explicable in terms of frequencies, degrees of belief, or anything else. In this paper I explore the question of what the semantic content of primitive chance claims could be. Every attempt I look at to supply such content either comes up empty-handed, or begs important questions against the skeptic who doubts the meaningfulness of primitive chance claims. In the second half of the paper I show that, by contrast, there are clear, and clearly contentful, ways to understand objective chance claims if we ground them on deterministic physical underpinnings.

Pareto surface construction for multi-objective optimization under uncertainty

This paper presents a novel approach for multi-objective optimization under both aleatory and epistemic sources of uncertainty. Given paired samples of the inputs and outputs from the system analysis model, a Bayesian network (BN) is built to represent the joint probability distribution of the inputs and outputs. In each design iteration, the optimizer provides the values of the design variables to the BN, and copula-based sampling is used to rapidly generate samples of the output variables conditioned on the input values. Samples from the conditional distributions are used to evaluate the objectives and constraints, which are fed back to the optimizer for further iteration. The proposed approach is formulated in the context of reliability-based design optimization (RBDO). The joint probability of multiple objectives and constraints is included in the formulation. The Bayesian network along with conditional sampling is exploited to select training points that enable effective construction of the Pareto front. A vehicle side impact problem is employed to demonstrate the proposed methodology.

Analysis of the equipment operation system in terms of availability

Abstract In the article the process of operating a set of aircraft put into service at one time is examined. In order to maintain a balanced ratio ready to use and avoid the accumulation of hangar's maintenance, analysed transient process operation determining the probability of objects reside in different operating states. An interesting issue is change of a readiness as dependence of the model of adopted qualification. The main result of this article is the value of the probability of being ready to use. The probability of reaching the limit value is assuming different depends on initial conditions and different models of the probability density distributions. The results indicate the need for further testing of models of probability distributions to determine the optimal method qualifications or technical object is in standby mode or not.

Essays on Risk and Uncertainty: Comparing J. M. Keynes and the Von Mises Brothers, Richard and Ludwig, on Probability and Decision Theory

Richard von Mises set forth a Limiting Frequency approach to probability for use primarily in physics and some areas of biology, chemistry and engineering. Emphasis was placed on the existence of series or sequences of events that resulted from a known generating mechanism. The series consisted of repeated, homogeneous events that were identical to each other, except for their particular place selection in an infinite series. This conception of probability is extremely limited and can play only a very limited role in liberal arts, social science, behavioral science, and especially in economics, business, and finance.Ludwig von Mises conception was that there were two different concepts of probability. First, there was a class concept of probability that was basically a version of a limiting frequency interpretation of probability. He had a second conception that he called case probability. Case probability was supposed to deal with unique events. It essentially is a subjective degree of belief approach that allows one to calculate no more than an ordinal relationship. Ludwig Von Mises is thus not a Bayesian Subjectivist. His dual approach to probability is reminiscent of Rudolf Carnap, although it is greatly underdeveloped technically when compared to Carnap.J. M. Keynes’s conception of probability is a logical theory of probability built on G. Boole’s earlier logical theory of probability. Keynes’s theory deals with the degree of rational belief one should believe and act on. It is not “a” or “the” degree of belief used by Subjectivists. It was a relative concept, which means that all probabilities are conditional probabilities. There is an objective probability relation that holds between a given body of evidence, the premises, E, and a conclusion or hypothesis, H. Thus, P (H/E) =α. The objective probability relation measures the degree of similarity (dissimilarity) that exists between the evidence, E (premises), and the conclusion or Hypothesis, H.There are many severe and numerous errors in Richard Von Mises book, Probability, Statistics and Truth, regarding Keynes’s logical theory of probability that will be identified and corrected in this paper. Neither of the Von Mises brothers understood Keynes’s interval valued approach to probability or had any clear cut understanding of the concept of weight or decision weights like Keynes’s conventional coefficient in chapter 26 of the A Treatise on Probability, although such an approach appears out of nowhere in Probability, Statistics and Truth in Lecture 4.Ludwig von Mises’s conception of case probability has no developed concept of the weight of the evidence underlying it. Its identification of probability as being ordinal probability would be too weak from Keynes’s point of view to help an entrepreneur in making decisions related to his revenues and costs and the question of whether he should invest in fixed capital now or wait to do so at some time in the future (liquidity preference and user cost of capital issues).

The Psychology of Human Risk Preferences and Vulnerability to Scare-Mongers: Experimental Economic Tools for Hypothesis Formulation and Testing

The Internet and social media have opened niches for political exploitation of human dispositions to hyper-alarmed states that amplify perceived threats relative to their objective probabilities of occurrence. Researchers should aim to observe the dynamic “ramping up” of security threat mechanisms under controlled experimental conditions. Such research necessarily begins from a clear model of standard baseline states, and should involve adding treatments to established experimental protocols developed by experimental economists. We review these protocols, which allow for joint estimation of risk preferences and subjective beliefs about probabilities and their distributions. Results we have obtained on such estimates, from populations in various countries, are gathered for comparison. Most people show moderate risk aversion in non-alarmed states. We also find universal heterogeneity in risk preference structures, with substantial sub-samples weighting probabilities in such a way as to display “probability pessimism” (rank dependent utility), while others make risky choices in accordance with expected utility theory.

Reconciling the Subjective and Objective Aspects of Probability

Since the early nineteenth century, the concept of objective probability has been dynamic. As we recognize this history, we can strengthen Professor Nozer Singpuwalla’s vision of reliability of survival analysis by aligning it with earlier conceptions elaborated by Laplace, Borel, Kolmogorov, Ville and Neyman. By emphasizing testing and recognizing the generality of the vision of Kolmogorov and Neyman, we gain a perspective that does not rely on exchangeability.

A critical note on Salience Theory of choice under risk

Salience Theory Bordalo et al. (2012a) is a context-dependent theory of choice under risk, where objective probabilities are replaced by decision weights distorted in favor of salient payoffs. The detailed analysis presented in this paper points out serious flaws in this model, the most serious of which is that the lottery certainty equivalent is undefined for some ranges of probabilities. Moreover, the model violates monotonicity. The origin of the peculiar features of the model lies in switching between different evaluation expressions that depend on salience conditions or the number of prospect payoffs. The number of evaluation expressions and switching values grows rapidly with the number of states considered.

Piecewise linear rank-dependent utility

Choice under risk is modelled using a piecewise linear version of rank-dependent utility. This model can be considered a continuous version of NEO-expected utility (Chateauneuf et al., J Econ Theory 137:538–567, 2007). In a framework of objective probabilities, a preference foundation is given, without requiring a rich structure on the outcome set. The key axiom is called complementary additivity.

Subjective foundation of possibility theory: Anscombe-Aumann approach

This paper presents a new characterization of subjective possibility theory. Anscombe and Aumann [1] pioneered a multiple-variable approach to characterize the subjective probability on the basis of its relationship with objective probability. We generalize the Anscombe-Aumann approach to define subjective possibility theory. To characterize the uncertainty of the variable of interest (H) we consider its relationship with a variable of probability and a variable of ignorance. Our axiomatization assumes that the preference over the acts contingent on the outcomes of the variables is a weak order and satisfies a monotonicity property; the preference over probabilistic lotteries is represented by linear utility; and the preference over acts under ignorance by a recently developed τ-anchor utility theory. We show that if H and the variable of ignorance are completely reversible in Anscombe-Aumann’s sense and H and the variable of probability are partially reversible then the uncertainty of H must obey the laws of possibility theory. We outline a framework to manage heterogeneous uncertainty that includes probability, possibility and ignorance in decision making.

Combining Active and Semisupervised Learning of Remote Sensing Data Within a Renyi Entropy Regularization Framework

Active and semisupervised learning are related techniques aiming at reducing the effort of creating training sets for classification and regression tasks. In this work, we present a framework for combining these two techniques on the basis of Renyi entropy regularization, enabling a synergy effect. We build upon the existing semisupervised learning model which attempts to balance the likelihood of labeled examples and the entropy of putative object probabilities within the unlabeled pool. To enable efficient optimization of the model, we generalize the deterministic annealing expectation–maximization (DAEM) algorithm, originally designed for Shannon entropy, to accommodate the use of Renyi entropies. The Renyi-regularized model is then applied to expected error reduction (EER), an active learning approach based on minimizing the entropy of unlabeled object probabilities. We investigate object preselection with a greedy approximation of the object feature matrix as a means to reduce computational complexity. To assess the performance of the proposed framework, we apply it to two real-world remote sensing problems with significantly different input data characteristics: detecting dead trees from color infrared aerial images (2-D) and detecting dead trunk stems in ALS point clouds (3-D). Our results show that for small training sets, the semisupervised Renyi-regularized classifier improves the classification rate by up to 11% and 10% points compared to the unregularized baseline for ALS and image data, respectively. This gain carries over to active learning, where the regularized EER achieves 90% of the final classification performance using 50% and 70% of the number of queries required by standard EER.

Embodiment in Whole-Brain Emulation and its Implications for Death Anxiety

The awareness of death is a central motivating force behind human activity. Their capacities for abstract and symbolic reasoning give human beings a unique foresight of their finite lifetime and forthcoming demise. Because of the overwhelming nature of this realization, we try to cope with the ensuing anxieties by means of various cognitive and existential strategies. One such strategy is to create a meaningful legacy during one’s lifetime that will outlive the single individual. Whole-brain emulation (WBE) is another approach, but is unusual because of its literal promise to abolish death. Starting from the premise that WBE is feasible and will advance to such a level that we can speak of uploaded minds, we explore the implications of an allegedly immortal existence in a computational substrate: for our embodiment in the first place, and for death anxiety in the second. We argue that uploading would change the nature of, but could ultimately never abolish, embodiment. Instead, the defining characteristic of all brains are their vital links to the bodies that contain them and their interactions with the environment that are mediated by the body. In this light, we discuss the limits of WBE’s potential to mitigate death anxieties: limits related to the (objective) probability of ceasing to exist, but also those that stem from the perception of the body as a proxy for death.

Drift analysis and prediction of debris from Malaysia Airlines flight MH370

Malaysia Airlines flight MH370 disappeared on 8 March 2014, while flying from Kuala Lumpur, Malaysia, to Beijing, China. The Malaysian Prime Minister concluded that “flight MH370 ended in the southern Indian Ocean” on 24 March 2014. A piece of marine debris, later confirmed to be a flaperon from flight MH370 by the French prosecutor, was found on Reunion Island in the western Indian Ocean on 29 July, 2015. In the present study, the aircraft debris are assumed to drift in the surface layer and the vertical movement is not taken into account. Based on the surface drifting buoys and maritime objects drift prediction model, the drifting trajectories and time scales of the debris are estimated. It was found that 100 drift buoys passed in the possible air crash waters and eleven of them finally reached Reunion according to analysis of surface drift buoys in Indian Ocean. Among these, two buoys drifted northwestward took about 500 days, close to the debris drift time, testified the possibility that debris from the possible air crash waters could drift to Reunion, from the point of observational facts. The Leeway factors were reparameterized and the wave effect was ignored. The OSCAR reanalysis currents and CFSR reanalysis winds in southern Indian Ocean were processed as forcing field. Then a maritime objects drift prediction model for the southern Indian Ocean was established based on Leeway maritime drift theory. Three scenarios experiments with different initial time (5 d apart) were designed. 1024 objects were placed in the possible air crash waters to enhance statistical significance. Each experiment was divided to three conditions with different leeway factors of 0.012, 0.015 and 0.018. The experiments were carried out to compute the drift trajectory of 9216 objects in total initially placed in the possible air crash waters from March 2014 to July 2015 for 500 d. The results show that the trajectories of the objects are basically the same with the surface drift buoys, indicating the robust performance of the drift prediction model. 53, 48 and 47 objects are found in Reunion Island area for the three experiments, with the probability of 17‰, 16‰ and 15‰. Three kinds of trajectory are concluded for the objects in Reunion Island area at the end of the prediction. The first kind is drifting northeastward then northwestward then westward; the second kind is drifting northward then westward; the third kind is drifting northwestward. The probabilities of objects arrive in the Reunion Island area with different leeway factors of 0.012, 0.015 and 0.018 are 7‰, 13‰ and 28‰. The probability increases along with the leeway factor. The possible reason is that during the drift area, the wind is mainly southeast trade wind. Due to the long integration time, position difference of every time step accumulates, eventually causing the large distance of different leeway factors. The possible air crash waters and currently search area estimated by relevant departments are correct, indirectly verified by this research.

The Rich Domain of Risk

We report on two experiments challenging the common assumption that events with objective probabilities constitute a unique source of uncertainty. We find that, similar to the domain of ambiguity, the domain of risk is rich in the sense that behavior is systematically different when subjects face risky bets based on simple or more complex events. Furthermore, we find a tight association between attitudes toward complex risky bets and attitudes toward both ambiguity and compound lotteries. These results raise questions about the characterization of ambiguity aversion and the modeling of decisions under uncertainty. This paper was accepted by James Smith, decision analysis.

An Efficient Bayesian Approach to Exploit the Context of Object-Action Interaction for Object Recognition

This research features object recognition that exploits the context of object-action interaction to enhance the recognition performance. Since objects have specific usages, and human actions corresponding to these usages can be associated with these objects, human actions can provide effective information for object recognition. When objects from different categories have similar appearances, the human action associated with each object can be very effective in resolving ambiguities related to recognizing these objects. We propose an efficient method that integrates human interaction with objects into a form of object recognition. We represent human actions by concatenating poselet vectors computed from key frames and learn the probabilities of objects and actions using random forest and multi-class AdaBoost algorithms. Our experimental results show that poselet representation of human actions is quite effective in integrating human action information into object recognition.

PAIRWISE-SVM FOR ON-BOARD URBAN ROAD LIDAR CLASSIFICATION

The common method of LiDAR classifications is Markov random fields (MRF). Based on construction of MRF energy function, spectral and directional features are extracted for on-board urban point clouds. The MRF energy function is consisted of unary and pairwise potentials. The unary terms are computed by SVM classifictaion. The initial labeling is mainly processed through geometrical shapes. The pairwise potential is estimated by Naïve Bayes. From training data, the probability of adjacent objects is computed by prior knowledge. The final labeling method is reweighted message-passing to minimization the energy function. The MRF model is difficult to process the large-scale misclassification. We propose a super-voxel clustering method for over-segment and grouping segment for large objects. Trees, poles ground, and building are classified in this paper. The experimental results show that this method improves the accuracy of classification and speed of computation.

PAIRWISE-SVM FOR ON-BOARD URBAN ROAD LIDAR CLASSIFICATION

Abstract. The common method of LiDAR classifications is Markov random fields (MRF). Based on construction of MRF energy function, spectral and directional features are extracted for on-board urban point clouds. The MRF energy function is consisted of unary and pairwise potentials. The unary terms are computed by SVM classifictaion. The initial labeling is mainly processed through geometrical shapes. The pairwise potential is estimated by Naïve Bayes. From training data, the probability of adjacent objects is computed by prior knowledge. The final labeling method is reweighted message-passing to minimization the energy function. The MRF model is difficult to process the large-scale misclassification. We propose a super-voxel clustering method for over-segment and grouping segment for large objects. Trees, poles ground, and building are classified in this paper. The experimental results show that this method improves the accuracy of classification and speed of computation.

Eliciting Subjective Probabilities in Anscombe and Aumann's Model

In this note, we propose an alternative version of Anscombe and Aumann's Subjective Expected Utilities (SEU) representation theorem. In Anscombe and Aumann's model, a randomizing device with objective probabilities is available. As pointed out by Sarin and Wakker, when such a randomizing device is available, there is a natural and direct method to elicit subjective probabilities. Anscombe and Aumann did not use this method, but employed an indirect way to derive subjective probabilities. We investigate what happens if we use this direct method to elicit subjective probabilities in Anscombe and Aumann's model.