Objective Probability Research Articles

Inferentialism and knowledge: Brandom\u2019s arguments against reliabilism

I take issue with Robert Brandom’s claim that on an analysis of knowledge based on objective probabilities it is not possible to provide a stable answer to the question whether a belief has the status of knowledge. I argue that the version of the problem of generality developed by Brandom doesn’t undermine a truth-tracking account of noninferential knowledge that construes truth-tacking in terms of conditional probabilities. I then consider Sherrilyn Roush’s claim that an account of knowledge based on probabilistic tracking faces a version of the problem of generality. I argue that the problems she raises are specific to her account, and do not affect the version of the view that I have advanced. I then consider Brandom’s argument that the cases that motivate reliabilist epistemologies are in principle exceptional. I argue that he has failed to make a cogent case for this claim. I close with the suggestion that the representationalist approach to knowledge that I endorse and Brandom rejects is in principle compatible with the kind of pragmatist approach to belief and truth that both Brandom and I endorse.

Role of Information and its Processing in Statistical Analysis

This paper discusses how real-life statistical analysis/inference deviates from ideal environments. More specifically, there often exist models that have equal statistical power as the actual data-generating model, given only limited information and information processing/computation capacity. This means that misspecification actually has two problems: first with misspecification around the model we wish to find, and that an actual data-generating model may never be discovered. Thus the role information - this includes data - plays on statistical inference needs to be considered more heavily than often done. A game defining pseudo-equivalent models is presented in this light. This limited information nature effectively casts a statistical analyst as a decider in decision theory facing an identical problem: trying best to form credence/belief of some events, even if it may end up not being close to objective probability. The sleeping beauty problem is used as a study case to highlight some properties of real-life statistical inference. Bayesian inference of prior updates can lead to wrong credence analysis when prior is assigned to variables/events that are not (statistical identification-wise) identifiable. A controversial idea that Bayesianism can go around identification problems in frequentist analysis is brought to more doubts. This necessitates re-defining how Kolmogorov probability theory is applied in real-life statistical inference, and what concepts need to be fundamental.

The valuation of social impact bonds: An introductory perspective with the Peterborough SIB

Social impact bonds (SIBs) are financial assets whose objective is to attract investors to fund social programs by providing them an incentive if the project meets its predefined targets. This article aimed at proposing a reflection about the development of a pricing method for this kind of financial assets in an uncertain environment. After having defined SIBs and presenting their intrinsic uncertainty in the first section, I will present, in the second one, an existing SIB (called Peterborough SIB) in financial terms. Afterwards, the last section offered an introductory perspective on the potential development of a Wang transformation based pricing method applied to this Peterborough SIB. By using this statistical operator as a statistical technique for converting objective probabilities (past observations) into subjective estimates of these probabilities, this paper investigates a specific way of integrating the uncertainty in related the valuation of SIBs.

An Adaptable, Probabilistic, Next-Best View Algorithm for Reconstruction of Unknown 3-D Objects

Autonomous mobile robots perform many tasks, such as grasping and inspection, that may require complete models of three-dimensional (3-D) objects in the environment. If little or no knowledge about an object is known a priori , the robot must take sensor measurements from strategically determined viewpoints in order to reconstruct a 3-D model of the object. We propose an autonomous object reconstruction approach for mobile robots that is very general, with no assumptions about object shape or size, such as a bounding box or predetermined set of candidate viewpoints. A probabilistic, volumetric method for determining the optimal next-best view is developed based on a partial model of a 3-D object of unknown shape and size. The proposed method integrates an object probability characteristic to determine sensor views that incrementally reconstruct a 3-D model of the object. Experiments in simulation and on a real-world robot validate the work and compare it to the state of the art.

A Naturalist’s Guide to Objective Chance

I argue that there are such things as nomological probabilities—probabilities that play a certain explanatory role with respect to stable, long-run relative frequencies. Indeed, I argue, we should be willing to accept nomological probabilities even if they turn out to be metaphysically weird or even wholly sui generis entities. I then give an example of one way in which this argument should shape future work on the metaphysics of chance by describing a challenge to a common group of analyses of objective probability—Humean analyses—understood as analyses of nomological probability.

Novel density-based and hierarchical density-based clustering algorithms for uncertain data

Uncertain data has posed a great challenge to traditional clustering algorithms. Recently, several algorithms have been proposed for clustering uncertain data, and among them density-based techniques seem promising for handling data uncertainty. However, some issues like losing uncertain information, high time complexity and nonadaptive threshold have not been addressed well in the previous density-based algorithm FDBSCAN and hierarchical density-based algorithm FOPTICS. In this paper, we firstly propose a novel density-based algorithm PDBSCAN, which improves the previous FDBSCAN from the following aspects: (1) it employs a more accurate method to compute the probability that the distance between two uncertain objects is less than or equal to a boundary value, instead of the sampling-based method in FDBSCAN; (2) it introduces new definitions of probability neighborhood, support degree, core object probability, direct reachability probability, thus reducing the complexity and solving the issue of nonadaptive threshold (for core object judgement) in FDBSCAN. Then, we modify the algorithm PDBSCAN to an improved version (PDBSCANi), by using a better cluster assignment strategy to ensure that every object will be assigned to the most appropriate cluster, thus solving the issue of nonadaptive threshold (for direct density reachability judgement) in FDBSCAN. Furthermore, as PDBSCAN and PDBSCANi have difficulties for clustering uncertain data with non-uniform cluster density, we propose a novel hierarchical density-based algorithm POPTICS by extending the definitions of PDBSCAN, adding new definitions of fuzzy core distance and fuzzy reachability distance, and employing a new clustering framework. POPTICS can reveal the cluster structures of the datasets with different local densities in different regions better than PDBSCAN and PDBSCANi, and it addresses the issues in FOPTICS. Experimental results demonstrate the superiority of our proposed algorithms over the existing algorithms in accuracy and efficiency.

On Weckstein's 1959, Keynesian, Weight of the Evidence Based Demolition of G L S Shackle's Attack on the Concept of Probability

R. Weckstein’s 1959 article in the February,1959 Symposium in Metroeconomica on Shackle’s theory of possibility demonstrated that Shackle’s attack on the concept of probability, as an approach to be used by decision makers in the real world, due to the theory of probability’s requirements, such as objectivity, complete ordering, the additivity of objective probabilities, divisibility, repetition, and repeatability, was applicable mainly to the relative and limiting frequency interpretations of probability. Shackle’s attack also held against the subjective theory of probability, which also made the assumptions of complete ordering and additivity. However, Weckstein demonstrated that all of Shackle’s objections to probability per se totally failed when confronted by logical theories of probability, in general, and J M Keynes’s Logical Theory of Probability, in particular, which explicitly criticized classical, limiting frequency, relative frequency, and subjective theories of probability. Keynes explicitly pointed out that all of these other theories of probability were actually special cases, sound and valid in their specific fields of application, but not general in scope or application. Keynes argued that only his logical theory of probability could be a general theory of probability, applicable to single events, infrequent events, and frequent events in the form of Boole’s propositional logic and development of indeterminate/imprecise/determinate probabilities. Specifically, it was the Keynesian concept of the weight of the evidence that leads to the complete refutation of Shackle’s attacks on probability per se. Shackle’s attacks on the concept of probability are sound when made against the Classical, Propensity, Subjective, Relative Frequency, and Limiting Frequency interpretations of probability, but are unsound when confronted with Keynes’s Theory of logical probability. Shackle never responded to Weckstein’s criticisms based on Keynes or logical theories of probability. In fact, he deliberately chose to respond mainly to Weckstein’s mention of Reichenbach’s posit approach to singular events in his article. In fact, Shackle never dealt with Keynes’s logical theory of probability in his lifetime since he never got past page 14 of the A Treatise on Probability. Instead, Shackle attempted to completely bypass the A Treatise on Probability and The General Theory, which is built on Keynes’s weight of the evidence, by claiming that Keynes’s February,1937 article in the Quarterly Journal of Economics represented Keynes’s final view of decision making and probability. A recent article by Derbyshire represents a continuation of Shackle’s severe misrepresentation of probability and especially of Keynes’s work on uncertainty, decision making, and probability. Keynes, building on the logical approach to probability of Boole, had already solved the problems that other theories of probability had in dealing with single, crucial decisions, additivity, and uncertainty. Keynes finished with his analysis in the 1908 Fellowship dissertation, which contained his interval valued, on linear, non-additive approach, when Shackle was five years old. This appears in the TP in Part II. Shackle never read the TP. He read little bits and pieces of it. He then wrote vague and ambiguous comments on the TP that made no sense when he wrote them and which still do not make any sense in 2017. Keynes’s approach would make a better foundation for scenario planning than Shackle’s, with his theory of possibility, if one assumes that academics are capable of actually reading the TP. However, it might be the case that academics are not capable of reading the TP. In that case, then, Shackles’s theory would be a second best choice.

Efficient Use of AUVs in the Maritime Environment

Autonomous underwater vehicle (AUV) a.k.a. underwater drones are subsea vehicles which operate in the underwater environment independently of direct human input. There is a growing interest in underwater data collection by using autonomous underwater vehicles within the oceanographic research community. In this paper, the Iver 2 AUV is examined to accomplish accurate side-scan data while executing well planned missions. Therefore, this papers goal is to establish the optimal use conditions for the AUV that RCN has so that we maximize the detection probability of sea bottom objects that can be risk factors and at the same time to cover a surface as large as possible during a single mission.

How to select a promising enterprise for venture capitalists with prospect theory under intuitionistic fuzzy circumstance?

Venture capitalists are confronted with decision-making problems under an uncertain investment circumstance, which lead them to rely heavily on intuition and psychological state to make their decisions in most cases. It has attracted more and more researches to focus on such behaviors of venture capitalists in recent years and along with the development of behavioral finance in venture capital field. Through the review of framework of venture capitalists’ decision-making and the investigation of background of venture capital market in China, we find that the decision-making framework, which is based on the traditional expected utility theory with hypothesis that the investor is completely rational, is inconsistent with reality. Moreover, the decision-making information is often depicted as crisp number with probability that couldn’t express the uncertainty which is the fundamental nature of venture capital circumstance. Therefore, a novel approach that considers both the bounded rationality of venture capitalists and the uncertain circumstance of venture capital in decision-making is urgent to select the promising enterprise in China. Fortunately, prospect theory, as one of the greatest achievement in behavioral finance, thinks that venture capitalists focus on subjective probabilities instead of objective probabilities and show the behavior characterized by risk aversion over gains and risk seeking over losses, which can depict the psychological state of venture capitalists properly. Furthermore, the intuitionistic fuzzy information can express essential uncertainty in venture capital circumstance accurately. Therefore, we adopt Intuitionistic Fuzzy Prospect Theory that integrates both the merits of prospect theory and intuitionistic fuzzy information to aid venture capitalists to make a better decision in the real world. In this paper, the detailed steps of how to select a promising enterprise has been illustrated. Then, a practical example of selecting the promising enterprise for venture capitalists in Ali Capital is provided to exhibit the process of application and exemplify the feasibility of this selecting approach. Meanwhile, from the comparison of ranking results derived by TOPSIS and this approach, we find that the approach proposed in this paper is superior to the TOPSIS in selecting the promising enterprise according to the subsequent funded results of enterprises.

The Identification of Attitudes towards Ambiguity and Risk from Asset Demand

Individuals behave differently when they know the objective probability of events and when they do not. The smooth ambiguity model accommodates both ambiguity (uncertainty) and risk. For an incomplete, competitive asset market, we develop a revealed preference test for asset demand to be consistent with the maximization of smooth ambiguity preferences; and we show that ambiguity preferences constructed from finite observations converge to underlying ambiguity preferences as observations become dense. Subsequently, we give sufficient conditions for the asset demand generated by smooth ambiguity preferences to identify the ambiguity and risk indices as well as the ambiguity probability measure. We do not require ambiguity beliefs to be observable: in a generalized specification, they may not even be defined. An ambiguity free asset plays an important role for identification.

The siren call of probability: Dangers associated with using probability for consideration of the future

Many tools for thinking about the future employ probability. For example, Delphi studies often ask expert participants to assign probabilities to particular future outcomes. Similarly, while some scenario planners reject probability, others insist that assigning probabilities to scenarios is required to make them meaningful. Formal modelling and forecasting methods often also employ probability in one way or another. The paper questions this widespread use of probability as a device for considering the future, firstly showing that objective probability, based on empirically-observed frequencies, has some well-known drawbacks when used for this purpose. However, what is less-widely acknowledged is that this is also true of the subjective probability used in, for example, Delphi. Subjective probability is less distinct from objective probability than proponents of its use might imply, meaning it therefore suffers from similar problems. The paper draws on the foundations of probability theory as set out by Kolmogorov, as-well-as the work of Keynes, Shackle, Aumann, Tversky and Kahneman, and others, to reassert the essential distinction between risk and uncertainty, and to warn about the dangers of inappropriate use of probability for considering the future. The paper sets out some criteria for appropriate use.

Clinical adequacy assessment of autocontours for prostate IMRT with meaningful endpoints.

To determine if radiation treatment plans created based on autosegmented (AS) regions-of-interest (ROI)s are clinically equivalent to plans created based on manually segmented ROIs, where equivalence is evaluated using probabilistic dosimetric metrics and probabilistic biological endpoints for prostate IMRT. Manually drawn contours and autosegmented ROIs were created for 167 CT image sets acquired from 19 prostate patients. Autosegmentation was performed utilizing Pinnacle's Smart Probabilistic Image Contouring Engine. For each CT set, 78Gy/39 fraction 7-beam IMRT treatment plans with 1cm CTV-to-PTV margins were created for each of the three contour scenarios; PMD using manually delineated (MD) ROIs, PAS using autosegmented ROIs, and PAM using autosegmented organ-at-risks (OAR)s and the manually drawn target. For each plan, 1000 virtual treatment simulations with different systematic errors for each simulation and a different random error for each fraction were performed. The statistical probability of achieving dose-volume metrics (coverage probability (CP)), expectation values for normal tissue complication probability (NTCP), and tumor control probability (TCP) metrics for all possible cross-evaluation pairs of ROI types and planning scenarios were reported. In evaluation scenarios, the root mean square loss (RMSL) and maximum absolute loss (MAL) of coverage probability of dose-volume objectives, E[TCP], and E[NTCP] were compared with respect to the base plan created and evaluated with manually drawn contours. Femoral head dose objectives were satisfied in all situations, as well as the maximum dose objectives for all ROIs. Bladder metrics were within the clinical coverage tolerances except D35Gy for the autosegmented plan evaluated with the manual contours. Dosimetric indices for CTV and rectum could be highly compromised when the definition of the ROIs switched from manually delineated to autosegmented. Seventy-two percent of CT image sets satisfied the worst-case CP thresholds for all dosimetric objectives in all scenarios, the percentage dropped to 50% if biological indices were taken into account. Among evaluation scenarios, (MD,PAM ) bore the highest resemblance to (MD,PMD ) where 99% and 88% of cases metall CP thresholds for bladder and rectum, respectively. When including daily setup variations in prostate IMRT, the dose-volume metric CP, and biological indices of ROIs were approximately equivalent for the plans created based on manually drawn targets and autosegmented OARs in 88% of cases. The accuracy of autosegmented prostates and rectums are impediment to attain statistically equivalent plans created based on manually drawn ROIs.

Cournot’s Notion of Hasard: An Objective Conception of Chance

According to Antoine Augustine Cournot, chance events are the result of the intersection between independent causal chains. This coincidental notion of chance is not a new one, but—as Cournot remarks—it comes from Saint Thomas Aquinas, Boethius, and more probably from Jean de La Placette. Such a conception of chance phenomena seems to be very important, not only because it is closely related to the Principle of Causality, but also since it grounds Cournot’s theory of objective probability. Starting from Martin’s work (Probabilites et Critique Philosophique selon Cournot. Vrin, Paris, 1996), the main attempt of this survey is to endorse the idea that Cournot’s coincidental notion of hasard is objective, that is it is ontic (i.e. it comes from some real feature of the world) and it does not depend—in some sense—on our degree of knowledge. In order to do that, a central role in the discussion will be given to the meaning of the independence between the intersecting causal chains and to Cournot’s conception of causation.

When Sleeping Beauty First Awakes

Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga’s seminal paper on the subject. Elga’s intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a three-dimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.

Urban Change Analysis with Multi-Sensor Multispectral Imagery

An object-based method is proposed in this paper for change detection in urban areas with multi-sensor multispectral (MS) images. The co-registered bi-temporal images are resampled to match each other. By mapping the segmentation of one image to the other, a change map is generated by characterizing the change probability of image objects based on the proposed change feature analysis. The map is then used to separate the changes from unchanged areas by two threshold selection methods and k-means clustering (k = 2). In order to consider the multi-scale characteristics of ground objects, multi-scale fusion is implemented. The experimental results obtained with QuickBird and IKONOS images show the superiority of the proposed method in detecting urban changes in multi-sensor MS images.

Prudence with Respect to Ambiguity

Under expected utility, prudence is equivalent to a positive third derivative of utility and plays a crucial role in precautionary saving behaviour. Eeckhoudt and Schlesinger (2006) proposed behavioural definitions of prudence and of higher order risk preferences. The present article proposes a similar definition for prudence with respect to ambiguity, i.e. situations in which objective probabilities are not available. Implications for several ambiguity models are derived. Ambiguity prudence is implied by Hansen and Sargent’s (2001) multiplier preferences, empirically correlates with financial behaviour and plays a key role in prevention behaviour.

Improved visual background extractor with adaptive range change

The visual background extractor (ViBe) has become one of the best motion object detection algorithms because of its good detection results and low memory requirements. However, the ViBe model cannot self-adjust the value range of the parameter that controls the number of samples chosen from the background template. In this paper, two models are proposed to help automatically change the parameter range in different environments. The blink energy model can detect dynamic backgrounds by increasing the range, while the object probability model can prevent corrosion of motion objects by decreasing the range. The experimental results show that our proposed method can both accurately recognize dynamic backgrounds and efficiently prevent object corrosion. In addition, our method shows better performance on benchmark datasets than several commonly used detection algorithms.

Objective probability and the mind-body relation

Objectiveprobability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked via two alternative interpretations of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory and to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing.

TEST DETERMINATION OF PROBABILITY OF AIRBORNE DETECTION OF GROUND SURFACE OBJECTS

The article presents the methods, mathematical model and its software implementation for calculating the efficiency indicators of visual and hardware search and detection of ground objects from the aircraft. The methods differ from the known ones in that they use modern information technologies and are adapted to solve practical test problems. In addition, finding values of the visual detection probability of ground objects in full-scale experiments is unrealizable due to the huge amount of required expenses. The proposed method allows estimating a particular efficiency indicator of an aircraft when searching for ground objects in the flight tests – the yield on a generic object. The developed mathematical model takes into account the known range of object detection by its linear dimensions. The software implementation allows performing calculations for different values of the meteorological situation. The convergence of simulation results and flight experiments is estimated. To determine the convergence, the results obtained in real flight tests on proof ground with different meteorological conditions were compared with the results of calculations obtained by modeling. The relative discrepancy between the indicators obtained in the flight experiment and calculated by the developed program is less than 5%. The author proposes new private efficiency indicators for the visual detection task of typical ground objects. This is the area of possible detection of the ground object and the area of guaranteed access to it. These indicators allow performing a comparative assessment of the capabilities of aircraft to detect ground objects in tests. These indicators, unlike the known ones, have greater visibility and informational content. The developed computer program reduces the time spent by the tester on the calculation of indicators and the preparation of materials to the act by 3 times due to automation and usability. It allows us to perform calculations by varying any indicators on which the probability of detecting a typical ground object in the wide range of their change depends on.

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.