A Dynamic Approach to Linear Statistical Calibration with an Application in Microwave Radiometry

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the 'classical' approach and the 'inverse' regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing an dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM's framework is used to capture the time-varying parameters that maybe changing or drifting over time. Two separate DLM based models are presented in this paper. A simulation study is conducted where the two models are compared to some well known 'static' calibration approaches in the literature from both the frequentist and Bayesian perspectives. The focus of the study is to understand how well the dynamic statistical calibration methods performs under various signal-to-noise ratios, r. The posterior distributions of the estimated calibration points as well as the 95% coverage intervals are compared by statistical summaries. These dynamic methods are applied to a microwave radiometry data set.Comment: 26 pages, 10 figure

Dynamic Bayesian Nonlinear Calibration

Statistical calibration where the curve is nonlinear is important in many areas, such as analytical chemistry and radiometry. Especially in radiometry, instrument characteristics change over time, thus calibration is a process that must be conducted as long as the instrument is in use. We propose a dynamic Bayesian method to perform calibration in the presence of a curvilinear relationship between the reference measurements and the response variable. The dynamic calibration approach adequately derives time dependent calibration distributions in the presence of drifting regression parameters. The method is applied to microwave radiometer data and simulated spectroscopy data based on work by Lundberg and de Mar\'{e} (1980)

Outlier-Resistant L1 Orthogonal Regression via the Reformulation-Linearization Technique

Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. L2-based methods such as ordinary least squares and orthogonal regression can be used to determine this relationship. However, both of these methods become impaired when influential values are present. This problem becomes compounded when outliers confound standard diagnostics. This work proposes an L1-norm orthogonal regression method (L1OR) formulated as a nonconvex optimization problem. Solution strategies for finding globally optimal solutions are presented. Simulation studies are conducted to assess the resistance of the method to outliers and the consistency of the method. The method is also applied to real-world data arising from an environmental science application

A preliminary longitudinal study of white matter alteration in cocaine use disorder subjects

Background Previous diffusion tensor imaging (DTI) studies have consistently shown that subjects with cocaine use disorder (CocUD) had altered white matter microstructure in the corpus callosum. It is believed that these alterations are due to preexisting factors, chronic cocaine use, or both. However, there is no published longitudinal DTI study on human cocaine users yet which could shed light on the relationship between cocaine use and DTI findings. Methods This study used a longitudinal design and DTI to test if the white matter microstructure shows quicker alteration in CocUD subjects than controls. DTI data were acquired from eleven CocUD subjects who participated a treatment study and eleven non-drug-using controls at baseline (Scan 1) and after ten weeks (Scan 2). The baseline fractional anisotropy (FA), a general measure of white matter microstucture, and the change in FA (ΔFA, equals Scan 1 FA minus Scan 2 FA) were both compared between groups. Results The two groups did not show a difference in FA at baseline. The CocUD subjects had significantly greater ΔFA than the controls in the left splenium of the corpus callosum. In CocUD subjects, greater ΔFA in this region was associated with shorter lifetime cocaine use and greater number of positive cocaine urine samples collected during the treatment. Conclusion The finding in the left splenium is consistent with previous animal studies and provide indirect evidence about the effects of chronic cocaine use on white matter alterations. The subject sample size is small, therefore the results should be treated as preliminary

SEIRD Model for Qatar Covid-19 Outbreak: A Case Study

The Covid-19 outbreak of 2020 has required many governments to develop mathematical-statistical models of the outbreak for policy and planning purposes. This work provides a tutorial on building a compartmental model using Susceptibles, Exposed, Infected, Recovered and Deaths status through time. A Bayesian Framework is utilized to perform both parameter estimation and predictions. This model uses interventions to quantify the impact of various government attempts to slow the spread of the virus. Predictions are also made to determine when the peak Active Infections will occur

Racial Comparisons in Police Officer Bench Press Strength over 12.5 Years

International Journal of Exercise Science 7(2) : 140-151, 2014. Strength, when considering gender and race, provides a basis for training, hiring, and retention for police officers. The purpose of this study is to identify muscular strength differences among racial groups from initial-recruit to in-service tests. Strength variables included bench press, bench press/lean mass and bench press/body mass. Scores were retrieved for the 1990 to 1995 recruit classes and were paired to the 2006 in-service fitness log. Sample included 309 officers: 30 females (13 black, 17 white) and 279 males (41 black, 238 white). Mean age of recruit was 24.6 ± 3.4 years and for in-service was 37.1 ± 3.7 years. Time between tests was 12.5 ± 2.0 years. Bench press strength significantly increased for all gender and racial groups. Black males were significantly stronger in bench press at initial-recruit and at in-service than white males. All racial and gender groups increased in bench press/lean mass, however, the increase in white females was not significant. No differences were found between black and white females in all strength variables at both testing periods. Black males were significantly stronger than white males in bench press/body mass only at the initial-recruit test. White males showed a significant increase in bench press/body mass over time, but they did not reach the strength level of the black males at in-service. Police departments, with a properly designed physical fitness program, can expect to see increases in strength of personnel over the first half of their careers; however, there are gender and racial differences