Consider a set of real valued observations collected over time. We pro¬pose a simple hidden Markow model for these realizations in which the the predicted distribution of the next future observation given the past is easily computed. The hidden or unobservable set of parameters is assumed to have a Markov structure of a special type. The model is quite flexible and can be used to incorporate different types of prior information in straightforward and sensible ways.
Most standard statistical methods treat numerical data as if they were real (infinite-number-of-decimal-places) observations. The issue of quantization or digital resolution can render such methods inappropriate and misleading. This article discusses some of the difficulties of interpretation and corresponding difficulties of inference arising in even very simple measurement contexts, once the presence of quantization is admitted. It then argues (using the simple case of confidence interval estimation based on a quantized random sample from a normal distribution as a vehicle) for the use of statistical methods based on "rounded data likelihood functions" as an effective way of handling the matter.
When training for hazardous operations, real-time stress detection is an asset for optimizing task performance and reducing stress. Stress detection systems train a machine-learning model with physiological signals to classify stress levels of unseen data. Unfortunately, individual differences and the time-series nature of physiological signals limit the effectiveness of generalized models and hinder both post-hoc stress detection and real-time monitoring. This study evaluated a personalized stress detection system that selects a personalized subset of features for model training. The system was evaluated post-hoc for real-time deployment. Further, traditional classifiers were assessed for error caused by indirect approximations against a benchmark, optimal probability classifier (Approximate Bayes; ABayes). Healthy participants completed a task with three levels of stressors (low, medium, high), either a complex task in virtual reality (responding to spaceflight emergency fires, n=27) or a simple laboratory-based task (N-back, n=14). Heart rate, blood pressure, electrodermal activity, and respiration were assessed. Personalized features and different interval window sizes were compared. Classification performance was compared for ABayes, support vector machine, decision tree, and random forest. The results demonstrate that a personalized model with time series intervals can classify three stress levels with high accuracy better than a generalized model. However, cross-validation and holdout performance varied for traditional classifiers vs. ABayes, suggesting error from indirect approximations. The selected features changed with windows size and differed between tasks, but blood pressure contributed to the most prominent features. The capability to account for individual difference is a prominent advantage of personalized models, and will likely have a growing presence in future detection systems.
An important prerequisite of any sensible data-based engineering study is the quantification of the precision of gauges or measuring equipment to be used in data collection. It has long been understood that in the event that more than one individual will use a particular gauge, “measurement variation” for that gauge can include not only a kind of “pure error” component but an “operator” or “technician” component as well. Furthermore, it is well known that the two-way random-effects model provides a natural framework for quantifying the different components of measurement variation. Some parts of standard practice in the “gauge R&R studies” aimed at quantifying measurement precision, however, are unfortunately at odds with what makes sense under this model. Thus, the purpose of this primarily expository article is to explain in elementary terms the use of a two-way random-effects model for gauge R&R studies, to critique current practice, and to point out some simple improvements that can follow from more careful attention to the model and well-established practice in the general linear model.
Abstract DeGroot and Fienberg (1982a) recently considered various aspects of the problem of evaluating the performance of probability appraisers. After briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts. We then discuss some simple Bayesian mechanisms for making probability assessments and study their calibration, semicalibration, sufficiency, and domination properties. Finally, several results concerning the comparison of finite dichotomous experiments, relevant to the present work, are collected in an Appendix.
We consider hierarchical Bayes analyses of an experiment conducted to enable calibration of a set of mass-produced resistance temperature devices (RTDs). These were placed in batches into a liquid bath with a precise NIST-approved thermometer, and resistances and temperatures were recorded approximately every 30 seconds. Under the assumptions that the thermometer is accurate and each RTD responds linearly to temperature change, we use hierarchical Bayes methods to estimate the parameters of the linear calibration equations. Predictions of the parameters for an untested RTD of the same type, and interval estimates of temperature based on a realized resistance reading are also available (both for the tested RTDs and for an untested one produced under the same production process conditions).
An important prerequisite of any sensible data-based engineering study is the quantification of the precision of gauges or measuring equipment to be used in data collection. It has long been understood that in the event that more than one individual will use a particular gauge, “measurement variation” for that gauge can include not only a kind of “pure error” component but an “operator” or “technician” component as well. Furthermore, it is well known that the two-way random-effects model provides a natural framework for quantifying the different components of measurement variation. Some parts of standard practice in the “gauge R&R studies” aimed at quantifying measurement precision, however, are unfortunately at odds with what makes sense under this model. Thus, the purpose of this primarily expository article is to explain in elementary terms the use of a two-way random-effects model for gauge R&R studies, to critique current practice, and to point out some simple improvements that can follow from more c...
Abstract A state-space process-control model involving adjustment error and deterministic drift of the process mean is presented. The optimal adjustment policy is developed by dynamic programming. This policy calls for a particular adjustment when a Kalman-filter estimator is outside a deadband defined by upper and lower action limits. The effects of adjustment cost, adjustment variance, and drift rate on the optimal policy are discussed. The optimal adjustment policy is computed for a real machining process, and a simulation study is presented that compares the optimal policy to two sensible suboptimal policies. KEY WORDS: Control chartDeadbandDynamic programmingKalman filterSimulationState-space model
