Relevant Probability Research Articles

Non-marginal decisions: A novel Bayesian multiple testing procedure

In this paper, we consider the problem of multiple testing where the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather than actually utilizing the dependency to increase efficiency. Moreover, the decisions regarding different hypotheses are marginal in the sense that they do not depend upon each other directly. However, in realistic situations, the hypotheses are usually dependent, and hence it is desirable that the decisions regarding the dependent hypotheses are taken jointly. In this article, we develop a novel Bayesian multiple testing procedure that coherently takes this requirement into consideration. Our method, which is based on new notions of error and non-error terms, substantially enhances efficiency by judicious exploitation of the dependence structure among the hypotheses. We show that our method minimizes the posterior expected loss associated with an additive “0-1” loss function; we also prove theoretical results on the relevant error probabilities, establishing the coherence and usefulness of our method. The optimal decision configuration is not available in closed form and we propose an efficient simulated annealing algorithm for the purpose of optimization, which is also generically applicable to binary optimization problems. Extensive simulation studies indicate that in dependent situations, our method performs significantly better than some existing popular conventional multiple testing methods, in terms of accuracy and power control. Moreover, application of our ideas to a real, spatial data set associated with radionuclide concentration in Rongelap islands yielded insightful results.

Decision tree analysis for prostate cancer prediction

Introduction/Objective. The use of serum prostate-specific antigen (PSA) test has dramatically increased the number of men undergoing prostate biopsy. However, the best possible strategies for selecting appropriate patients for prostate biopsy have yet to be defined. The aim of the study was to develop a classification and regression tree (CART) model that could be used to identify patients with significant prostate cancer (PCa) on prostate biopsy in patients referred due to abnormal PSA, digital rectal examination (DRE) findings, or both, regardless of the PSA level. Methods. The data on clinicopathological characteristics regarding prebiopsy assessment collected from patients who had undergone ultrasound-guided prostate biopsies included the following: age, PSA, DRE, volume of the prostate, and PSA density (PSAD). The CART analysis was carried out using all predictors identified by univariate logistic regression analysis. Different aspects of predictive performance and clinical utility risk prediction model were assessed. Results. In this retrospective study, significant PCa was detected in 92 (41.6%) out of 221 patients. The CART model had three splits based on PSAD, as the most decisive variable, prostate volume, DRE, and PSA. Our model resulted in an 83.3% area under the receiver operating characteristic curve. Decision curve analysis showed that the regression tree provided net benefit for relevant threshold probabilities compared with the logistic regression model, PSAD, and the strategy of biopsying all patients. Conclusion. The model helps to reduce unnecessary biopsies without missing significant PCa.

Demystifying the Mystery Room

The Mystery Room problem is a close variant of the Mystery Bag scenario (due to Titelbaum). It is argued here that dealing with this problem requires no revision of the Bayesian formalism, since there exists a solution to this problem in which indexicals or demonstratives play no essential role. The solution does require labels, which are internal to the probabilistic model. While there needs to be a connection between at least one label and one indexical or demonstrative, that connection is external to the probabilistic model that is used to determine the relevant conditional probability; hence, it does not complicate the update procedure.

744: Aspirin strategies for preeclampsia prevention: a cost-effectiveness analysis

To evaluate the cost-effectiveness of aspirin (ASA) prophylaxis guided by biomarker values and ultrasound indices for preeclampsia prevention compared to approaches based on clinical risk assessment. We designed a decision analysis model to compare the costs and effectiveness of four strategies to guide ASA use in pregnancy: (1) biomarkers and ultrasound risk assessment (2) the United States Preventive Services Task Force (USPSTF) risk factor based approach, (3) universal ASA, and (4) no ASA. In the base case model, we assumed that ASA reduced the risk of preterm preeclampsia by 61% but did not reduce the risk of term preeclampsia. Sensitivity analyses that varied these and other assumptions were performed to assess the model’s robustness. Threshold analyses were performed to identify the costs and risks of ASA-related complications (e.g., gastrointestinal bleeding and respiratory sensitivity) at which the preferred strategy shifted. The primary outcome was the incremental cost effectiveness ratio (ICER) defined as the cost needed to avert one case of preeclampsia. An ICER less than 100,000 USD was considered cost-effective based on literature describing maternal and neonatal costs associated with preeclampsia. Under baseline estimates, universal ASA use is the dominant strategy (i.e., costs the least and provides the greatest health benefit). For every 100,000 women, universal ASA use would save $19,216,551 and result in 308 fewer cases of preeclampsia compared to ASA use guided by biomarker and ultrasound risk assessment (Table 1). In univariate and multivariate analyses, the model was sensitive only to the probability of ASA administration. When ASA use in the universal strategy was below 55%, following USPSTF guidelines became more cost effective. Threshold analysis revealed that only when the rate of GI bleeding with ASA exceeded 0.94% or the rate of respiratory complications exceeded 38% was universal ASA no longer the dominant strategy. In a Monte Carlo analysis, universal ASA was the most cost-effective strategy in 89% of simulations. Universal aspirin administration, as compared to several other strategies for preeclampsia risk assessment and selected ASA use is a dominant strategy across a broad range of relevant probabilities.

On the three-slit experiment and quantum mechanics

It has been suggested by Sorkin that a three-slit Young experiment could reveal the validity a fundamental ingredient in the foundations of one of the cornerstones in modern physics namely quantum mechanics. In terms of a certain parameter κS, it was argued that a non-zero value could imply a breakdown of the fundamental Born’s rule as well as the superposition principle. Here we argue that a physical realization of such arguments could lead to an erroneous conclusion and contradict the basic rules of quantum mechanics. In fact, we argue that a straightforward interpretation of the procedures involved in a physical determination of κS does not necessarily lead to κS = 0. In order to show this we consider a mono-chromatic source of photons prepared in an arbitrary quantum state and a simple version of the well-established photon detection theory of Glauber which, by construction, obeys all the rules of quantum mechanics. It is, however, also argued that after a proper identification of the relevant quantum-mechanical probability amplitudes one can be reach κS = 0. As long as one only consider a single photon detector, it is verified that, in this context, there is no fundamental difference between quantum-mechanical interference and interference as expressed in terms of classical electro-magnetic waves.

SonReb concrete assessment for spatially correlated NDT data

In this paper the existence of a spatial correlation on the readings of the rebound hammer tests and ultrasonic pulse velocity tests is firstly investigated by means of experimental evaluations on two RC walls. The effect of this correlation is then transferred in the concrete strength evaluation by means of the well known SonReb method. Monte Carlo simulations, carried out to check the goodness of the evaluation with the SonReb standard procedure, highlighted a relevant probability of under- or over-estimation as well as the possibility of not negligible absolute errors of the expected mean compression strengths for the investigated structural elements. A simple modification to the standard procedure is, finally, proposed in order to take into account the concrete spatial correlation and improve the goodness of the SonReb evaluation. This modification, that basically consists in increasing the relative distance between the location of the individual test readings, allows the reduction of the unconservative maximum percentage overestimation error from roughly 15% to 5%.

A Unified Prostate Cancer Risk Prediction Model Combining the Stockholm3 Test and Magnetic Resonance Imaging

BackgroundRisk prediction models and magnetic resonance imaging (MRI) of the prostate can reduce unnecessary biopsies and overdiagnosis of low-risk prostate cancer. However, it is unclear how these tools should be used in concert. ObjectiveTo develop a unified risk prediction model (S3M-MRI) that combines the Stockholm3 score (based on protein and genetic markers and clinical variables) and Prostate Imaging-Reporting and Data System v.2 scores modified for MRI without contrast (modPI-RADS). Design, setting, and participantsWe used data for 532 men from the prospective multicentre STHLM3-MRI diagnostic study to construct S3M-MRI. We compared S3M-MRI to Stockholm3 and modPI-RADS alone with respect to model discrimination, calibration, and net benefit. We also compared clinical outcomes for five diagnostic strategies according to the use of combinations of the three models. Results and limitationsThe area under the receiver operating characteristic curve (AUC) was 0.88 (95% confidence interval [CI] 0.85–0.91) for S3M-MRI, which was significantly higher (p=0.04) than for Stockholm3 (0.86, 95% CI 0.83–0.89) and modPI-RADS (0.83, 95% CI 0.79–0.87). S3M-MRI had a higher net benefit on decision curve analysis for clinically relevant probability thresholds for biopsy recommendation in comparison to Stockholm3 and modPI-RADS. However, for different diagnostic strategies, sequential use of Stockholm3 followed by MRI only for Stockholm3-positive men resulted in a similar number of unnecessary biopsies (64 vs 69) and diagnosed International Society of Urological Pathology (ISUP) grade group 1 cancers (56 vs 51) at similar sensitivity for ISUP grade group ≥2 cancers, while avoiding 38% of MRI scans. Limitations include the ethnically homogeneous study population. ConclusionsThe unified S3M-MRI model was superior to the Stockholm3 model and modPI-RADS alone. However, the S3M-MRI improvement was marginal compared to sequential use of Stockholm3 followed by MRI, and resulted in 60% more MRI scans. Patient summaryA new risk prediction model combining clinical variables, genetic and protein biomarkers, and results from prostate magnetic resonance imaging improved the clinical outcome performance of prostate cancer diagnostics.

Application of conditioned structure functions to exploring influence of premixed combustion on two-point turbulence statistics

In order to investigate the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush, a new method is introduced. The method consists in analyzing structure functions of the velocity field, which characterize velocity difference in two points A and B, with the structure functions being conditioned to various events; (i) unburned reactants in both points, (ii) combustion products in both points, (iii) intermediate states of the mixture in both points, (iv) the reactants in one point and the products in another point, (v) the reactants in one point and an intermediate state in another point, and (vi) the products in one point and an intermediate state in another point. Such structure functions and relevant probabilities are defined in the paper. Subsequently, the structure functions and the probabilities are extracted from Direct Numerical Simulation (DNS) data obtained from two statistically 1D, planar, fully-developed, weakly turbulent, premixed flames characterized by two significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results indicate that (i) the conditioned structure functions differ significantly from the mean structure functions and (ii) the newly introduced approach could convey information important for understanding fundamentals of flame–turbulence interaction and finding issues that require further research. In particular, application of the approach to the aforementioned DNS data shows that the combustion-induced thermal expansion substantially affects small-scale two-point velocity statistics in the incoming constant-density turbulent flow of unburned reactants within a premixed flame brush.

A Novel Computational Method for the Identification of Potential miRNA-Disease Association Based on Symmetric Non-negative Matrix Factorization and Kronecker Regularized Least Square.

Increasing evidence has indicated that microRNAs (miRNAs) are associated with numerous human diseases. Studying the associations between miRNAs and diseases contributes to the exploration of effective diagnostic and treatment approaches for diseases. Unfortunately, the use of biological experiments to reveal the potential associations between miRNAs and diseases is time consuming and costly. Therefore, it is very necessary to use simple and efficient calculation models to predict potential disease-related miRNAs. Considering the limitations of other previous methods, we proposed a novel computational model of Symmetric Nonnegative Matrix Factorization for MiRNA-Disease Association prediction (SNMFMDA) to reveal the relation of miRNA-disease pairs. SNMFMDA could be applied to predict miRNAs associated with new diseases. Compared to the direct use of the integrated similarity in previous computational models, the integrated similarity need to be interpolated by symmetric non-negative matrix factorization (SymNMF) before application in SNMFMDA, and the relevant probability of disease-miRNA was obtained mainly through Kronecker regularized least square (KronRLS) method in our model. What's more, the AUC of global leave-one-out cross validation (LOOCV) reached 0.9007, and the AUC based on local LOOCV was 0.8426. Besides, the mean and the standard deviation of AUCs achieved 0.8830 and 0.0017 respectively in 5-fold cross validation. All of the above results demonstrated the superior prediction performance of SNMFMDA. We also conducted three different case studies on Esophageal Neoplasms, Breast Neoplasms and Lung Neoplasms, and 49, 49, and 48 of the top 50 of their predicted miRNAs respectively were confirmed by databases or related literatures. It could be expected that SNMFMDA would be a model with the ability to predict disease-related miRNAs efficiently and accurately.

Quantum computational finance: Monte Carlo pricing of financial derivatives

Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence. This work provides a starting point for further research at the interface of quantum computing and finance.

Probabilistic multi-word spotting in handwritten text images

Keyword spotting techniques are becoming cost-effective solutions for information retrieval in handwritten documents. We explore the extension of the single-word, line-level probabilistic indexing approach described in our previous works to allow for page-level search of queries consisting in Boolean combinations of several single-keywords. We propose heuristic rules to combine the single-word relevance probabilities into probabilistically consistent confidence scores of the multi-word boolean combinations. An empirical study, also presented in this paper, evaluates the search performance of word-pair queries involving AND and OR Boolean operations. Results of this study support the proposed approach and clearly show its effectiveness. Finally, a web-based demonstration system based on the proposed methods is presented.

Face Repetition Probability Does Not Affect Repetition Suppression in Macaque Inferotemporal Cortex.

Repetition suppression, which refers to reduced neural activity for repeated stimuli, is typically explained by bottom-up or local adaptation mechanisms. However, recent theories have emphasized the role of top-down processes, suggesting that this response reduction reflects the fulfillment of perceptual expectations. To support this, an influential human fMRI study showed that the magnitude of suppression is modulated by the probability of a repetition. No such repetition probability effect was found in macaque inferior temporal (IT) cortex for spiking activity despite the presence of repetition suppression. Contrary to the human fMRI studies that showed an effect of repetition probability, the macaque single-unit study used a large variety of unfamiliar stimuli and the monkeys were not required to attend the stimuli. Here, as in the human fMRI studies, we used faces as stimuli and made the monkeys attend to the stimulus content. We simultaneously recorded spiking activity and local field potentials (LFPs) in the middle lateral face patch (ML) of one monkey (male) and a face-responsive region of another (female). Although we observed significant repetition suppression of spiking activity and high gamma-band LFPs in both animals, there were no effects of repetition probability even when repetitions were task relevant and repetition probability affected behavioral decisions. In conclusion, despite the use of face stimuli and a stimulus-related task, no neural signature of repetition probability was present for faces in a face responsive patch of macaque IT. This further challenges a general perceptual expectation account of repetition suppression.SIGNIFICANCE STATEMENT Repetition suppression is a reduced brain activity for repeated stimuli commonly observed across species. In the predictive coding framework, such suppression is thought to reflect fulfilled perceptual expectations. Although this hypothesis is supported by several human fMRI studies reporting an effect of repetition probability on repetition suppression, this could not be replicated in single-cell recordings in monkey inferior temporal (IT) cortex. Subsequent studies narrowed down the conditions for the effect to requiring attention and being limited to particular stimulus categories such as faces. Here, we show that, even under these conditions, repetition suppression in monkey IT neurons is still unaffected by repetition probability, even in a task with a behavioral effect, challenging the perceptual expectation account of repetition suppression.

Analysis of Sustainability Decision Trees Generated by Qualitative Models Based on Equationless Heuristics

Sustainability processes are complex and therefore ill-known, inconsistent, and subjective, and must be studied despite a shortage of information. It is prohibitively difficult to study them on quantitative levels using quantitative methods. The presented qualitative approach enables us to solve these issues. There are just three values used to describe the qualitative variables and their derivatives, plus/increasing, zero/constant, and negative/decreasing. An n-dimensional equation-less qualitative model is a set of pairwise relations. Such relations represent a shallow knowledge of the sustainability systems being studied. The solution of the qualitative model is a set of scenarios. The behaviour of this model is described by all of the possible transitions among these scenarios. A decision maker can easily compile a decision tree if he/she knows all of the possible transitions. The generated tree can be evaluated using traditional methods if all of the relevant probabilities are known. Otherwise, some heuristics are used to evaluate the best decision.

Effects of ultra-light dark matter on the gravitational quantum well

We study the influence of a periodic perturbation of the effective masses of fermions, due to the assumed semiclassical ultra-light dark matter (ULDM) background, on the motion of neutrons in a gravitational quantum well (GQW). Our focus is on the transition probability between the lowest two energy states, with the Rabi frequency in the kHz region corresponding to the series of “sweet spot” DM masses in the [Formula: see text][Formula: see text]eV ballpark. The relevant probability is written in terms of the specific mass and of the effective coupling to the ordinary matter. These parameters can be constrained by the nonobservation of any significant deviations of the measured transition probabilities from the DM-free picture.

Comment on “Measurements without probabilities in the final state proposal”

The final state proposal [G.T. Horowitz and J.M. Maldacena, J. High Energy Phys. 2004(2), 8 (2004)] is an attempt to relax the apparent tension between string theory and semiclassical arguments regarding the unitarity of black hole evaporation. The authors of [R. Bousso and D. Stanford, Phys. Rev. D 89, 044038 (2014)] analyze thought experiments where an infalling observer first verifies the entanglement between early and late Hawking modes and then verifies the interior purification of the same Hawking particle. They claim that "probabilities for outcomes of these measurements are not defined" and therefore suggest that "the final state proposal does not offer a consistent alternative to the firewall hypothesis." We show, in contrast, that one may define all the relevant probabilities based on the so-called ABL rule [Y. Aharonov, P.G. Bergmann, and J.L. Lebowitz, Phys. Rev. 134, 1410 (1964)], which is better suited for this task than the decoherence functional. We thus assert that the analysis of Bousso and Stanford cannot yet rule out the final state proposal.

Toward the automatic detection of manually labeled irregular pitch periods

Irregular pitch periods (IPPs) occur in a wide variety of speech contexts and can support automatic speech recognition systems by signaling word boundaries, phrase endings, and certain prosodic contours. IPPs can also provide information about emotional content, dialect, and speaker identity. The ability to automatically detect IPPs is particularly useful because accurately identifying IPPs by hand is time-consuming and requires expertise. In this project, we use an algorithm developed for creaky voice analysis by Kane et al. (2013) incorporating features from Ishi et al. (2008) to automatically identify IPPs in recordings of speech from the American English Map Task database. Short-term power, intra-frame periodicity, inter-pulse similarity, subharmonic energy, and glottal pulse peakiness measures are input into an artificial neural network to generate frame-by-frame creak probabilities. To determine a perceptually relevant threshold probability, the creak probabilities are compared to IPPs hand-labeled by experienced raters. Preliminary results yielded an area under the receiver operating characteristic curve of 0.82. Thresholds above 0.1 produced very high specificity, but even lower thresholds yielded fairly high sensitivity and specificity. These results indicate generally good agreement between hand-labeled IPPs and automatic detection, calling for future work investigating effects of linguistic and prosodic context.

From Skills to Symbols: Learning Symbolic Representations for Abstract High-Level Planning

We consider the problem of constructing abstract representations for planning in high-dimensional, continuous environments. We assume an agent equipped with a collection of high-level actions, and construct representations provably capable of evaluating plans composed of sequences of those actions. We first consider the deterministic planning case, and show that the relevant computation involves set operations performed over sets of states. We define the specific collection of sets that is necessary and sufficient for planning, and use them to construct a grounded abstract symbolic representation that is provably suitable for deterministic planning. The resulting representation can be expressed in PDDL, a canonical high-level planning domain language; we construct such a representation for the Playroom domain and solve it in milliseconds using an off-the-shelf planner. We then consider probabilistic planning, which we show requires generalizing from sets of states to distributions over states. We identify the specific distributions required for planning, and use them to construct a grounded abstract symbolic representation that correctly estimates the expected reward and probability of success of any plan. In addition, we show that learning the relevant probability distributions corresponds to specific instances of probabilistic density estimation and probabilistic classification. We construct an agent that autonomously learns the correct abstract representation of a computer game domain, and rapidly solves it. Finally, we apply these techniques to create a physical robot system that autonomously learns its own symbolic representation of a mobile manipulation task directly from sensorimotor data---point clouds, map locations, and joint angles---and then plans using that representation. Together, these results establish a principled link between high-level actions and abstract representations, a concrete theoretical foundation for constructing abstract representations with provable properties, and a practical mechanism for autonomously learning abstract high-level representations.

A Game Theoretic Analysis of the Adversarial Retrieval Setting

The main goal of search engines is ad hoc retrieval: ranking documents in a corpus by their relevance to the information need expressed by a query. The Probability Ranking Principle (PRP) --- ranking the documents by their relevance probabilities --- is the theoretical foundation of most existing ad hoc document retrieval methods. A key observation that motivates our work is that the PRP does not account for potential post-ranking effects; specifically, changes to documents that result from a given ranking. Yet, in adversarial retrieval settings such as the Web, authors may consistently try to promote their documents in rankings by changing them. We prove that, indeed, the PRP can be sub-optimal in adversarial retrieval settings. We do so by presenting a novel game theoretic analysis of the adversarial setting. The analysis is performed for different types of documents (single-topic and multi-topic) and is based on different assumptions about the writing qualities of documents' authors. We show that in some cases, introducing randomization into the document ranking function yields an overall user utility that transcends that of applying the PRP.

Switching probability of all-perpendicular spin valve nanopillars

In all-perpendicular spin valve nanopillars the probability density of the free-layer magnetization is independent of the azimuthal angle and its evolution equation simplifies considerably compared to the general, nonaxisymmetric geometry. Expansion of the time-dependent probability density to Legendre polynomials enables analytical integration of the evolution equation and yields a compact expression for the practically relevant switching probability. This approach is valid when the free layer behaves as a single-domain magnetic particle and it can be readily applied to fitting experimental data.

Comments on the properties of Mittag-Leffler function

The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schr\"odinger type and heat-type fractional partial differential equations and explore the problem of operatorial ordering finding appropriate rules when non-commuting operators are involved. We discuss the coherent states associated with the fractional Sch\"odinger equation, analyze the relevant Poisson type probability amplitude and compare with analogous results already obtained in the literature.