# Operations Research, Systems Engineering and Industrial Engineering Commons™

Series

2005

Statistics and Probability

Keyword

Articles 1 - 3 of 3

## Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Likelihood-Based Statistical Estimation From Quantized Data, Stephen B. Vardeman, Chiang-Sheng Lee Jan 2005

#### Likelihood-Based Statistical Estimation From Quantized Data, Stephen B. Vardeman, Chiang-Sheng Lee

##### Industrial and Manufacturing Systems Engineering Publications

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.

Sheppard's Correction For Variances And The "Quantization Noise Model", Stephen B. Vardeman Jan 2005

#### Sheppard's Correction For Variances And The "Quantization Noise Model", Stephen B. Vardeman

##### Industrial and Manufacturing Systems Engineering Publications

In this paper, we examine the relevance of Sheppard's correction for variances and (both the original and a valid weak form of) the so-called "quantization noise model" to understanding the effects of integer rounding on continuous random variables. We further consider whether there is any real relationship between the two. We observe that the strong form of the model is not really relevant to describing rounding effects. We demonstrate using simple cases the substantial limitations of the Sheppard correction, and use simple versions of a weak form of the model to establish that there is no real connection between ...

Likelihood And Bayesian Methods For Accurate Identification Of Measurement Biases In Pseudo Steady-State Processes, Sriram Devanathan, Stephen B. Vardeman, Derrick K. Rollins Sr. Jan 2005

#### Likelihood And Bayesian Methods For Accurate Identification Of Measurement Biases In Pseudo Steady-State Processes, Sriram Devanathan, Stephen B. Vardeman, Derrick K. Rollins Sr.

##### Industrial and Manufacturing Systems Engineering Publications

Two new approaches are presented for improved identification of measurement biases in linear pseudo steady-state processes. Both are designed to detect a change in the mean of a measured variable leading to an inference regarding the presence of a biased measurement. The first method is based on a likelihood ratio test for the presence of a mean shift. The second is based on a Bayesian decision rule (relying on prior distributions for unknown parameters) for the detection of a mean shift. The performance of these two methods is compared with that of a method given by Devanathan et al. (2000 ...