scholarly journals A Novel Intelligent Technique of Invariant Statistical Embedding and Averaging via Pivotal Quantities for Optimization or Improvement of Statistical Decision Rules under Parametric Uncertainty

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Probability Distributions ◽  
Decision Rules ◽  
Parametric Uncertainty ◽  
Decision Criterion ◽  
Unknown Parameters ◽  
Statistical Decision ◽  
Intelligent Technique ◽  
Statistical Decisions ◽  
Statistical Tolerance ◽  
Future Outcomes

In the present paper, for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a decision criterion and averaging this criterion over pivots’ probability distributions is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging via pivotal quantities (ISE&APQ) is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate unknown parameters from the problem and to find the efficient statistical decision rules, which often have smaller risk than any of the well-known decision rules. The aim of the present paper is to show how the technique of ISE&APQ may be employed in the particular case of optimization, estimation, or improvement of statistical decisions under parametric uncertainty. To illustrate the proposed technique of ISE&APQ, illustrative examples of intelligent constructing exact statistical tolerance limits for prediction of future outcomes coming from log-location-scale distributions under parametric uncertainty are given

Effective Optimization of Statistical Decisions for Age Replacement Problems under Parametric Uncertainty

2017 ◽  
pp. 1-16
Author(s):  
N. A. Nechval ◽  
K. N. Nechval
Keyword(s):  
Original Problem ◽  
Decision Rules ◽  
Parametric Uncertainty ◽  
Statistical Technique ◽  
Unknown Parameters ◽  
Sample Statistic ◽  
Invariant Embedding ◽  
Replacement Model ◽  
Statistical Decisions ◽  
Age Replacement

In this chapter, an innovative model for age replacement is proposed. The costs included in the age replacement model are not assumed to be constants. For effective optimization of statistical decisions for age replacement problems under parametric uncertainty, based on a past random sample of lifetimes, the pivotal quantity averaging (PQA) approach is suggested. The PQA approach represents a simple and computationally attractive statistical technique. In this case, the transition from the original problem to the equivalent transformed problem (in terms of pivotal quantities and ancillary factors) is carried out via invariant embedding a sample statistic in the original problem. The approach allows one to eliminate unknown parameters from the problem and to find the better decision rules, which have smaller risk than any of the well-known decision rules. Unlike the Bayesian approach, the proposed approach is independent of the choice of priors. For illustration, numerical examples are given.

Intelligent Constructing Exact Tolerance Limits for Prediction of Future Outcomes Under Parametric Uncertainty

2021 ◽  
pp. 701-729
Author(s):  
Nicholas A. Nechval
Keyword(s):  
Parametric Uncertainty ◽  
Statistical Problem ◽  
Tolerance Limits ◽  
Novel Technique ◽  
Simulation Monte Carlo ◽  
Statistical Tolerance ◽  
Future Outcomes ◽  
Tolerance Factors ◽  
Two Parameter ◽  
Future Sample

The problem of constructing one-sided exact statistical tolerance limits on the kth order statistic in a future sample of m observations from a distribution of log-location-scale family on the basis of an observed sample from the same distribution is considered. The new technique proposed here emphasizes pivotal quantities relevant for obtaining tolerance factors and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. The exact tolerance limits on order statistics associated with sampling from underlying distributions can be found easily and quickly making tables, simulation, Monte Carlo estimated percentiles, special computer programs, and approximation unnecessary. Finally, numerical examples are given, where the tolerance limits obtained by using the known methods are compared with the results obtained through the proposed novel technique, which is illustrated in terms of the extreme-value and two-parameter Weibull distributions.

scholarly journals A Satisficing Framework for Environmental Policy Under Model Uncertainty

2021 ◽  
Author(s):  
Stergios Athanasoglou ◽  
Valentina Bosetti ◽  
Laurent Drouet
Keyword(s):  
Environmental Policy ◽  
Model Uncertainty ◽  
Probability Distributions ◽  
Success Probability ◽  
Economic Assessment ◽  
Decision Criterion ◽  
Probability Criterion ◽  
Change Context ◽  
Future Consumption ◽  
Point Of Departure

AbstractWe propose a novel framework for the economic assessment of environmental policy. Our main point of departure from existing work is the adoption of a satisficing, as opposed to optimizing, modeling approach. Along these lines, we place primary emphasis on the extent to which different policies meet a set of goals at a specific future date instead of their performance vis-a-vis some intertemporal objective function. Consistent to the nature of environmental policymaking, our model takes explicit account of model uncertainty. To this end, the decision criterion we propose is an analog of the well-known success-probability criterion adapted to settings characterized by model uncertainty. We apply our criterion to the climate-change context and the probability distributions constructed by Drouet et al. (2015) linking carbon budgets to future consumption. Insights from computational geometry facilitate computations considerably and allow for the efficient application of the model in high-dimensional settings.

scholarly journals Reporting of the Role of the Expert Searcher in Cochrane Reviews

2006 ◽  
Vol 1 (4) ◽  
pp. 3 ◽  
Author(s):  
Li Zhang ◽  
Margaret Sampson ◽  
Jessie McGowan
Keyword(s):  
Systematic Reviews ◽  
Search Strategy ◽  
Data Extraction ◽  
Cochrane Library ◽  
Eligibility Criteria ◽  
Statistical Decision ◽  
Cochrane Reviews ◽  
Statistical Decisions ◽  
Search Quality

Introduction - This study applied the principles of evidence based information practice to clarify the role of information specialists and librarians in the preparation of Cochrane systematic reviews and to determine whether information specialists impact the quality of searching in Cochrane systematic reviews. Objectives - This research project sought to determine how the contribution of the person responsible for searching in the preparation of Cochrane systematic reviews was reported; whether the contribution was recognized through authorship or acknowledgement; the qualifications of the searcher; and the association between the type of contributorship and characteristics of the search strategy, assessability, and the presence of certain types of errors. Methods - Data sources: The Cochrane Database of Systematic Reviews, The Cochrane Library 3 (2002). Inclusion criteria: The study included systematic reviews that met the following criteria: one or more sections of the Cochrane Highly Sensitive Search Strategy were utilised, primary studies were either randomised controlled trials (RCTs) or quasi-RCTs, and included and excluded studies were clearly identified. Data extraction: Two librarians assessed the searches for errors, establishing consensus on discordant ratings. Results - Of the 169 reviews screened for this project, 105 met all eligibility criteria. Authors fulfilled the searching role in 41.9% of reviews studied, acknowledged persons or groups in 13.3%, a combination in 9.5%, and the role was not reported in 35.2% of reviews. For the 78 reviews in which meta-analyses were performed, the positions of those responsible for statistical decisions were examined for comparative purposes. The statistical role was performed by an author in 47.4% of cases and unreported in the same number of cases. Insufficient analyzable data was obtained regarding professional qualifications (3/105 for searching, 2/78 for statistical decisions). Search quality was assessed for 66 searches across 74 reviews. In general, it was more possible to assess the search quality when the searcher role was reported. An association was found between the reporting of searcher role and the presence of a consequential error. There was no association between the number of consequential errors and how the contribution of the searcher was reported. Conclusions - Qualifications of the persons responsible for searching and statistical decision-making were poorly reported in Cochrane reviews, but more complete role reporting is associated with greater assessability of searches and fewer substantive errors in search strategies.

scholarly journals Statistical sequential hypotheses testing on para meters of probability distributions of random binary data

2021 ◽  
pp. 60-66
Author(s):  
Alexey Yu. Kharin
Keyword(s):  
Binary Data ◽  
Random Number ◽  
Probability Distributions ◽  
Mathematical Problem ◽  
Decision Rules ◽  
Performance Characteristics ◽  
Sequential Testing ◽  
Computer Data ◽  
Independent Observations ◽  
Error Probabilities

An important mathematical problem of computer data analysis – the problem of statistical sequential testing of simple hypotheses on parameters of probability distributions of observed binary data – is considered in the paper. This problem is being solved for two models of observation: for independent observations and for homogeneous Markov chains. Explicit expressions of the sequential tests statistics are derived, transparent for interpretation and convenient for computer realisation. An approach is developed to calculate the performance characteristics – error probabilities and mathematical expectations of the random number of observations required to guarantee the requested accuracy for decision rules. Asymptotic expansions for the mentioned performance characteristics are constructed under «contamination» of the probability distributions of observed data.

Adaptive Synchronized Control for a Planar Parallel Manipulator: Theory and Experiments

2005 ◽  
Vol 128 (4) ◽  
pp. 976-979 ◽  
Author(s):  
Lu Ren ◽  
James K. Mills ◽  
Dong Sun
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Control Method ◽  
Parametric Uncertainty ◽  
Synchronization Error ◽  
Tracking Accuracy ◽  
Unknown Parameters ◽  
High Acceleration ◽  
Planar Parallel Manipulator ◽  
Synchronized Control

In this paper, we develop a new control method, termed adaptive synchronized (A-S) control, for improving tracking accuracy of a P-R-R type planar parallel manipulator with parametric uncertainty. The novelty of A-S control, a combination of synchronized control and adaptive control, is in the application of synchronized control to a single parallel manipulator so that tracking accuracy is improved during high-speed, high-acceleration tracking motions. Through treatment of each chain as a submanipulator; the P-R-R manipulator is thus modeled as a multi-robot system comprised of three submanipulators grasping a common payload. Considering the geometry of the platform, these submanipulators are kinematically constrained and move in a synchronous manner. To solve this synchronization control problem, a synchronization error is defined, which represents the coupling effects among the submanipulators. With the employment of this synchronization error, tracking accuracy of the platform is improved. Simultaneously, the estimated unknown parameters converge to their true values through the use of a bounded-gain-forgetting estimator. Experiments conducted on the P-R-R manipulator demonstrate the validity of the approach.

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