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Technological Evolution of Wireless Neurochemical Sensing with Fast-Scan Cyclic Voltammetry
Published in Iniewski Krzysztof, Integrated Microsystems, 2017
Dan P. Covey, Kevin E. Bennet, Charles D. Blaha, Pedram Mohseni, Kendall H. Lee, Paul A. Garris
The analysis of dopamine transients has been improved by two mathematical procedures. In the first procedure, an automated algorithm was developed that “marches” through the voltammetric record and, using a moving background, calculates a background-subtracted cyclic voltammogram for each scan [30]. These voltammograms are then statistically compared using correlation to the voltammogram originating from electrically evoked dopamine, which is used as a standard reference signal. In Figure 7.5, electrically evoked dopamine is the larger signal in both the trace and the color plot. Also note how well the voltammograms for the evoked dopamine and the transient signal overlap (inset). In the second procedure, principal component regression is used to obtain a statistically verifiable dopamine trace [31], which is then amenable to analysis using peak-fitting algorithms [32]. This chemometrics approach is required for some applications, because the trace collected at the peak oxidation potential for dopamine may contain contributions from interferents whose voltammogram overlaps dopamine. Another advantage of principal component regression is that it can resolve slow changes in baseline dopamine levels.
Metabolomics of Microbial Biofilms
Published in Chaminda Jayampath Seneviratne, Microbial Biofilms, 2017
Tanujaa Suriyanarayanan, Chaminda Jayampath Seneviratne, Wei Ling Ng, Shruti Pavagadhi, Sanjay Swarup
There are several sequential steps to be followed in metabolomics data analysis, which are represented in Figure 7.2. The first step of metabolomics data analysis enables pattern recognition, or clustering of groups such as normal versus mutant, or planktonic versus biofilm, based on differences in their spectral patterns. Interpretation of scores from this analysis provides information about the relationships/trends/groupings among samples as well as the presence of outliers. But the quantity and complexity of data arising from NMR and MS studies necessitate the use of computer-aided statistical interpretation in majority of metabolic profiling studies to obtain meaningful information from the complex raw data. Two major types of pattern recognition processes, unsupervised and supervised, are used in multivariate statistics of large data sets. Hierarchical cluster analysis and principal component analysis are examples of unsupervised approaches, which measure the innate variation in data sets; principal component regression and neural networks are examples of supervised approaches, which use prior information to generate pattern clusters [92]. Many other statistical approaches are also available, including spectral decomposition, linear discriminant analysis, Bayesian spectral decomposition and other chemometric methods [93]. Some of the common tools used for depicting metabolite profile differences after multivariate statistical analysis are shown in Figure 7.3.
Compression–decompression modulus (CDM) – an alternative/complementary approach to Heckel’s analysis
Published in Pharmaceutical Development and Technology, 2022
Devang B. Patel, Vivek D. Patel, Yash Patel, John C. Sturgis, Robert Sedlock, Rahul V. Haware
A multivariate statistical analysis was performed using Unscrambler® v10 software (CAMO Software AS, Trondheim, Norway). A qualitative principal component analysis (PCA) and a quantitative principal component regression (PCR) analysis was used to evaluate the data set. All variables were weighed and scaled by dividing them with their standard deviation to avoid the undue influence of variable experimental range on the model outcome. X-variables considered in the PCA were CM, decompression modulus, YPpl, YPel, WoC, and TMS. A quantitative PCR was used to quantify statistically significant and insignificant contributions of the main effects of various X-variables. The X-variables used in this analysis were material type, compression pressure, compression speed, CM, decompression modulus, WoC, and yield pressures (YPpl and YPel). The Y-variable was the TMS. Each material was coded as 0 and 1. These coded variables were split to separate the individual effect of each material on the TMS. The X and Y variables were initially weighted by dividing with their respective standard deviation before each modeling to give an equal weighting to each variable. The models were validated with a full cross-validation and the Jack-Knifing method (Martens and Martens 2000). The statistical significance of the model was measured at α < 0.05.
A statistical methodology to select covariates in high-dimensional data under dependence. Application to the classification of genetic profiles in oncology
Published in Journal of Applied Statistics, 2022
B. Bastien, T. Boukhobza, H. Dumond, A. Gégout-Petit, A. Muller-Gueudin, C. Thiébaut
We cite here some statistical methods that have been developed to select covariates in high-dimensional contexts. The state of the art about the control of false discoveries in multiple testing procedures is very extensive. The famous correction proposed by Bonferroni [6] to control the Family Wise Error Rate (FWER) has been emulated and we can find a review about these methods in [10]. Alternative methods focused on the control of the False Discovery Rate (FDR) [4,5], or of the local FDR [12] or the q-value [24–26]. For a review (in french) of the methods, see [3]. Regarding regression in the framework of high dimensional data (et al. [28] is a kind of principal component regression. The Lasso regression proposed by Tibshirani [29] performs both variable selection and regularization in penalizing the sums of squares by the 20], or network inference [21]. Another versatile tool to select covariates in different non-parametric contexts is given by the random forests, with the concept of importance of covariates [16].
An automatic robust Bayesian approach to principal component regression
Published in Journal of Applied Statistics, 2021
Philippe Gagnon, Mylène Bédard, Alain Desgagné
Principal component regression (PCR) is the name given to a linear regression model using principal components (PCs) as regressors. It is based on a principal component analysis (PCA), which is commonly used to summarise the information contained in covariates. The principle is to find new axes in the covariate space by exploiting the correlation structure between the covariates and then encode the covariate observations in that new coordinate system. The resulting variables, called principal components (PCs), are linearly independent and have the remarkable property that the first q PCs retain the maximum amount of information carried by the original observations (compared to any other q-dimensional summary). Regrouping correlated variables to produce linearly independent ones is appealing in a linear regression context, as strongly correlated variables are known to carry redundant information, leading to unstable estimates. Companies within the same economic sector in stock market indices like S&P 500 and S&P/TSX are an example of such correlated variables. Linear independence also allows visualising the relationship between the dependent variable and the PCs by plotting the dependent variable against each of the PCs.