Jane C. Miller

Bio: Jane C. Miller is an academic researcher. The author has contributed to research in topics: Polynomial regression & Simple linear regression. The author has an hindex of 2, co-authored 2 publications receiving 3777 citations.

Statistics and Chemometrics for Analytical Chemistry

Abstract: 1 Introduction 11 Analytical problems 12 Errors in qunatitative analysis 13 Types of error 14 Random and systematic errors in titrimetric analysis 15 Handling systematic errors 16 Planning and design of experiments 17 Calculators and computers in statistical calculations 2 Statistics of Repeated Measurements 21 Mean and standard deviation 22 The distribution of repeated measurements 23 Log-normal distribution 24 Definition of a 'sample' 25 The sampling distribution of the mean 26 Confidence limits of the mean for large samples 27 Confidence limits of the mean for small samples 28 Presentation of results 29 Other uses of confidence limits 210 Confidence limits of the geometric mean for a log-normal distribution 211 Propagation of random errors 212 Propagation of systematic errors 3 Significance Tests 31 Introduction 32 Comparison of an experimental mean with a known value 33 Comparison of two experimental means 34 Paired t-test 35 One-sided and two-sided tests 36 F-test for the comparison of standard deviations 37 Outliers 38 Analysis of variance 39 Comparison of several means 310 The arithmetic of ANOVA calculations 311 The chi-squared test 312 Testing for normality of distribution 313 Conclusions from significance tests 314 Bayesian Statistics 4 The Quality of Analytical Measurements 41 Introduction 42 Sampling 43 Separation and estimation of variances using ANOVA 44 Sampling strategy 45 Quality control methods - Introduction 46 Stewhart charts for mean values 47 Stewhart charts for ranges 48 Establishing the process capability 49 Average run length: cusum charts 410 Zone control charts (J-charts) 411 Proficiency testing schemes 412 Method performance studies (collaborative trials) 413 Uncertainty 414 Acceptable sampling 415 Method validation 5 Calibration Methods in Instumental Analysis 51 Introduction: instrumentational analysis 52 Calibration graphs in instrumental analysis 53 The product-moment correlation coefficient 54 The line of regression of y on x 55 Errors in the slope and intercept of the regression line 56 Calculation of a concentration and its random error 57 Limits of detection 58 The method of standard additions 59 Use of regression lines for comparing analytical methods 510 Weighted regression lines 511 Intersection of two straight lines 512 ANOVA and regression calculations 513 Curvilinear regression methods - Introduction 514 Curve fitting 515 Outliers in regression 6 Non-parametric and Robust Methods 61 Introduction 62 The median: initial data analysis 63 The sign test 64 The Wald-Wolfowitz runs test 65 The Wilcoxon signed rank test 66 Simple tests for two independent samples 67 Non-parametric tests for more than two samples 68 Rank correlation 69 Non-parametric regression methods 610 Robust methods: introduction 611 Simple robust methods: trimming and winsorization 612 Further robust estimates of location and spread 613 Robust ANOVA 614 Robust regression methods 615 Re-sampling statistics 616 Conclusions 7 Experiimental Design and Optimization 71 Introduction 72 Randomization and blocking 73 Two-way ANOVA 74 Latin squares and other designs 75 Interactions 76 Identifying the important factors: factorial designs 77 Fractional factorial designs 78 Optimization: basic principles and univariate methods 79 Optimization using the alternating variable search method 710 The method of steepest ascent 711 Simplex optimization 712 Simulated annealing 8 Multivariate Analysis 81 Introduction 82 Initial analysis 83 Prinicipal component analysis 84 Cluster analysis 85 Discriminant analysis 86 K-nearest neighbour method 87 Disjoint class modelling 88 Regression methods 89 Multiple linear regression 810 Principal component regression 811 Partial least squares regression 812 Natural computation methods artificial neural networks 813 Conclusions Solutions to Exercises Appendix 1 Commonly used statistical significance tests Appendix 2 Statistical tables Index

Applied Chemometrics for Scientists

Abstract: Preface. 1 Introduction. 1.1 Development of Chemometrics. 1.2 Application Areas. 1.3 How to Use this Book. 1.4 Literature and Other Sources of Information. References. 2 Experimental Design. 2.1 Why Design Experiments in Chemistry? 2.2 Degrees of Freedom and Sources of Error. 2.3 Analysis of Variance and Interpretation of Errors. 2.4 Matrices, Vectors and the Pseudoinverse. 2.5 Design Matrices. 2.6 Factorial Designs. 2.7 An Example of a Factorial Design. 2.8 Fractional Factorial Designs. 2.9 Plackett-Burman and Taguchi Designs. 2.10 The Application of a Plackett-Burman Design to the Screening of Factors Influencing a Chemical Reaction. 2.11 Central Composite Designs. 2.12 Mixture Designs. 2.13 A Four Component Mixture Design Used to Study Blending of Olive Oils. 2.14 Simplex Optimization. 2.15 Leverage and Confidence in Models. 2.16 Designs for Multivariate Calibration. References. 3 Statistical Concepts. 3.1 Statistics for Chemists. 3.2 Errors. 3.3 Describing Data. 3.4 The Normal Distribution. 3.5 Is a Distribution Normal? 3.6 Hypothesis Tests. 3.7 Comparison of Means: the t-Test. 3.8 F-Test for Comparison of Variances. 3.9 Confidence in Linear Regression. 3.10 More about Confidence. 3.11 Consequences of Outliers and How to Deal with Them. 3.12 Detection of Outliers. 3.13 Shewhart Charts. 3.14 More about Control Charts. References. 4 Sequential Methods. 4.1 Sequential Data. 4.2 Correlograms. 4.3 Linear Smoothing Functions and Filters. 4.4 Fourier Transforms. 4.5 Maximum Entropy and Bayesian Methods. 4.6 Fourier Filters. 4.7 Peakshapes in Chromatography and Spectroscopy. 4.8 Derivatives in Spectroscopy and Chromatography. 4.9 Wavelets. References. 5 Pattern Recognition. 5.1 Introduction. 5.2 Principal Components Analysis. 5.3 Graphical Representation of Scores and Loadings. 5.4 Comparing Multivariate Patterns. 5.5 Preprocessing. 5.6 Unsupervised Pattern Recognition: Cluster Analysis. 5.7 Supervised Pattern Recognition. 5.8 Statistical Classification Techniques. 5.9 K Nearest Neighbour Method. 5.10 How Many Components Characterize a Dataset? 5.11 Multiway Pattern Recognition. References. 6 Calibration. 6.1 Introduction. 6.2 Univariate Calibration. 6.3 Multivariate Calibration and the Spectroscopy of Mixtures. 6.4 Multiple Linear Regression. 6.5 Principal Components Regression. 6.6 Partial Least Squares. 6.7 How Good is the Calibration and What is the Most Appropriate Model? 6.8 Multiway Calibration. References. 7 Coupled Chromatography. 7.1 Introduction. 7.2 Preparing the Data. 7.3 Chemical Composition of Sequential Data. 7.4 Univariate Purity Curves. 7.5 Similarity Based Methods. 7.6 Evolving and Window Factor Analysis. 7.7 Derivative Based Methods. 7.8 Deconvolution of Evolutionary Signals. 7.9 Noniterative Methods for Resolution. 7.10 Iterative Methods for Resolution. 8 Equilibria, Reactions and Process Analytics. 8.1 The Study of Equilibria using Spectroscopy. 8.2 Spectroscopic Monitoring of Reactions. 8.3 Kinetics and Multivariate Models for the Quantitative Study of Reactions 8.4 Developments in the Analysis of Reactions using On-line Spectroscopy. 8.5 The Process Analytical Technology Initiative. References. 9 Improving Yields and Processes Using Experimental Designs. 9.1 Introduction. 9.2 Use of Statistical Designs for Improving the Performance of Synthetic Reactions. 9.3 Screening for Factors that Influence the Performance of a Reaction. 9.4 Optimizing the Process Variables. 9.5 Handling Mixture Variables using Simplex Designs. 9.6 More about Mixture Variables. 10 Biological and Medical Applications of Chemometrics. 10.1 Introduction. 10.2 Taxonomy. 10.3 Discrimination. 10.4 Mahalanobis Distance. 10.5 Bayesian Methods and Contingency Tables. 10.6 Support Vector Machines. 10.7 Discriminant Partial Least Squares. 10.8 Micro-organisms. 10.9 Medical Diagnosis using Spectroscopy. 10.10 Metabolomics using Coupled Chromatography and Nuclear Magnetic Resonance. References. 11 Biological Macromolecules. 11.1 Introduction. 11.2 Sequence Alignment and Scoring Matches. 11.3 Sequence Similarity. 11.4 Tree Diagrams. 11.5 Phylogenetic Trees. References. 12 Multivariate Image Analysis. 12.1 Introduction. 12.2 Scaling Images. 12.3 Filtering and Smoothing the Image. 12.4 Principal Components for the Enhancement of Images. 12.5 Regression of Images. 12.6 Alternating Least Squares as Employed in Image Analysis. 12.7 Multiway Methods In Image Analysis. References. 13 Food. 13.1 Introduction. 13.2 How to Determine the Origin of a Food Product using Chromatography. 13.3 Near Infrared Spectroscopy. 13.4 Other Information. 13.5 Sensory Analysis: Linking Composition to Properties. 13.6 Varimax Rotation. 13.7 Calibrating Sensory Descriptors to Composition. References. Index.

Review of multidimensional data processing approaches for Raman and infrared spectroscopy

Abstract: Raman and Infrared (IR) spectroscopies provide information about the structure, functional groups and environment of the molecules in the sample. In combination with a microscope, these techniques can also be used to study molecular distributions in heterogeneous samples. Over the past few decades Raman and IR microspectroscopy based techniques have been extensively used to understand fundamental biology and responses of living systems under diverse physiological and pathological conditions. The spectra from biological systems are complex and diverse, owing to their heterogeneous nature consisting of bio-molecules such as proteins, lipids, nucleic acids, carbohydrates etc. Sometimes minor differences may contain critical information. Therefore, interpretation of the results obtained from Raman and IR spectroscopy is difficult and to overcome these intricacies and for deeper insight we need to employ various data mining methods. These methods must be suitable for handling large multidimensional data sets and for exploring the complete spectral information simultaneously. The effective implementation of these multivariate data analysis methods requires the pretreatment of data. The preprocessing of raw data helps in the elimination of noise (unwanted signals) and the enhancement of discriminating features. This review provides an outline of the state-of-the-art data processing tools for multivariate analysis and the various preprocessing methods that are widely used in Raman and IR spectroscopy including imaging for better qualitative and quantitative analysis of biological samples.