Functional Data Analysis on Test Science Research Document Library https://research.testscience.org/keywords/functional-data-analysis/ Recent content in Functional Data Analysis on Test Science Research Document Library Hugo -- 0.129.0 en-us Institute for Defense Analyses Mon, 01 Jan 2024 00:00:00 +0000 A Preview of Functional Data Analysis for Modeling and Simulation Validation https://research.testscience.org/post/2024-a-preview-of-functional-data-analysis-for-modeling-and-simulation-validation/ Mon, 01 Jan 2024 00:00:00 +0000 https://research.testscience.org/post/2024-a-preview-of-functional-data-analysis-for-modeling-and-simulation-validation/ Modeling and simulation (M&S) validation for operational testing often involves comparing live data with simulation outputs. Statistical methods known as functional data analysis (FDA) provides techniques for analyzing large data sets (“large” meaning that a single trial has a lot of information associated with it), such as radar tracks. We preview how FDA methods could assist M&S validation by providing statistical tools handling these large data sets. This may facilitate analyses that make use of more of the data available and thus allows for better detection of differences between M&S predictions and live test results.

Modeling and simulation (M&S) validation for operational testing often involves comparing live data with simulation outputs. Statistical methods known as functional data analysis (FDA) provides techniques for analyzing large data sets (“large” meaning that a single trial has a lot of information associated with it), such as radar tracks. We preview how FDA methods could assist M&S validation by providing statistical tools handling these large data sets. This may facilitate analyses that make use of more of the data available and thus allows for better detection of differences between M&S predictions and live test results. We demonstrate some fundamental FDA approaches with a notional example of live and simulated radar tracks of a bomber’s flight

Suggested Citation

Medlin, Rebecca M, and Curtis G Miller. A Preview of Functional Data Analysis for Modeling and Simulation Validation. IDA Product ID 3001829. Alexandria, VA: Institute for Defense Analyses, 2024.

Slides:

]]> Regularization for Continuously Observed Ordinal Response Variables with Piecewise-Constant Functional Predictors https://research.testscience.org/post/2016-regularization-for-continuously-observed-ordinal-response-variables-with-piecewise-constant-functional-predictors/ Fri, 01 Jan 2016 00:00:00 +0000 https://research.testscience.org/post/2016-regularization-for-continuously-observed-ordinal-response-variables-with-piecewise-constant-functional-predictors/ This paper investigates regularization for continuously observed covariates that resemble step functions. The motivating examples come from operational test data from a recent United States Department of Defense (DoD) test of the Shadow Unmanned Air Vehicle system. The response variable, quality of video provided by the Shadow to friendly ground units, was measured on an ordinal scale continuously over time. Functional covariates, altitude and distance, can be well approximated by step functions. This paper investigates regularization for continuously observed covariates that resemble step functions. The motivating examples come from operational test data from a recent United States Department of Defense (DoD) test of the Shadow Unmanned Air Vehicle system. The response variable, quality of video provided by the Shadow to friendly ground units, was measured on an ordinal scale continuously over time. Functional covariates, altitude and distance, can be well approximated by step functions. Two approaches for regularizing these covariates are considered, including a thinning approach commonly used within the DoD to address autocorrelated time series data, and a novel “smoothing” approach, which first approximates the covariates as step functions and then treats each “step” as a uniquely observed data point. Data sets resulting from both approaches are fit using a mixed model cumulative logistic regression, and we compare their results. While the thinning approach identifies altitude as having a significant impact on video quality, the smoothing approach finds no evidence of an effect. This difference is attributable to the larger effective sample size produced by thinning. System characteristics make it unlikely that video quality would degrade at higher altitudes, suggesting that the thinning approach has produced a Type 1 error. By accounting for the functional characteristics of the covariates, the novel smoothing approach has produced a more accurate characterization of the Shadow’s ability to provide full motion video to supported units.

Suggested Citation

Avery, Matthew, Mark Orndorff, Timothy Robinson, and Laura Freeman. “Regularization for Continuously Observed Ordinal Response Variables with Piecewise-Constant Functional Covariates.” Quality and Reliability Engineering International 32, no. 6 (2016): 2033–42. https://doi.org/10.1002/qre.2037.

Paper:

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