Michael D. McKay's research while affiliated with Los Alamos National Laboratory and other places
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Publications (22)
Two methods for reducing the computer time necessary to investigate changes in distribution of random inputs to large simulation computer codes are presented. The first method produces unbiased estimators of functions of the output variable under the new distribution of the inputs. The second method generates a subset of the original outputs that h...
This paper addresses the analysis of uncertainty in the output of computer models arising from uncertainty in inputs (parameters). Uncertainty of this type, which is separate and distinct from the randomness of a stochas-tic model, most often arises when proper input values are imprecisely known. Uncertainty in the output is quantified in its proba...
A flyer plate experiment involves forcing a plane shock wave through stationary test
samples of material and measuring the free surface velocity of the target as a function of
time. These experiments are conducted to learn about the behavior of materials subjected
to high strain rate environments. Computer simulations of flyer plate experiments are...
When outputs of computational models are time series or functions of other continuous variables like distance, angle, etc., it can be that primary interest is in the general pattern or structure of the curve. In these cases, model sensitivity and uncertainty analysis focuses on the effect of model input choices and uncertainties in the overall shap...
The importance of individual inputs of a computer model is sometimes assessed using indices that reflect the amount of output variation that can be attributed to random variation in each input. We review two such indices, and consider input sampling plans that support estimation of one of them, the variance of conditional expectation or VCE (Mckay,...
this paper will illustrate the pursuit of a systematic treatment of this problem via an example. The validation of transmission of shock energy through a complex, jointed structural assembly is the problem of interest, and the solution uncertainty is neglected for the purposes of the example. (This neglecting is legitimate, as the uncertainties int...
The topic of this paper is experiment planning, particularly fractional factorial designs or orthogonal arrays, for computer experiments to assess important inputs. The work presented in the paper is motivated by considering a non-stochastic computer simulation which has many inputs and which can, in a reasonable period of time, be run thousands of...
Input values are a source of uncertainty for model predictions. When input uncertainty is characterized by a probability distribution, prediction uncertainty is characterized by the induced prediction distribution. Comparison of a model predictor based on a subset of model inputs to the full model predictor leads to a natural decomposition of the p...
This paper examines the feasibility and value of using nonparametric variance-based methods to supplement parametric regression methods for uncertainty analysis of computer models. It shows from theoretical considerations how the usual linear regression methods are a particular case within the general framework of variance-based methods. Examples o...
To develop activity-based travel models using microsimulation, individual travelers and households must be considered. Methods for creating baseline synthetic populations of households and persons using 1990 census data are given. Summary tables from the Census Bureau STF-3A are used in conjunction with the Public Use Microdata Sample (PUMS), and I...
When studying the probability distribution of an output from a model, it is essential that one examine the effects of uncertainties in the distribution of inputs. When the price that must be paid for model runs is high, there is a tendency to perform studies with a simplified approximation model. The value of these approaches is highly questionable...
Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators that includes the sample mean and the empirical distribution function. 6 figures.
Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
Sample sizes affect identification of important inputs for computer models. For illustrative purposes, a partial differential equations model with 84 input variables is used to investigate the behavior of Râ as an importance indicator for various sample sizes and designs.
The authors discussed some directions for research and development of methods for assessing simulation variability, input uncertainty, and structural model uncertainty. Variance-based measures of importance for input and simulation variables arise naturally when using the quadratic loss function of the difference between the full model prediction y...
Two types of sampling plans are presented as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to the variance of a class of estimators which includes the sample mean and the sample cumulative distribution function. The partial rank correlation coefficien...
Quantification of prediction uncertainty is an important consideration when using mathematical models of physical systems. This paper proposes a way to incorporate ''validation data'' in a methodology for quantifying uncertainty of the mathematical predictions. The report outlines a theoretical framework.
This paper, condensed from McKay et al. (1992) outlines an analysis of uncertainty in the output of computer models arising from uncertainty in inputs (parameters). Uncertainty of this type most often arises when proper input values are imprecisely known. Uncertainty in the output is quantified in its probability distribution, which results from tr...
In environmental surveillance work, one is often faced with the task of determining by a random sample that hazardous waste is stored safely. In many cases such waste is kept in drums which are accumulated at various sites, and some of these sites are thought to have a more deleterious effect on the drums than other sites. In this paper, knowledge'...
The field of computational structural dynamics is on the threshold of revolutionary change. The ever-increasing costs of physical experiments coupled with advances in massively parallel computer architecture are steering the engineering analyst to be more and more reliant on numerical calculations with little to no data available for experimental c...
Prediction uncertainty in stochastic simulation models can be described by a hierarchy of components: stochastic variability at the lowest level, input and parameter uncertainty at a higher level, and structural model uncertainty at the top. It is argued that a usual paradigm for analysis of input uncertainty is not suitable for application to stru...
Citations
... In general, optimization problems involve the maximization or minimization of a real objective function by selecting appropriate input variables within a permissible range and calculating the value of the objective function [188]. Optimization encompasses a diverse range of techniques and approaches employed in applied mathematics to tackle a wide array of problems [189,190]. ...
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... Variance Analysis McKay et al. (1992) suggests the conditional variance of the output as a meaningful measure of importance in identifying inputs having significant impact on the simulation results. Analogous to analysis of variance (ANOVA), output variability is decomposed into components that can each be attributable to an input variable of interest; these quantities are then compared to the total variability. ...
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... Consequently, we need to select an appropriate sampling method. Various methods are available, including uniform sampling with equidistant points, random sampling, Latin hypercube sampling [86,87], and Sobol sampling [88]. The choice of method is somewhat arbitrary, with greater impact when considering fewer time points, as its significance diminishes as the sample size approaches infinity. ...
... A small sample may not yield accurate statistical data, while a large sample will consume unnecessary computing resources. In [8], the authors described sample size effect for certain assessment of model input importance. This issue is also addressed in Schuyler's article [9] on ''how many trials is enough''. ...
... Note that for Brown legitimate stakeholders refers to those stakeholders who "either rightfully 7 Furthermore, combining multiple lines of evidence emphasises the role of experts' subjective judgement in weighing different lines of evidence when issuing a sensitivity estimate. This suggests a more significant role for experts' own values, albeit not all subjective factors are value-judgments (Morrison, 2014). participate in or affect the decisions in question, or who will be affected by the decision" (Brown, 2020, 21). ...
... Improvement to the LHS has been demonstrated by selecting LHS with a structure incorporating both orthogonal arrays and distance or correlation-based criteria (John, 1971;Johnson et al., 1990;Tang, 1993;Owen, 1994;Wu and Hamada, 2000). This approach to designing and conducting a simulation experiment provides data that supports both uncertainty analysis and sensitivity analysis (Moore and McKay, 2002). For the pandemic influenza sensitivity study, the experimental design was an orthogonal array-based LHS plan (strength three, allowing evaluation of main effects with reduced bias from two factor interactions), using 80 runs for each of the 24 mitigation scenarios and varying 40 input variables based on their input distributions for a total of 1920 runs. ...
... Statistical contributions to our discussion arise due to (i) use of observational data, (ii) the Bayesian treatment of all unknowns including fixed parameters as if they are random variables, and (iii) treatment of model errors as stochastic processes. Related research include [6,22]. ...
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... Firstly, the class of objective functions (e.g., [2,3]) consists of all transformations of the model outputs that do not modify the initial distribution of the model inputs. It includes transformations done by i) projecting the model outputs onto a given basis ( [4,5,6]), using the kernel-based principal components, using feature maps of the outputs ( [7,8,9]); ii) considering the probabilities of the stochastic and dynamic outputs to exceed a given threshold ( [10]), iii) using a regression-based classifier ( [11]), and iv) considering the membership functions from either a crisp (a.k.a binary) or fuzzy clustering ( [12]). ...
... Consider a pool of candidate samples containing realizations of the random vector generated by an arbitrary sampling technique, e.g., Latin Hypercube Sampling (LHS) [50,51] or Coherence sampling [8,52,53]. From this pool of candidates, we select the best sample using a method inspired by the sequential sampling proposed in [26] and based on Koksma-Hlawka inequality [54]. ...
... Refs. [19][20][21]). These methods consist of two main elements: feature extraction and quantitative assessment. ...
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