Statistical Inference in Linear Models. Statistical Methods of Model Building, Vol 1.

1987 ◽  
Vol 150 (2) ◽  
pp. 169
Author(s):  
M. Stone ◽  
Helga Bunke ◽  
Olaf Bunke
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Model Building ◽  
Linear Models

Non-Standard Parametric Statistical Inference

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Model Building ◽  
Parametric Bootstrap ◽  
Basic Knowledge ◽  
Standard Theory ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Bootstrap Resampling ◽  
Distributional Properties

This book discusses the fitting of parametric statistical models to data samples. Emphasis is placed on (i) how to recognize situations where the problem is non-standard, when parameter estimates behave unusually, and (ii) the use of parametric bootstrap resampling methods in analysing such problems. Simple and practical model building is an underlying theme. A frequentist viewpoint based on likelihood is adopted, for which there is a well-established and very practical theory. The standard situation is where certain widely applicable regularity conditions hold. However, there are many apparently innocuous situations where standard theory breaks down, sometimes spectacularly. Most of the departures from regularity are described geometrically in the book, with mathematical detail only sufficient to clarify the non-standard nature of a problem and to allow formulation of practical solutions. The book is intended for anyone with a basic knowledge of statistical methods typically covered in a university statistical inference course who wishes to understand or study how standard methodology might fail. Simple, easy-to-understand statistical methods are presented which overcome these difficulties, and illustrated by detailed examples drawn from real applications. Parametric bootstrap resampling is used throughout for analysing the properties of fitted models, illustrating its ease of implementation even in non-standard situations. Distributional properties are obtained numerically for estimators or statistics not previously considered in the literature because their theoretical distributional properties are too hard to obtain theoretically. Bootstrap results are presented mainly graphically in the book, providing easy-to-understand demonstration of the sampling behaviour of estimators.

scholarly journals modelBuildR: an R package for model building and feature selection with erroneous classifications

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10849
Author(s):  
Maximilian Knoll ◽  
Jennifer Furkel ◽  
Juergen Debus ◽  
Amir Abdollahi
Keyword(s):  
Feature Selection ◽  
Cross Validation ◽  
Model Building ◽  
Linear Models ◽  
Binary Classification ◽  
Ground Truth ◽  
R Package ◽  
Methylation Array ◽  
Survival Difference ◽  
Error Probabilities

Background Model building is a crucial part of omics based biomedical research to transfer classifications and obtain insights into underlying mechanisms. Feature selection is often based on minimizing error between model predictions and given classification (maximizing accuracy). Human ratings/classifications, however, might be error prone, with discordance rates between experts of 5–15%. We therefore evaluate if a feature pre-filtering step might improve identification of features associated with true underlying groups. Methods Data was simulated for up to 100 samples and up to 10,000 features, 10% of which were associated with the ground truth comprising 2–10 normally distributed populations. Binary and semi-quantitative ratings with varying error probabilities were used as classification. For feature preselection standard cross-validation (V2) was compared to a novel heuristic (V1) applying univariate testing, multiplicity adjustment and cross-validation on switched dependent (classification) and independent (features) variables. Preselected features were used to train logistic regression/linear models (backward selection, AIC). Predictions were compared against the ground truth (ROC, multiclass-ROC). As use case, multiple feature selection/classification methods were benchmarked against the novel heuristic to identify prognostically different G-CIMP negative glioblastoma tumors from the TCGA-GBM 450 k methylation array data cohort, starting from a fuzzy umap based rough and erroneous separation. Results V1 yielded higher median AUC ranks for two true groups (ground truth), with smaller differences for true graduated differences (3–10 groups). Lower fractions of models were successfully fit with V1. Median AUCs for binary classification and two true groups were 0.91 (range: 0.54–1.00) for V1 (Benjamini-Hochberg) and 0.70 (0.28–1.00) for V2, 13% (n = 616) of V2 models showed AUCs < = 50% for 25 samples and 100 features. For larger numbers of features and samples, median AUCs were 0.75 (range 0.59–1.00) for V1 and 0.54 (range 0.32–0.75) for V2. In the TCGA-GBM data, modelBuildR allowed best prognostic separation of patients with highest median overall survival difference (7.51 months) followed a difference of 6.04 months for a random forest based method. Conclusions The proposed heuristic is beneficial for the retrieval of features associated with two true groups classified with errors. We provide the R package modelBuildR to simplify (comparative) evaluation/application of the proposed heuristic (http://github.com/mknoll/modelBuildR).

BAYESIAN STATISTICAL METHODS FOR ASTRONOMY PART III: MODEL BUILDING

2020 ◽  
pp. 59-76
Author(s):  
David C. Stenning ◽  
David A. van Dyk
Keyword(s):  
Statistical Methods ◽  
Model Building

Empirical Analysis of the Effects of Parasitic Magnetic Stray Field on Force Output of Electromagnetic Actuators

2016 ◽  
Vol 1140 ◽  
pp. 384-391 ◽  
Author(s):  
Andreas Heyder ◽  
Stefan Steinbeck ◽  
Matthaeus Brela ◽  
Alexander Meyer ◽  
Sandra Abersfelder ◽  
...  
Keyword(s):  
Statistical Methods ◽  
Model Building ◽  
Field Measurements ◽  
Relevant Information ◽  
Field Analysis ◽  
Stray Field ◽  
Force Output ◽  
Electromagnetic Actuators ◽  
Magnetic Actuators ◽  
Six Sigma Methodology

Electromagnetic actuators are used in a variety of technical applications especially in the automotive industry. In-line process control methods are an essential component of the Lean and Six Sigma methodology to ensure process quality. However, the current state of the art in process and quality control is largely limited to end-of-line measurements of the force output. Analysing the magnetic stray field is a promising method that can be used to draw conclusions on the properties and defects of the flux-conducting magnetic materials. This phenomenon can potentially be used to identify defects in magnetic actuators thus allowing inline quality-monitoring. In order to realize this feature, patterns in the magnetic stray field of an actuator have to be identified and linked to a specific defect. The resulting challenge is the analysis of large datasets in order to characterize the stray field anomalies. This paper summarizes the results of a study on linear magnetic actuators trying to prove a relationship between parasitic magnetic stray field and the overall force output of an actuator by analysing the data with statistical methods. The findings of this study suggest that certain statistical methods, like regression, are not well suited to build a prediction model for defects in actuators using a similar approach of measuring stray field outside the actuator. This is mainly due to the fact that prerequisites for model building are difficult to full fill within the context of stray field analysis. Nevertheless, the findings also suggest that methods of exploratory data analysis can be used to derive quality relevant information from data of stray field measurements. The paper elaborates on the problem of defining a population, choosing variables for model building, as well as model error.

scholarly journals Simple methods for estimating confidence levels, or tentative probabilities, for hypotheses instead of p values

2019 ◽  
Vol 12 (1) ◽  
pp. 205979911982651
Author(s):  
Michael Wood
Keyword(s):  
Statistical Inference ◽  
Confidence Intervals ◽  
Statistical Methods ◽  
Null Hypothesis ◽  
Significance Tests ◽  
P Values ◽  
Confidence Levels ◽  
Alternative Approach ◽  
Degree Of Certainty ◽  
Natural Way

In many fields of research, null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious concerns about the suitability of p values for this purpose. An alternative approach is to cite confidence intervals for a statistic of interest, but this does not directly tell readers how certain a hypothesis is. Here, I suggest how the framework used for confidence intervals could easily be extended to derive confidence levels, or “tentative probabilities,” for hypotheses. I also outline four quick methods for estimating these. This allows researchers to state their confidence in a hypothesis as a direct probability, instead of circuitously by p values referring to a hypothetical null hypothesis—which is usually not even stated explicitly. The inevitable difficulties of statistical inference mean that these probabilities can only be tentative, but probabilities are the natural way to express uncertainties, so, arguably, researchers using statistical methods have an obligation to estimate how probable their hypotheses are by the best available method. Otherwise, misinterpretations will fill the void.

scholarly journals Statistical inferences about injury and persistence of environmentally stressed bacteria

1975 ◽  
Vol 74 (2) ◽  
pp. 149-155 ◽  
Author(s):  
Martin A. Hamilton ◽  
Gary K. Bissonnette
Keyword(s):  
Statistical Inference ◽  
Poisson Distribution ◽  
Statistical Methods ◽  
Standard Technique ◽  
Binomial Data ◽  
Selective Media ◽  
Statistical Inferences ◽  
Table Data

SUMMARYA standard technique for ascertaining the survival characteristics of bacteria after being environmentally stressed is to incubate the bacteria on both selective and non-selective media and count the colonies produced. Based on these colony counts, indexes of injury and persistence of the bacteria are calculated. To compare the stress of two different environments, a persistence ratio is calculated. In this paper, methods of statistical inference concerning these indexes and ratios are presented. These statistical methods use well-known procedures for analysis of binomial data and 2 × 2 table data, and are appropriate when the colony counts follow a Poisson distribution.

Some Comments on Teaching Biostatistics in Medical and Health Sciences

1990 ◽  
Vol 29 (01) ◽  
pp. 41-43 ◽  
Author(s):  
H. Sahai
Keyword(s):  
Statistical Inference ◽  
Statistical Methods ◽  
Medical Diagnosis ◽  
Health Sciences ◽  
Diagnosis And Prognosis ◽  
Teachers And Students ◽  
Health Sciences Students

AbstractThe role of statistical methods is now well recognized in health sciences since these disciplines are concerned with the study of communities or populations where the principles of sampling and statistical inference are clearly applicable. However, many medical and health sciences teachers and students have been slower to perceive the need for knowledge of biostatistical methods, even though all aspects of medical diagnosis and prognosis are governed by the laws of probability. Some of them are still skeptical about the value and importance of biostatistical principles to their fields and raise questions about the meaning, content, and nature of biostatistics and relevance of its teaching to health sciences disciplines. The purpose of this essay is to address some of these issues with the hope to invoke comments and responses from other biostatistics instructors who have encountered similar predicaments in their teaching and consulting roles to health sciences students and professionals.

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