Statistical Decision Theory Research Articles

Hypothesis Testing in Presence of Adversaries

We present an extension to the classical problem of hypothesis testing by incorporating actions of an adversary who intends to mislead the decision-maker and attain a certain benefit. After presenting the general problem within an adversarial statistical decision theory framework, we consider the cases of adversaries who can either perturb the data received or modify the underlying data-generating process parametrically. Supplemental materials for this article are available online.

Assessment of PET and SPECT phantom image quality through automated binary classification of cold rod arrays.

Evaluation of positron emission tomography (PET) or single photon emission computed tomography (SPECT) performance often involves qualitative assessment of phantom images, namely the visibility of hot or cold structures in a warm background. Structure-to-background contrast is a quantitative measure of scanner performance; however, contrast measurements do not account for image noise and its effect on task performance. Although task-based performance could be evaluated over an ensemble of phantom scans, a more practical approach is desired. Repeated structures, such as the cold rod arrays of the American College of Radiography (ACR) PET and SPECT phantoms, offer an opportunity to evaluate image quality based on statistical decision theory. Images are co-registered to a digital template for placement of numerous regions of interest (ROIs) in multiple thick slices centered on each cold rod and on each midpoint between rods. The assumption is made that each ROI corresponds to a statistically independent measurement, known to be of either a cold rod or the background. A receiver operating characteristic (ROC) curve then is generated for each cold rod sector of the phantom. The area under the ROC curve (AUC) provides a quantitative measure of cold rod visibility. In addition, signal-to-noise ratio (SNR) is calculated, under the assumption that the rod and background ROI measurements are distributed normally. Using this approach, data from PET and SPECT phantom studies from prior annual physics surveys were analyzed retrospectively. Rod and background ROI measurements had nearly normal (PET) or approximately normal (SPECT) distributions. Resultant ROC curves illustrated the varying degrees of overlap between rod and background histograms vs cold rod diameter. Both AUC and SNR correlated well with visual image assessment and had high consistency between phantom studies, demonstrating the quantitative accuracy of the automated analysis. AUC reliably quantified cases where cold rods were partially or mostly resolved, while SNR provided further characterization when cold rods were completely resolved. In comparison, contrast measurements often mirrored AUC and SNR but were inconsistent in cases of varying noise. Automated analysis of phantom cold rod arrays using binary classification provides informative quantitative measures of image quality and is practical for routine use. This approach avoids observer dependencies associated with visual assessment and potentially can benefit quality assurance, physics surveys, laboratory accreditation, and harmonization of multicenter image quality.

Treatment Choice With Trial Data: Statistical Decision Theory Should Supplant Hypothesis Testing

A central objective of empirical research on treatment response is to inform treatment choice. Unfortunately, researchers commonly use concepts of statistical inference whose foundations are distant from the problem of treatment choice. It has been particularly common to use hypothesis tests to compare treatments. Wald’s development of statistical decision theory provides a coherent frequentist framework for use of sample data on treatment response to make treatment decisions. A body of recent research applies statistical decision theory to characterize uniformly satisfactory treatment choices, in the sense of maximum loss relative to optimal decisions (also known as maximum regret). This article describes the basic ideas and findings, which provide an appealing practical alternative to use of hypothesis tests. For simplicity, the article focuses on medical treatment with evidence from classical randomized clinical trials. The ideas apply generally, encompassing use of observational data and treatment choice in nonmedical contexts.

Dynamic semiparametric models for expected shortfall (and Value-at-Risk)

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of “elicitability” for ES by jointly modeling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES–VaR models outperform forecasts based on GARCH or rolling window models.

Contiguity of States and Super Wave Operators

This paper characterises contiguity for families of states defined on a von Neumann algebra. It extends earlier research of my own published in [1], motivated by scattering theory and the celebrated work of Lucien Le Cam in classical probability. It is well-known that Le Cam did a major contribution to develop asymptotic methods in statistical decision theory, defining various new concepts, among them, contiguity of probability measures. In particular, contiguity of quantum states allows to explore different aspects of the large time behaviour of noncommutative Markov semigroups, among them, the super wave operator characterisation. I illustrate these results via quantum and classical examples of evolutions.

Signal detection theory and psychoacoustics

This talk will trace the early history of signal detection theory (SDT) with a particular emphasis on its applications in psychoacoustics. SDT, as developed at the University of Michigan (U-M) in the mid-1950s, revolutionized psychophysics by introducing a core assumption: all sensory judgements are limited by “noise” of one sort or another and, as such, are reflective of underlying decision processes. To test and flesh-out this new theory, early empirical work in vision quickly turned to audition and a remarkably fruitful 12-year period followed, from roughly 1954 to 1966. This talk will focus on that 12-year period, bracketed, on the one end, by the establishment of an auditory research laboratory at U-M by Wilson P. “Spike” Tanner and, on the other, by the publication of Green and Swets’ (1966) seminal text. The principle documents and publications of that period—particularly those that appeared in this society’s Journal—will be reviewed, with a discussion of their intellectual and historical context. Emphasis will be given to the investigations of the Electronic Defense Group at U-M and those of other legendary psychoacousticians. In particular, the work of Tanner, the key instigator in the transition from “statistical decision theory” to SDT in psychoacoustics, will be discussed.

Lessons learned from signal-detection-theory-oriented studies of the processing of auditory patterns

One extension of Fechner’s (1860) methods by which the influence of sensory stimuli on human observers could be quantified in physical units, sometimes termed a psychophysics was Stevens (1938) theory and methodology of perceived magnitude estimation that attempted to bridge the gap between sensation and perception. A more far-reaching second extension began in 1954, when Peterson, Birdsall, and Fox applied statistical decision theory to the recovery of physical signals embedded in background noise and Tanner, Green, and Swets applied those principles to develop a new psychophysical methodology. What became known as “signal detection theory” provided methods of determining the capacity of systems to detect, discriminate, or recognize physical stimuli, a second psychophysics. The two alternatives to Fechner represent complimentary approaches to a single set of phenomena, one of which can be characterized as the study of sensory capabilities and the other of response proclivities. The two require entierly different methods of measurement and address fundamentally different questions. Both are of practical and theoretical importance. Levels of stimulus uncertainty and the type and duration of experience with stimuli can have profound influences on measurements of both types. Examples of these effects for complex sounds, both speech and nonspeech, will be presented.

APPLICATION OF THE SYSTEMIC ANALYSIS FOR SOLVING THE PROBLEMS OF DEPENDENT EVENTS IN AGRICULTURAL LANDS - CHARACTERISTICS AND METHODOLOGY

Systemic analysis for the first time provides a generalized problem-solving methodology based on the system concept. By its nature, the problem-solving function is close to the highest levels of functional representation of human activity. Therefore, this function and its serving methodology are most integrative and include all the private functions required for its implementation. Systemic analysis, such as problem-solving methodology, claims to play the role of unifying all the necessary methods, knowledge and action to solve problems. This is what determines his attitude to such areas as operations research, theory of statistical decisions, decision theory, organization theory, and others. For the implementation of management functions, the methods of the search and discovery theory, statistical methods, factor analysis, experimental theories, methods of study of the operations, methods of forecasting and others can be used. The assessment of the ratio of system analysis and its related disciplines is based on the contribution of the individual discipline in the methodology for solving the problem. The main content of the system analysis is not in the formal mathematical apparatus describing the systems and the problem solving and it is not in the special mathematical methods but in the conceptual apparatus, its ideas, approach and formulations. Systemic analysis defines the base nomenclature of the functions that need to be implemented to solve the problem, that is to say, it defines the structure of the process performed by the organization as opposed to the traditional approach to the organization that determines its administrative structure. A / Types of problems A problem is called the situation, which is characterized by the difference between the required (desired) output and the existing outcome. Exit is necessary if it is absent threatens the existence and development of the system. Existing output is provided by the existing system. The desired output is achieved by the desired system. The problem may be to prevent a reduction in output or increase. The condition of the problem is set by the existing system (the "known"). The requirement - this is the desired system. The solution to the problem is what fills the difference between the existing and the desired system. The system that fills this difference is the object of construction and is called a solution to the problem. Problems can be manifested by symptoms. The systematic manifestation of symptoms is a tendency. Detecting the problem is a result of identifying the symptoms. Identification is possible provided that the desired behavior of the system is known. Once the problem has been identified, it is necessary to predict its development and to assess the timeliness of the decision, that is to say, what will be the state of the system for an unresolved problem.

Reality and risk: A refutation of S. Rendón’s analysis of the Peruvian Truth and Reconciliation Commission’s conflict mortality study

We refute S. Rendón’s recent criticism of the 2003 Peruvian Truth and Reconciliation Commission (TRC) conflict mortality study. We first show that his most important result, an alternative estimate of the mortality due to the Maoist guerrillas of Shining Path ( Sendero Luminoso), is lower than existing observed data and is therefore impossible. We then analyze his statistical approach and find that it is affected by a subtle form of selection bias. We contrast his approach to the TRC’s using tools from statistical decision theory, and determine that his method is inadequate for this problem—and that the TRC’s approach is, at minimum, better. Without advocating for the TRC’s original results, we conclude that Rendón’s approach and methods are inferior to the TRC’s original work.

Fiscal Policy and the Assessment of Output Gaps in Real Time: An Exercise in Risk Management

Fiscal policymakers are expected to conduct countercyclical policies to mitigate cyclical fluctuations of output, but the assessment of cyclical conditions in real time is subject to considerable uncertainty. They face two types of risk: (i) launching discretionary measures to support or dampen aggregate demand when no measures are required (type I error), or (ii) not launching any stabilising measures when this is warranted by cyclical conditions (type II error). A rational policymaker could manage these risks by correcting real-time estimates for past errors, notably the apparent tendency to underestimate good times when they occur. In practice, however, fiscal policy has been largely pro-cyclical or a-cyclical at best. Using statistical decision theory, we calculate thresholds for realtime output gap estimates beyond which governments could launch stabilisation measures, so as to reduce the risk of running pro-cyclical policies. We consider different preferences for avoiding type I or type II errors, and for addressing upside and downside growth risks. We show that the tendency to run pro-cyclical fiscal policy and the ensuing deficit bias can reflect two factors: a preference for activism that is, attaching a lower cost to type I errors, combined with an inclination to be gloomy about cyclical conditions.

The Explanation Game: A Formal Framework for Interpretable Machine Learning

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealized explanation game in which players collaborate to find the best explanation(s) for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal patterns of variable granularity and scope. We characterize the conditions under which such a game is almost surely guaranteed to converge on a (conditionally) optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions.

Performance Measurement in Agency Models

This note explores how to evaluate an agent’s performance in standard incentive contracts. We show that the MPS criterion proposed by Kim (1995) becomes a tight condition for one performance measurement system to be more informative than another, as long as the first-order approach can be justified. In the one-signal case obeying the monotone likelihood ratio property, the MPS criterion is equivalent to the way of ordering signals developed by Lehmann (1988), establishing a link to statistical decision theory. Our results demonstrate that depending on the agent’s potential deviations, ideal performance measures can be different.

TO THE QUESTION ABOUT THE ASSESSMENT OF THE CONSTRUCTION OF RAILWAY STATIONS

The purpose of the work is to develop methods for the integrated assessment of design options for railroad track development and their comparative analysis to select the most rational design solution based on modern mathematical methods. Methodology. To solve the problem, the methods of statistical analysis, graph theory and decision theory are used. Findings. The constructive characteristics and quality indicators of various schemes of the station track development were obtained. As a result of a comparative analysis of the considered variants of design decisions, their numerical estimates (priorities) were determined, on the basis of which the most rational scheme of track development of the railway station was chosen. The originality lies in the fact that the procedure for choosing a rational scheme for the track development of a railway station from a variety of options is formalized as a multi-criteria task, for solving which the hierarchy analysis method is used. The practical value of the presented methodology will allow expanding the range of considered competitive options for railroad track development schemes and increasing the objectivity of their comparative analysis not only taking into account design features, but also taking into account quality indicators.

Liberation From the P Value's Tyranny.

> P-values, next to nuclear weapons, are the worst invention of the 20th century . > > —Herman Rubin, Purdue University, 1981 More than a half century ago, the P value was selected as the measuring tool for health care research by administrators. The difficulties generated by statistical hypothesis testing in addition to the constraints it places on cardiovascular trial researchers must now be declared unacceptable by the cardiology research community. Developed >90 years ago by statistician, Ronald Fisher, while working on a manure experiment in England,1,2 P values have risen to dominate the field of cardiovascular investigation for no other reasons than those of custom and habit. The abuse of P values has become so rampant that the American Statistical Association in 2016 was compelled to provide a consensus statement decrying their misuse.3 Counterpoint, see p 1049 Statistical hypothesis testing and P values were criticized by scientists from the beginning. They thought that its reverse logic—embracing a null hypothesis that one did not think, only to have the data reject it compelling the scientist to accept what one did think—was tortured and unnecessarily complex. P values rose to prominence in health care when grant administrators, journal editors, and Food and Drug Administration officials, overwhelmed by the post–World War II explosion in research, chose the P value instrument to help identify worthy research.4 The P value was not chosen because it had any basis in epidemiology, biology, pathophysiology, or cardiovascular medicine. It was selected because these administrators needed a metric to help them to separate the research wheat from the chaff, and they could see no alternative. The fledgling clinical trial research community accepted this P value imprimatur, not realizing that this nonmalicious selection portended pernicious consequences. Even though the P value’s sole, small role was to …

Алгоритм класифікації ділянок кусково-однорідних зображень для систем виявлення та спостереження

The questions of construction of algorithm of classification of piece-homogeneous images are considered with the use of two-dimensional stochastic linear models, that generate two-dimensional casual processes to that procedures of theory of statistical decisions are applied. For the model of mixture autoregressive and polynomial presentations expression is got for a decision rule and the algorithm of classification of areas of piece-homogeneous images is built for operative treatment in the systems of discovery and supervision.

Blind Image Watermark Detection Algorithm Based on Discrete Shearlet Transform Using Statistical Decision Theory

Blind watermarking targets the challenging recovery of the watermark when the host is not available during the detection stage. This paper proposes Discrete Shearlet Transform (DST) as a new embedding domain for blind image watermarking. Our novel DST blind watermark detection system uses a nonadditive scheme based on the statistical decision theory. It first computes the Probability Density Function (PDF) of the DST coefficients modeled as a Laplacian distribution. The resulting likelihood ratio is compared with a decision threshold calculated using Neyman–Pearson criterion to minimize the missed detection subject to a fixed false alarm probability. Our method is evaluated in terms of imperceptibility, robustness, and payload against different attacks (Gaussian noise, blurring, cropping, compression, and rotation) using 30 standard grayscale images covering different characteristics (smooth, more complex with a lot of edges, and high detail textured regions). The proposed method shows greater windowing flexibility with more sensitive to directional and anisotropic features when compared against discrete wavelet and contourlets.

Rescuing Collective Wisdom when the Average Group Opinion Is Wrong

The total knowledge contained within a collective supersedes the knowledge of even its most intelligent member. Yet the collective knowledge will remain unaccessible to us unless we are able to find efficient knowledge aggregation methods which produce reliable decisions based on the behavior or opinions of the collective's members. It is often stated that simple averaging of a pool of opinions is a good and in many cases the optimal way to extract knowledge from a crowd. The method of averaging has been applied to analysis of decision-making in very different fields such as forecasting, collective animal behavior, individual psychology and machine learning. Two mathematical theorems, Condorcet's theorem and Jensen's inequality, provide a general theoretical justification for the averaging procedure. Yet the necessary conditions which guarantee the applicability of these theorems are often not met in practice. Under such circumstances, averaging can lead to suboptimal and sometimes very poor performance. Practitioners in many different fields have independently developed procedures to counteract the failures of averaging. We review such knowledge aggregation procedures and interpret the methods in the light of a statistical decision theory framework to explain when their application is justified. Our analysis indicates that in the ideal case, there should be a matching between the aggregation procedure and the nature of the knowledge distribution, correlations and associated error costs. This leads us to explore how machine learning techniques can be used to extract near-optimal decision rules in a data-driven manner. We end with a discussion of open frontiers in the domain of knowledge aggregation and collective intelligence in general.

Fractal and topological sustainable methods of overcoming expected uncertainty in the radiolocation of low-contrast targets and in the processing of weak multi-dimensional signals on the background of high-intensity noise: A new direction in the statistical decision theory

The main purpose of this work is to interpret the main directions of radio physics, radio engineering and radio location in “fractal” language that makes new ways and generalizations on future promising radio systems. We introduce a new kind and approach of up-to-date radiolocation: fractal-scaling or scale-invariant radiolocation. The new topologic signs and methods of detecting the low-contrast objects against the high-intensity noise background are presented. It leads to basic changes in the theoretical radiolocation structure itself and also in its mathematical apparatus. The fractal radio systems conception, sampling topology, global fractal-scaling approach and the fractal paradigm underlie the scientific direction established by the author in Russia and all over the world for the first time ever.

THE EFFECTIVENESS OF VALIDATION MEASUREMENTS IN AUTOMATED SYSTEMS OF THE POWER SUPPLY SYSTEMS CONTROL IN ACCORDANCE WITH LIMIT VALUES

A high level of operational reliability of power supply systems is virtually impossible to provide without operational control of the reliability of the measurement variables (currents, voltages, powers, energies, temperatures, pressures) that characterize the condition of power equipment and technological processes. Reforming the power engineering and its transition to market relations necessitate one to toughen the requirements for the reliability of the measuring information. Inaccurate measurements are a potential source of misdiagnosis of malfunctions of equipment and they cause incorrect operation of emergency control equipment and erroneous actions of operating personnel in the control of technological processes. Operational methods of reliability control that enhance the operational reliability of the measuring information are based on the usage of the semantic value of the measured data, their consistency, process consistency, and consistency of balance. These methods use technological sense of the measured variables and they complement the methods of hardware status monitoring of automated control systems based on digital codes. That improves the overall operational reliability of the transmission, collection and processing of information. The most common semantic method of control is the method of limits (“fork”) that compares the numeric value of the measured variable with the upper and lower boundaries of valid values. The disadvantage of limit values in many cases is its poor resolution, due to the wide range of appearance of results of measurements. This reduces the probability of detection of gross and systematic errors of measurements more than it may be accepted. With this regard, the objective of a reasonable narrowing of the range of valid values of the variables, that uses the theory of statistical decisions, acquires high relevance.

Social Influence Spectrum at Scale

Given a social network, the Influence Maximization (InfMax) problem seeks a seed set of k people that maximizes the expected influence for a viral marketing campaign. However, a solution for a particular seed size k is often not enough to make an informed choice regarding budget and cost-effectiveness. In this article, we propose the computation of Influence Spectrum (InfSpec), the maximum influence at each possible seed set size k within a given range [ k lower , k upper ], thus providing optimal decision making for any availability of budget or influence requirements. As none of the existing methods for InfMax are efficient enough for the task in large networks, we propose LISA (sub-Linear Influence Spectrum Approximation), an efficient approximation algorithm for InfSpec (and also InfMax) with the best-known worst-case guarantees for billion-scale networks. LISA returns an (1-1/e -ϵ)-approximate influence spectrum with high probability (1-δ), where ϵ, δ are precision parameters provided by users. Using statistical decision theory, LISA has an asymptotic optimal running time (in addition to optimal approximation guarantee). In practice, LISA surpasses the state-of-the-art InfMax methods, taking less than 15 minutes to process a network of 41.7 million nodes and 1.5 billions edges.