Statistical Decision Theory Research Articles

Limits on the accuracy of contact inhibition of locomotion.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor-much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false-positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

Defining metrics of visual acuity from theoretical models of observers.

Many experimental studies show that metrics of visual image quality can predict changes in visual acuity due to optical aberrations. Here we use statistical decision theory and Fourier optics formalism to demonstrate that two metrics known in the field of vision sciences are approximations of two different theoretical models of linear observers. The theory defines metrics of visual acuity to potentially predict changes in visual acuity due to optical aberrations, without needing a posteriori scale or offset. We illustrate our approach with experiments, using combinations of defocus and spherical aberration, and pure coma.

Toward Patient-Centered Drug Approval for Treatment of Rare Diseases

ObjectivesThis commentary seeks to improve the design and analysis of trials undertaken to obtain approval of drugs for treatment of rare diseases. MethodsMethodological analysis reveals that use of hypothesis testing in the Food and Drug Administration drug approval process is harmful. Conventional asymmetric error probabilities bias the approval process against approval of new drugs. Hypothesis testing is inattentive to the relative magnitudes of losses to patient welfare when types 1 and 2 errors occur. Requiring the sample size to be large enough to guarantee the specified statistical power particularly inhibits the development of new drugs for treating rare diseases. Rarity of a disease makes it difficult to enroll the number of trial subjects needed to meet the statistical power standards for drug approval. ResultsUse of statistical decision theory in drug approval would overcome these serious deficiencies of hypothesis testing. Sample size would remain relevant to drug approval, but the criterion used to evaluate sample size would change. Rather than judging sample size by statistical power, the Food and Drug Administration could require a sample to be large enough to provide a specified nearness to optimality of the approval decision. ConclusionsUsing nearness to optimality to set sample size and making approval decisions to minimize distance from optimality would particularly benefit the evaluation of drugs for treatment of rare diseases. It would enable a dramatic reduction in sample size relative to current norms, without compromising the clinical informativeness of trials.

Josephson radiation threshold detector

A Josephson radiation threshold detector (JRTD) that is based on the threshold behaviour of a current bias Josephson junction (CBJJ) is designed and fabricated for infrared radiation (IR@1550nm) detection at low temperatures. To achieve the optimal performance, we develop a binary hypothesis detection method to calibrate Josephson threshold behaviours (i.e. the switching current distributions of the CBJJ with the Al/AlOx/Al junction) in the absence and presence of radiation. In the absence of IR radiation, the junction transitioned with a measurable voltage drop across the junction, and this signal was treated as the events of hypothesis H0. The events of junction transition observed in the presence of the IR radiation served as hypothesis H1. Considering the usual Gaussian noise and based on statistical decision theory, the accumulated data of the measured switching current distributions are processed, and the threshold sensitivity of the demonstrated JRTD device is estimated. The minimum detectable IR radiation power of the proposed detector is approximately 0.74 pW, which corresponds to the photon rate of 5.692 × 106 photons/second. Further optimisation of JRTDs to implement the desired binary detection of a single photon is still a subject of argument, at least theoretically.

Comprehensive Oos Evaluation of Predictive Algorithms with Statistical Decision Theory

Comprehensive Oos Evaluation of Predictive Algorithms with Statistical Decision Theory

Substantiation of source data on the parametric algorithms for the classification of weather hazards

The meteorological situation is one of the decisive factors determining the safety and frequency of civil aviation flights. Weather hazards (WH), associated with cumulonimbus clouds, such as a heavy shower, thunderstorm, hail, combined with high atmosphere turbulence, quite often lead to aviation events and even accidents. Currently, a domestic weather radar system of the near airfield zone (WR) “Monocle” has been developed and successfully operated. The criteria for the classification of meteorological phenomena (MP), used in the WR, have been developed individually for each phenomenon and have some heuristic character. These criteria are cumbersome and complicate the process of automating the WH classification. In this case, there is a natural desire to generalize the criteria and optimize them in accordance with the theory of distinguishing statistical hypotheses. This article discusses the application of the Bayesian approach to the WH classification. The statistical Bayesian decision theory assumes decision-making in terms of the probability theory when all significant probabilistic values, so-called sufficient statistics, are known. In order to obtain statistical descriptions of the probability distributions of reflectivity and the eddy dissipation rate (EDR), an analysis of radar signals, reflected from such MP as a rain shower, thunderstorm, hail was carried out. The article provides brief descriptions of the methods of conducting experiments to form statistical database and its analysis. Based on the above methods, the statistical parameter H(EDRmax) analysis for a rain shower, the amplitude distribution of reflectivity parameters and the EDR (Zmax, EDRmax) for thunderstorms and hail was carried out, which showed the low distinguishing ability of each individual parameter when solving the problem to classify MP within the assigned alphabet. The obvious solution is dictated by the theory of recognition. To increase the classification confidence, it is essential to share information parameters, for example, in the form of multidimensional distribution densities of the probabilities of random parameters. The article presents a parametric description of the MP “rain shower-thunderstorm-hail” classification features. An analysis to evaluate the probabilistic characteristics of the WH classification for the adopted empirical classification criteria in the WR shows that the adopted criteria are far from optimal in terms of the probabilities of the correct classification, especially in the rain shower case. It is obvious that a problem solution of the assigned classification confidence is associated with the optimization of the feature space and classification criteria. Based on the data obtained, it is necessary to build an algorithm to classify the WH “rain shower-thunderstorm-hail”.

Risk, ambiguity, and misspecification: Decision theory, robust control, and statistics

SummaryWhat are “deep uncertainties” and how should their presence influence prudent decisions? To address these questions, we bring ideas from robust control theory into statistical decision theory. Decision theory has its origins in axiomatic formulations by von Neumann and Morgenstern, Wald, and Savage. After Savage, decision theorists constructed axioms that formalize a notion of ambiguity aversion. Meanwhile, control theorists constructed decision rules that are robust to some model misspecifications. We reinterpret axiomatic foundations of decision theories to express ambiguity about a prior over a family of models along with concerns about misspecifications of the corresponding likelihood functions.

Preface to the Special Issue on “Statistical Decision Theory and Treatment Choice”

Preface to the Special Issue on “Statistical Decision Theory and Treatment Choice”

Statistical decision theory respecting stochastic dominance

The statistical decision theory pioneered by (Wald, Statistical decision functions, Wiley, 1950) has used state-dependent mean loss (risk) to measure the performance of statistical decision functions across potential samples. We think it evident that evaluation of performance should respect stochastic dominance, but we do not see a compelling reason to focus exclusively on mean loss. We think it instructive to also measure performance by other functionals that respect stochastic dominance, such as quantiles of the distribution of loss. This paper develops general principles and illustrative applications for statistical decision theory respecting stochastic dominance. We modify the Wald definition of admissibility to an analogous concept of stochastic dominance (SD) admissibility, which uses stochastic dominance rather than mean sampling performance to compare alternative decision rules. We study SD admissibility in two relatively simple classes of decision problems that arise in treatment choice. We reevaluate the relationship between the MLE, James–Stein, and James–Stein positive part estimators from the perspective of SD admissibility. We consider alternative criteria for choice among SD-admissible rules. We juxtapose traditional criteria based on risk, regret, or Bayes risk with analogous ones based on quantiles of state-dependent sampling distributions or the Bayes distribution of loss.

Gaussian assumptions-free interpretable linear discriminant analysis for locating informative frequency bands for machine condition monitoring

Interpretable learning models become an emerging topic in the domain of machine condition monitoring to connect signal processing algorithms with statistical learning and machine learning. Compared with traditional signal processing algorithms that show strong ability in data analysis, signal-processing-related interpretable learning models could generate interpretable learnable weights/parameters as advanced physically interpretable fault features for both machine condition monitoring and fault diagnosis. It is well-known that linear discriminant analysis (LDA) is one of the most popular and interpretable algorithms for machine condition monitoring. However, this popular algorithm needs Gaussian assumptions in their derivations and parameter estimations. In this paper, Gaussian assumptions-free interpretable LDA is proposed as an interpretable learning model to physically locate informative frequency bands and fault characteristic frequencies for machine condition monitoring. Firstly, statistical decision theory is introduced to connect the nature of regression with that of classification, which poses a foundation for the Gaussian assumptions-free interpretable LDA for machine condition monitoring. Secondly, two propositions are given to mathematically show that LDA can be realized by an equivalent linear regression analysis, which provides a perspective for the Gaussian assumptions-free interpretable LDA for simultaneous machine condition monitoring and fault diagnosis. Finally, linear regression analysis with a sparse Lp-norm regularization term is introduced to realize the Gaussian assumptions-free interpretable LDA for physically locating informative frequency bands and fault characteristic frequencies for machine condition monitoring. Two case studies are provided as illustrative examples to experimentally demonstrate that the Gaussian assumptions-free interpretable LDA is capable of indicating informative frequency bands and fault characteristic frequencies.

Consistency of Decision in Finite and Numerable Multinomial Models

The multinomial distribution is often used in modeling categorical data because it describes the probability of a random observation being assigned to one of several mutually exclusive categories. Given a finite or numerable multinomial model M|n,p whose decision is indexed by a parameter θ and having a cost cθ,p depending on θ and on p, we show that, under general conditions, the probability of taking the least cost decision tends to 1 when n tends to ∞, i.e., we showed that the cost decision is consistent, representing a Statistical Decision Theory approach to the concept of consistency, which is not much considered in the literature. Thus, under these conditions, we have consistency in the decision making. The key result is that the estimator p˜n with components p˜n,i=nin,i=1,⋯, where ni is the number of times we obtain the ith result when we have a sample of size n, is a consistent estimator of p. This result holds both for finite and numerable models. By this result, we were able to incorporate a more general form for consistency for the cost function of a multinomial model.

НЕЙРОСЕТЕВОЙ АЛГОРИТМ ДЕТЕКТИРОВАНИЯ СИГНАЛОВ С ДВОИЧНОЙ ПОЗИЦИОННО-ИМПУЛЬСНОЙ МОДУЛЯЦИЕЙ

In the work, a neural network method for detecting signals with binary position-pulse modulation was studied. The detection process was reduced to distinguishing signals by a neural network, the architecture of which included convolutional and fully-connected layers. The network was trained on the basis of a set of labeled realizations of a sum of signals with noise, which were represented by discrete samples. The TensorFlow library was used to model and train the network. A bell video pulse and a quasi-radio signal with a bell modulating function were used as possible signal models. The functioning efficiency of the trained neural network was studied by the methods of statistical modeling on a computer. The detection quality of the neural network algorithm is compared with the classical one synthesized in the framework of the statistical decision theory. The possibility of training a neural network detector with an unknown duration of the received signals is investigated. The efficiency of the neural network detector is compared with the quasi-optimal one, which does not take into account the possible unknown of the signal duration. It is shown that the neural network detection algorithm is significantly inferior to the optimal one synthesized by the maximum likelihood method. However, in the presence of a priori uncertainty about the signal duration, the quasi-optimal detector is inferior in efficiency to the neural network one. Recommendations are formulated for a reasonable choice of the detector, depending on the required quality of its work.

Evaluating Targeted Double Scoring for the Performance Assessment for School Leaders Using Imputation and Decision Theory

In a targeted double‐scoring procedure for performance assessments that are used for licensure and certification purposes, a subset of responses receives an independent second rating if the first rating falls into a preidentified critical score range (CSR) where an additional rating would lead to considerably more reliable pass‐fail decisions. This study evaluates the CSRs using two approaches—one based on imputation of missing scores and the other based on statistical decision theory—using data from the Performance Assessment for School Leaders (PASL). Results from the evaluation indicate that the currently used CSRs are effective.

Reflections of an ancient document processor

The bulk of the documents that affect our lives are digital or born digital. Our laborious investigations of layout, script, font and graphics, are turning into mere exercises with little influence on pursuits outside the Document Analysis and Recognition (DAR) community. Recent performance improvements on such tasks, even if based on deep learning and AI, are as much the result of advances in computer hardware as of breakthroughs in document research. It is time to automate tasks beyond transcription. This Commentary addresses our mission, our approach to some technical issues, and the role of AI in DAR. Opportunities for a wider role for document analysis include more pervasive application of statistical decision theory, integrated genre analysis, summarization, interpretation and information extraction, bolder goals in content analysis, and alternative modalities, induced by the open source movement, for sharing research results. Importantly, expanding the scope of our research incurs increased responsibility for retaining human prerogatives in critical decision making and preserving essential human skills like good writing and discriminative reading.

Reduction of uncertainty using adaptive modeling under stochastic criteria of information content

Entropy is the concepts from the science of information must be used in the situation where undefined behaviors of the parameters are unknown. The behavior of the casual parameters representing the processes under investigation is a problem that the essay explores from many angles. The provided uniformity criterion, which was developed utilizing the maximum entropy of the metric, has high efficiency and straightforward implementation in manual computation, computer software and hardware, and a variety of similarity, recognition, and classification indicators. The tools required to automate the decision-making process in real-world applications, such as the automatic classification of acoustic events or the fault-detection via vibroacoustic methods, are provided by statistical decision theory to the noise and vibration engineer. Other statistical analysis issues can also be resolved using the provided uniformity criterion.

Theoretical and Numerical Estimate of Signal-to-Noise Ratio in the Analysis of Josephson Junctions Lifetime for Photon Detection

The performances of a Josephson junction employed to reveal a train of pulses (a rough model for single photon detection) are analyzed with a theoretical estimate that exploits an index employed in statistical decision theory, the Kumar–Carroll index. The approximate analysis compares the numerically simulated performances of the device through the receiver operating characteristics, that offer an overview of the rate of false detection, as well as the probability to miss a signal (in this case, a pulse train). It is thus demonstrated the usefulness and the limits of the succinct Kumar–Carroll parameter. On the first side, it is proven that an increase of the parameter corresponds to an improvement of the detection. However, on the side of the limitations, the expected performances are not quite accurate, for the actual performances are systematically worse than the theoretical estimates. The results may be relevant to characterize Josephson junctions as detectors of weak signals, as those stemming from axions.

A Study on Estimation of Distribution from Survey Data with Selection Bias based on Statistical Decision Theory

A Study on Estimation of Distribution from Survey Data with Selection Bias based on Statistical Decision Theory

The Role of Foreign Direct Investment in Economic Development of Developing Countries

Derive the importance of foreign direct investment in the world, particularly in the developing countries. FDI is critical for the developing countries which need multinational funding and expertise to expand, give structure, and guide their will to boost manufacturing and service sectors. Due to its role in promoting the growth and development wheel, providing financial resources complementary to national savings, and contributing to the transfer of technology and skills associated with modern production methods, it has emerged as one of the most significant sources of support for development. As the deteriorating economic conditions of developing countries did not leave them with many options or other solutions, their only option was to open their economies. The research touches on multiple subjects such as: Statistical Decision Theory by using statistical data to prove some of the research points, Multidimensional Statistical Analysis, Financial Econometrics which includes the financial related remarks as GDP part of the research, etc. In this sense, the goals of this paper are to highlight the importance of FDI in achieving the development in developing countries.

On the radiometric resolution of SAR signals

In accordance with the provisions of the theory of statistical decisions, an expression for the error probability of discriminating the intensities of two signals as a function of the radiometric resolution of a synthetic aperture radar is obtained. The result of observing fluctuations at the input of the processing channel over a finite interval is represented by a sequence of complex samples that are the sum of samples of uncorrelated normal noise and signal samples. This sequence is considered as a normal complex random vector with a specified normalized correlation matrix, while the processing algorithm is assumed to be given. The proposed approach is compared with known methods for determining the radiometric resolution: the heuristic method and the differential radio contrast method. The advantages of the proposed method are demonstrated.

Rationality Now!

Rationality Now!