Statistical Decision Research Articles

Minimax Efficient Random Experimental Design Strategies With Application to Model-Robust Design for Prediction

In game theory and statistical decision theory, a random (i.e., mixed) decision strategy often outperforms a deterministic strategy in minimax expected loss. As experimental design can be viewed as a game pitting the Statistician against Nature, the use of a random strategy to choose a design will often be beneficial. However, the topic of minimax-efficient random strategies for design selection is mostly unexplored, with consideration limited to Fisherian randomization of the allocation of a predetermined set of treatments to experimental units. Here, for the first time, novel and more flexible random design strategies are shown to have better properties than their deterministic counterparts in linear model estimation and prediction, including stronger bounds on both the expectation and survivor function of the loss distribution. Design strategies are considered for three important statistical problems: (i) parameter estimation in linear potential outcomes models, (ii) point prediction from a correct linear model, and (iii) global prediction from a linear model taking into account an L 2-class of possible model discrepancy functions. The new random design strategies proposed for (iii) give a finite bound on the expected loss, a dramatic improvement compared to existing deterministic exact designs for which the expected loss is unbounded. Supplementary materials for this article are available online.

Timely and Accurately Predict Rainfall by using Ensemble Predictive Models

Weather and rainfall are important factors for human life. By depends upon the rainfall agriculture, horticulture harvesting, and goods transportation. These all are goods and supply chain processes. If in supply chain process breaks any point, Ultimately, the farmer will get the loss. Timely predicting rainfall helps the farmers and agriculture and horticulture stock manage to maintain people require India’s coastal area. For these reasons, this paper proposes the Ensemble Models (Catboost, Boost). Most of the authors are working on rainfall prediction using statistical models. Using statistical models to analyze and predict a huge amount of data is very difficult, depending upon the features. But using Ensemble models is likely to boost up the elements, and apply the classification to prediction makes it easy. This paper discusses and Compares the statistical decision tree model with ensemble models to find out the difference between the characteristics of algorithms and how they impact the timely predict the rainfall.

New hybrid-based approach for improving the accuracy of coastal aquifer vulnerability assessment maps

Due to excessive exploitation, groundwater resources of coastal regions are exposed to seawater intrusion. Therefore, vulnerability assessments are essential for the quantitative and qualitative management of these resources. The GALDIT model is the most widely used approach for coastal aquifer vulnerability assessment, but suffers from subjectivity of the identification of rates and weights. This study aimes at developing a new hybrid framework for improving the accuracy of coastal aquifer vulnerability assessment using various statistical, metaheuristic, and Multi-Attribute Decision Making (MADM) methods to improve the GALDIT model. The Gharesoo-Gorgan Rood coastal aquifer in northern Iran is used as study site. In order to meet this aim, the Differential Evolution (DE) and Biogeography-Based Optimization (BBO) metaheuristic algorithms were employed to optimize the GALDIT weights. In addition, a novel MADM method, named Step-wise Weight Assessment Ratio Analysis (SWARA), and the bivariate statistical method called statistical index (SI) were used to modify the GALDIT ratings. Finally, correlation coefficients between the maps obtained from each method and Total Dissolved Solid (TDS) as an indicator of seawater intrusion were computed to evaluate the models' prediction power. Correlation coefficients of 0.72, 0.75, 0.76 and 0.78 were obtained for the GALDITSWARA-BBO, GALDITSI-BBO, GALDITSWARA-DE and GALDITSI-DE models, respectively. The results from the GALDITSI-DE model outperformed all other models at improving the accuracy of the vulnerability assessment. Moreover, the statistical-metaheuristic method yielded more accurate results than SWARA-metaheuristic hybrid models. The vulnerability map of the studied region indicates that the northwestern and western areas are very highly vulnerable. According to GALDITSI-DE model, 42%, 17%, 18% and 22% of the aquifer areas respectively have a low, medium, high and very high vulnerability to seawater intrusion. The research findings could be applied by regional authorities to manage and protect groundwater resources.

RRH Clustering Using Affinity Propagation Algorithm with Adaptive Thresholding and Greedy Merging in Cloud Radio Access Network.

Affinity propagation (AP) clustering with low complexity and high performance is suitable for radio remote head (RRH) clustering for real-time joint transmission in the cloud radio access network. The existing AP algorithms for joint transmission have the limitation of high computational complexities owing to re-sweeping preferences (diagonal components of the similarity matrix) to determine the optimal number of clusters as system parameters such as network topology. To overcome this limitation, we propose a new approach in which preferences are fixed, where the threshold changes in response to the variations in system parameters. In AP clustering, each diagonal value of a final converged matrix is mapped to the position (x,y coordinates) of a corresponding RRH to form two-dimensional image. Furthermore, an environment-adaptive threshold value is determined by adopting Otsu’s method, which uses the gray-scale histogram of the image to make a statistical decision. Additionally, a simple greedy merging algorithm is proposed to resolve the problem of inter-cluster interference owing to the adjacent RRHs selected as exemplars (cluster centers). For a realistic performance assessment, both grid and uniform network topologies are considered, including exterior interference and various transmitting power levels of an RRH. It is demonstrated that with similar normalized execution times, the proposed algorithm provides better spectral and energy efficiencies than those of the existing algorithms.

Model Selection for Treatment Choice: Penalized Welfare Maximization

This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best‐subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model‐selection using a “holdout” procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.

Statistical Decision Functions with Judgment

A decision maker tests whether the gradient of the loss function evaluated at a judgmental decision is zero. If the test does not reject, the action is the judgmental decision. If the test rejects, the action sets the gradient equal to the boundary of the rejection region. This statistical decision rule is admissible and conditions on the sample realization. The confidence level reflects the decision maker’s aversion to statistical uncertainty. The decision rule is applied to a problem of asset allocation. JEL Classification: C1, C11, C12, C13, D81

Quickest Detection of COVID-19 Pandemic Onset.

This paper develops an easily-implementable version of Page's CUSUM quickest-detection test, designed to work in certain composite hypothesis scenarios with time-varying data statistics. The decision statistic can be cast in a recursive form and is particularly suited for on-line analysis. By back-testing our approach on publicly-available COVID-19 data we find reliable early warning of infection flare-ups, in fact sufficiently early that the tool may be of use to decision-makers on the timing of restrictive measures that may in the future need to be taken.

The Effects of Parametric, Non-Parametric Tests and Processes in Inferential Statistics for Business Decision Making <br/>—A Case of 7 Selected Small Business Enterprises in Uganda

The article gives a critique of parametric and nonparametric tests and processes of inferential statistics in forecasting customer flows in 7 selected small business enterprises in Uganda. Forecasting is one of the decision making tools in a business enterprise. This may include forecasting customer flows, volumes of sales and many others. This is a vital component of small businesses success. In the long run, what drives business success is the quality of decisions and their implementation. Decisions based on a foundation of knowledge and sound reasoning can lead the company into long-term prosperity; conversely, decisions made on the basis of flawed logic, emotionalism, or incomplete information can quickly put a business out of commission. In many instances, business decisions have been guided by parametric tests and processes and /or non-parametric tests and processes of inferential statistics, which have subsequently affected the futures of business differently. As we refer to population mean knowledge for hypothesis testing using parametric tests, we only refer to mediums for samples, for nonparametric tests. A parameter is a characteristic that describes a population. These may include μ (the Mean), δ2 (the variance) of a distribution. We commonly refer to the normal distribution, when it is symmetric, with the measures of central tendency (Mean = medium = mode). Usually these parameters are very useful, when testing hypotheses to enable researchers and decision makers infer about the population using samples. It would always be better to have knowledge of or/and about the population parameters, but more often than not, we find ourselves with very minimal, or no knowledge about the population parameters. To make the generalization about the population from the sample, statistical tests are used. In other words, we want to know if we have relationships, associations, or differences within our data and whether statistical significance exists. Inferential statistics help us make these determinations and allow us to generalize the results to a larger population. We employ parametric and nonparametric statistics to show basic inferential statistics by examining the associations among variables and tests of differences between groups. It is recommended by many scholars that business analysis uses parametric and nonparametric inferential statistics in making decisions about effects of independent variables on dependent variables. On the contrary, it is argued that the use of inferential statistics adds nothing to the complex and admittedly subjective, no statistical methods that are often employed in applied business decision making analysis. There are several attacks made on inferential statistics, perhaps with increasing frequency, by those who are not business analysts. These attackers are not in for the use of inferential statistics in research and business decision making, and commonly recommend the use of interval estimation or the method of confidence intervals. However, interval estimation is shown to be contrary to the fundamental assumption of business decision making analysis.

Analysis of Retailer and Corporate Payment Habits in Hungary

The study looks at the payment habits of retailers and companies in Hungary, especially the acceptance and share of electronic payments in 2019. In doing so, data from two questionnaire-based surveys and the online cash register database are analysed using statistical methods, decision trees and regressions. The results show that retailer payments are typically cash intensive, while credit transfer transactions dominate at companies. The factors with the largest impact on card acquiring and the share of cash at points of sale is sales revenue and the value of the purchase in the case of retailers, and the proportion of cash wage payments in the case of companies. Costs also play an important role in card acquiring, therefore instant payment, which provides cheaper electronic payment solutions, could be crucial when it comes to smaller retailers and companies offering electronic payments. Public policy measures could mainly target retailers and the micro and small enterprise segment.

Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own seminal development of statistical decision theory. Haavelmo favorably cited Wald, but econometrics did not embrace statistical decision theory. Instead, it focused on study of identification, estimation, and statistical inference. This paper proposes use of statistical decision theory to evaluate the performance of models in decision making. I consider the common practice ofas‐if optimization: specification of a model, point estimation of its parameters, and use of the point estimate to make a decision that would be optimal if the estimate were accurate. A central theme is that one should evaluate as‐if optimization or any other model‐based decision rule by its performance across the state space, listing all states of nature that one believes feasible, not across the model space. I apply the theme to prediction and treatment choice. Statistical decision theory is conceptually simple, but application is often challenging. Advancing computation is the primary task to complete the foundations sketched by Haavelmo and Wald.

Comprehensive evaluation of combining CFD simulation and entropy weight to predict natural ventilation strategy in a sliding cover solar greenhouse

This study proposed a comprehensive evaluation system to incorporate the contribution of both numerical simulation and statistical decision theory in ventilation performance assessment. A high-resolution model based on the finite volume approach was established to analyze the influence of rotation angles (i.e., side vent flip angle and roof vent flip angle) of the rack-and-pinion ventilated structure on the greenhouse microclimate. The water circulating system and tomato seeding canopies were considered. Heat removal efficiency and mean age of air were employed as quantitative attributes to reflect the internal thermal environment and the airflow organization in the sliding cover solar greenhouse. The simulation model was verified with the temperature profile measured and the average relative error was 1.74%. The results demonstrate that the rotating angles of ventilation schemes have a substantial impact on the microclimate and inhomogeneity of the tomato seeding canopies. The results suggest the average velocity and its inhomogeneity are the crucial predictors, and their entropy weight values are 0.231 and 0.218, respectively. The relative degree of membership of the side vent flip angle of 45° is 36% and 97% higher than that of the side vent flip angle of 35° and the side vent flip angle of 25°, respectively. This study can provide a reference to evaluate the ventilated strategies of the sliding cover solar greenhouse for the regional and central government. Keywords: sliding cover solar greenhouse, natural ventilation, CFD simulation, entropy weight, comprehensive evaluation DOI: 10.25165/j.ijabe.20211406.6793 Citation: Li H, Ji D, Hu X, Xie T, Song W T, Tian S B. Comprehensive evaluation of combining CFD simulation and entropy weight to predict natural ventilation strategy in a sliding cover solar greenhouse. Int J Agric & Biol Eng, 2021; 14(6): 213–221.

Methods of comprehensive statistical analysis

The article presents an algorithm of a complicated statistical analysis of atmospheric air pollution over certain urban territories, based on methods of multivariate statistical analysis and a statistical decisions theory. Statistical analysis of the concentrations obtained from the observation posts network provides the data on the atmospheric air pollution background characteristics. This analysis enables us to find the spatial correlations between the concentrations of the ingredient under various synoptic conditions. The proposed set of statistical methods is advisable to be applied in the development of a state monitoring program for atmospheric air protection over specific zones or territories (urban agglomeration) as part of the implementation of a new management procedure for state monitoring of atmospheric air protection in Ukraine.

ЗАСТОСУВАННЯ ЗМІШАНИХ СТРАТЕГІЙ ПРИ УПРАВЛІННІ МІЖНАРОДНИМИ ВАНТАЖНИМИ ПЕРЕВЕЗЕННЯМИ

This article considers the use of the mathematical apparatus of the theory of games with nature to model such a socio-economic phenomenon as the process of international freight transportation when performing delivery by own and borrowed vehicles on Kyiv-Warsaw route. Calculations are made with the use of existing costs and tariffs for the selected direction of transportation. The object of research is the process of international freight transportation management. The purpose of the work is to study the peculiarities of decision-making with the use of mixed strategies. The research method is the theory of statistical decisions, namely the theory of decision-making in the conditions of playing with nature. The player, i.e. the person who will make the decision, is the company that performs the carriage of goods by road in international traffic and is fully responsible for organizing the process of delivery of goods by road on the route. The situation is modeled using variants of various demand for transportation. This demand acts as the uncertainty of different variations of nature's strategies. Recommendations are given for the application of four decision making criteria: Wald, Savage, Laplace and Hurwitz criteria. Appropriate calculations were performed and the obtained results were commented on, because each criterion offers a new solution to a given situation. Calculations of application of mixed strategies are presented in the Excel spreadsheet. KEY WORDS: GAME THEORY, DECISION MAKING CRITERIA, UNCERTAINTY CONDITIONS, RISK, STRATEGY, INTERNATIONAL FREIGHT TRANSPORTATION

Probabilistic Prediction for Binary Treatment Choice: With Focus on Personalized Medicine

This paper extends my research applying statistical decision theory to treatment choice with sample data, using maximum regret to evaluate the performance of treatment rules. The specific new contribution is to study as-if optimization using estimates of illness probabilities in clinical choice between surveillance and aggressive treatment. Beyond its specifics, the paper sends a broad message. Statisticians and computer scientists have addressed conditional prediction for decision making in indirect ways, the former applying classical statistical theory and the latter measuring prediction accuracy in test samples. Neither approach is satisfactory. Statistical decision theory provides a coherent, generally applicable methodology.

Comparison of Information Structures for Zero-Sum Games and a Partial Converse to Blackwell Ordering in Standard Borel Spaces

In statistical decision theory involving a single decision maker, an information structure is said to be better than another one if for any cost function involving a hidden state variable and an ac...

Developing Genomic Predictive Biomarkers for Survival Benefit from Adjuvant Chemotherapy in Early-Stage Lung Cancer Patients for Personalized Medicine

Surgical resection only remains the standard choice for the treatment of early-stage non-small cell lung cancer (NSCLC) patients. Preliminary studies suggest that the application of adjuvant chemotherapy with surgery (ACT) is associated with a better prognosis for more severe NSCLC patients compared to those who only underwent surgical resection. However, at an individual level, not all patients may benefit from ACT. Given the well-known adverse effects and toxicity of ACT, finding the patients that are most likely to benefit from ACT is paramount. Thus, the purpose of this research is to utilize gene expression and clinical data from lung cancer patients to develop a statistical decision support algorithm to find predictive genomic biomarkers and identify subgroups of patients who benefit from ACT. Cox regression models are trained using a randomized controlled trial gene expression data from the National Center for Biotechnology Information (NCBI) utilizing explicit treatment interaction terms. To handle high dimensions inherent in gene expression data, a regularized Cox regression model with lasso penalty is applied to find the most significant interacting markers. Risk scores are estimated from the proposed model and are used to stratify patients into a high risk or low risk group respective to ACT treatment. After applying the model to an independent validation genomic data set, we show that patients who underwent the recommended treatment according to their risk group estimated by our proposed algorithm exhibit a slightly higher survival rate than those who do not.

A Novel Unified Computational Approach to Constructing Shortest-Length or Equal Tails Confidence Intervals in Terms of Pivotal Quantities and Quantile Functions

A confidence interval is a range of values that gives the user a sense of how precisely a statistic estimates a parameter. In the present paper, a new simple computational method is proposed for simultaneous constructing and comparing confidence intervals of shortest length and equal tails in order to make efficient decisions under parametric uncertainty. This method represents a simple and computationally attractive numerical technique for finding the shortest-length and equal tails confidence intervals using pivotal quantities, which are developed from either maximum likelihood estimates or sufficient statistics. In statistics, a pivotal quantity (or pivot) is a function of observations and unobservable parameters such that the function’s probability distribution does not depend on the unknown parameters (including nuisance parameters). Finding a pivotal quantity is not discussed, but the choice a “good” pivotal quantity is essential for the resulting confidence interval to be useful. The unified computational technique yields intervals in several situations which have previously required separate analyses using more advanced techniques and tables for numerical solutions. Unlike the Bayesian approach, the proposed approach is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate nuisance parameters from the problem via the technique of invariant statistical embedding and averaging in terms of pivotal quantities (ISE&APQ). It should be noted that the well-known classical approach to constructing confidence intervals of the shortest length considers at least three versions of possible solutions and is in need of information about the form of the probability distribution of pivotal quantity in order to determine an adequate version of the correct solution. The proposed method does not need such information. It receives this information through the quantiles of the probability distribution of pivotal quantity. Therefore, the proposed method automatically recognizes an adequate version of the correct solution. To illustrate this method, numerical examples are given. In detail, the Pareto distribution is discussed.

Admissibility of Solution Estimators for Stochastic Optimization

We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample...

Non-Cooperative Spectrum Sensing Based on Cyclostationary Model of Digital Signals in the Context of Cognitive Radio

This paper addresses the problem of the opportunistic spectrum access in Cognitive Radio. Indeed, most spectrum sensing algorithms suffer from a high computational cost to achieve the detection process. They need a prior knowledge of signal characteristics and present a bad performance in low Signal to Noise Ratio (SNR) environment. The choice of the optimal detection threshold is another issue for these spectrum sensing algorithms. To overcome the limits of spectrum detectors, we propose in this paper, a blind detection method based on the cyclostationary features of communication signals. Our detector evaluates the level of hidden periodicity contained in the observed signal to make decision on the state of a bandwidth. In order to reduce the computational cost, we take advantage of the FFT Accumulation Method to estimate the cyclic spectrum of the observed signal. Then, we generate the Cyclic Domain Profile of the cyclic spectrum which allows us to evaluate the level of the hidden periodicity in the signal. This level of periodicity is quantified through the crest factor of Cyclic Domain Profile, which represents the decision statistic of the proposed detector. We have established the analytic expression of the optimal threshold of the detection and the probability of detection to evaluate the performance of the proposed detector. Simulation results show that the proposed detector is able to detect the presence of a communication signal on a bandwidth in a very low SNR scenario.

Distributed Decision Fusion with M-ary Signaling and k-bit Transmission on Sensor Observation in Wireless Sensor Networks

Multi-level decisions on sensor detection is able to improve the detection performance on the final decision made at the fusion center (FC) in wireless sensor networks (WSN). In this paper, the performance analysis of an M-ary signaling (MS) scheme using analog transmission and a k-bit transmission (KB) scheme is both examined for distributed binary detection. Under the multi-level decision algorithms, each sensor sends a signal carrying the information of a quantized version of a local decision statistic such as the conditional mean or the log-likelihood ratio. In MS, the output of the quantizer is transmitted directly without digitalizing and coding process, while in KB, each quantization output is coded with k bits and hereby a sensor sends a k-bit hard local decision to the FC. At the FC, the linear combiner detection rule on the transmission schemes is both adopted to make the final decision. The effects of the sensor decision and the transmission errors are incorporated in the analysis of the erroneous performance of the final decision. The goal of the proposed schemes is to minimize the final errors at the FC via optimizing the region allocation on the multi-level decision at the sensor. The numerical results illustrate that the proposed schemes achieve significant improvement in error performance over the conventional schemes under either additive white Gaussian noise (AWGN) channel or Rayleigh faded channel.