Simfit tutorials and worked examples

Essentials

Data files

Results files

Statistical analysis

Statistical calculations

Multivariate analysis

Survival analysis

Curve and surface fitting

Data smoothing, calibration, and time series

Simulation

Numerical analysis

Simulating and fitting differential equations

Graph plotting

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Essentials

• Essential information for first time users
• Essential simplified simfit options
• Essential data analysis techniques
• Essential details for using Simfit tutorials
• Essential details for transferring data from Excel into Simfit
• Essential details for transferring tables from Simfit into Word or LaTeX

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Data files

• Introduction to data preparation
• Formatting details for Simfit data files
• Creating and editing Simfit data files
• Incomplete matrices with missing values
• List of Simfit test data files, models, and configuration scripts

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Results files

• Introduction to results files
• Extracting tables from Simfit results files

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Statistical analysis

• Statistical distributions

  • Introduction to statistical distributions
  • uniform distribution
  • normal distribution
  • t distribution
  • chi-square distribution
  • F distribution
  • binomial distribution
  • Poisson distribution
  • bivariate normal distribution
  • Generating pseudo-random numbers

• Simple statistical tests

  • Introduction to simple statistical tests
  • 1-sample t test
  • 1-sample Kolomogorov-Smirnov test
  • 1-sample Shapiro-Wilks test
  • 1-sample Poisson distribution test
  • 2-sample unpaired t test
  • 2-sample paired t test
  • 2-sample Kolmogorov-Smirnov test
  • 2-sample Wilcoxon-Mann-Whitney U test
  • 2-sample Wilcoxon signed ranks test
  • Chi-square test on observed and expected frequencies
  • Chi-square, Fisher-Exact and loglinear contingency tables tests
  • McNemar test
  • Cochran Q test
  • Binomial test
  • Sign test
  • Run test
  • F test for excess variance
  • Median, Mood and David tests for equal dispersion
  • Bartlett and Levene tests for homogeneity of variance
  • Kendall coefficient of concordance

• Data exploration

  • Introduction to data exploration
  • Exhaustive analysis of a vector (i.e. a column of numbers)
  • Exhaustive analysis of a matrix (i.e. a table of numbers)
  • Exhaustive analysis of a multivariate normal matrix
  • t tests on groups defined by column across rows of a matrix
  • Nonparametric tests on groups defined by column across rows of a matrix
  • All pairwise comparisons of n samples
  • Robust analysis of 1 sample
  • Robust analysis of 2 samples

• Analysis of variance (ANOVA)

  • Introduction to ANOVA
  • 1-way ANOVA
  • 1-way ANOVA (Kruskal-Wallis nonparametric)
  • Tukey Q post-ANOVA test
  • 2-way ANOVA)
  • 2-way ANOVA (Friedman nonparametric)
  • Repeat measures ANOVA
  • 3-way ANOVA Latin square design
  • Groups and subgroups ANOVA
  • Factorial ANOVA

• Analysis of frequencies and proportions

  • Introduction to analysis of frequencies and proportions
  • Binomial proportions: the analysis of dichotomous data
  • Trinomial proportions: the analysis of trichotomous data
  • Cochran-Mantel-Haenszel Meta Analysis
  • Bioassay, dose response curves, and LD50.

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Statistical calculations

• Power and sample size
• Parameter confidence limits
• Robust analysis of 1 sample
• Robust analysis of 2 samples
• Shannon-Brillouin-Simpson indices of diversity
• Non-central statistical distributions
• Ligand binding cooperativity analysis
• Gaussian kernel density estimation by FFT
• False discovery rates by FDR(BH)

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Multivariate analysis

• Introduction to multivariate analysis

• Correlation analysis

  • Introduction to correlation analysis
  • Pearson product-moment correlation
  • Kendall tau and Spearman rank nonparametric correlation
  • Partial correlation
  • Canonical correlation

• Cluster analysis

  • Introduction to cluster analysis
  • Dendrograms
  • Classical metric and non-metric (ordinal) scaling
  • K-means clustering

• Multivariate projection and display techniques

  • Principal components
  • Factor analysis
  • Procrustes analysis
  • Varimax and Quartimax rotation
  • Biplots in two or three dimensions
  • Partial least squares (PLS)
  • Plotting labels

• Multivariate ANOVA

  • Introducation to multivariate analysis of variance (MANOVA)
  • MANOVA worked examples

• Comparing groups

  • Canonical variates
  • Discriminant analysis: Mahalanobis distances
  • Discriminant analysis: Allocating observations to training sets

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Survival analysis

• Introduction to survival analysis
• 1-sample Kaplan-Meier survivor function
• 1-sample Weibull survivor function
• 1-sample GLM survivor function with covariates
• 2-sample Mantel-Haenszel test
• n-sample Cox regression

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Curve and surface fitting

• Introduction to curve and surface fitting
• Goodness of fit

• Linear regression

  • Fitting a straight line: simple least squares regression
  • Fitting a straight line: comprehensive least squares regression
  • Fitting a straight line: othogonal least squares regression
  • Fitting a polynomial: weighted least squares polynomial regression
  • Multilinear least squares regression
  • Partial least squares (PLS)

• Generalized linear models (GLM)

  • GLM: Summary of techniques
  • GLM: Examples using standard formats
  • GLM: Exponential, Weibull, extreme-value, and Cox survivor functions
  • GLM: Dose-response curves, bioassay, percentiles, and LD50
  • GLM: Loglinear contingency table analysis
  • GLM: Logistic regression
  • GLM: Binary logistic regression

• Nonlinear curve fitting: simple

  • Fitting Michaelis-Menten enzyme kinetic models
  • Fitting High-Low affinity ligand binding models
  • Fitting allosteric and cooperative ligand binding models
  • Fitting deviations from Michaelis-Menten kinetics
  • Fitting exponential functions
  • Fitting growth, decay, or survival models
  • Fitting inital rates, half times, lag times, and asymptotes

• Nonlinear curve fitting: advanced

  • Introduction to constrained nonlinear regression
  • Choosing parameter starting estimates and limits
  • Calculating with the best fit curve
  • Fitting a mixture of two normal distributions
  • Fitting a beta distribution to observations
  • Graphical deconvolution of best-fit models
  • Plotting contours of the objective function at solution points
  • Plotting contours with residuals and sections across a best fit surface
  • Simultaneously fitting multiple functions of one variable
  • Fitting a convolution integral
  • Fitting a single differential_equation

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Data smoothing, calibration, and time series

• Introduction to data smoothing

• Spline smoothing

  • Fitting piecewise cubic splines
  • Using cubic splines for calculations
  • Using cubic splines to compare curves

• Interpolation

  • Smooth interpolation of discrete data

• Calibration

  • Introduction to calibration and bioassay
  • Using straight line standard curves
  • Using polynomial standard curves
  • Using cubic spline standard curves
  • Dose-response curves, bioassay, percentiles, and LD50 using GLM
  • Multivariate calibration using partial least squares (PLS)

• Time series

  • Running medians, moving averages, and the Tukey-Hanning 4253H twice smoother
  • Lags, auto-correlations, and partial auto-correlation functions
  • Auto-correlation and Cross-correlation matrices
  • Autoregressive integrated moving average models (ARIMA) with forecasts

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Simulation

• Introduction to simulation

• Simulation: random numbers

  • Generating a random vector
  • Generating a random matrix
  • Generating a randomly shuffled list
  • Generating a random Latin square
  • Generating a random walk
  • Testing a random number generator

• Simulation: user selected models

  • Simulating a function of one variable
  • Simulating a function of two variables
  • Simulating a differential equation
  • Simulating a user-defined model: summary of commands
  • Simulating a user-defined model: creating a model-file
  • Simulating a user-defined model: simple examples
  • Simulating a user-defined model: parametric curves
  • Simulating a user-defined model: adding experimental error

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Numerical analysis

• Introduction to numerical analysis

• Free standing calculations

• • Zeros of a polynomial
  • Deteminant, inverse, eigenvalues, and eigenvectors of a matrix
  • Singular value decomposition of a matrix (SVD)
  • Pseudo-inverse (i.e. the generalised inverse) of a matrix
  • LU factorization, norms, and condition numbers of a matrix
  • QR factorization of a matrix
  • Cholesky factorization of a positive definite matrix
  • Matrix multiplication AB, A^TB, AB^T, A^TB^T
  • Evaluation of quadratic forms x^TAx or x^TA^-1x
  • Solving exact linear equations Ax = b
  • Solving overdetermined linear equations Ax = b
  • Solving symmetric eigenvalue problems like Ax = λBx
  • Fitting inital rates, half times, lag times, and asymptotes
  • Trapezoidal estimate of area under a curve and proportions above thresholds

• Calculations requiring user supplied models

  • Locating zeros of 1 function of 1 variable
  • Locating zeros of n functions of n variables
  • Integration of 1 function of 1 variable
  • Integration of 1 function of m variables
  • Integration of n functions of m variables
  • Bound-constrained quasi-Newton optimization
  • Optimization contours with a trajectory overlay
  • Evaluation of convolution integrals for plotting or fitting

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Simulating and fitting differential equations

• Introduction to simulating and fitting differential equations
• The von Bertalanffy allometric differential equation
• The Lotka-Volterra predator-prey equations
• The epidemic differential equations
• The recurrent epidemic differential equations

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Graph plotting

• Introduction to graph plotting

• Simple techniques

  • Lines, symbols, and text
  • Sizes, shapes, and aspect ratios
  • Pie charts
  • Bar charts
  • Box and whisker plots
  • Standard plots
  • Double plots with two y axes
  • Plotting error bars
  • Plotting labels
  • Plotting mathematical equations interactively

• Advanced techniques

  • Using configuration files, templates, and metafiles
  • The Log Odds plot
  • The Log Odds Ratios or Forest plot
  • The Scatchard plot
  • The Hill plot and cooperativity analysis
  • Dendrograms
  • Biplots in two or three dimensions
  • Vector field diagrams in two or three dimensions
  • Plotting three-dimensional surfaces
  • Plotting two-dimensional contour diagrams
  • Plotting trinomial parameter confidence contours
  • Plotting three-dimensional skyscraper and cylinder-type bar charts
  • Plotting curves in three-dimensional space
  • Plotting parameterized families of curves in two or three dimensions
  • Adding text, arrows, and graphical objects to graphs

• PostScript procedures

  • Overview of Simfit Postscript features
  • Introduction to the structure of Simfit PostScript files
  • Displaying standard and non-standard PostScript fonts
  • Editing PostScript text, symbols, and lines
  • Scaling, rotating, and stretching Simfit PostScript files
  • Using PostScript Specials
  • Exploiting LaTeX functionality
  • Creating collages, overlays, and insets
  • Editing PostScript colours
  • Creating alternative types of graphics files from eps files

• Scalable Vector Graphics procedures

  • Overview of SVG techniques
  • Introduction to SVG
  • How to import LaTeX chemical formulas into SVG files
  • How to import LaTeX maths equations into SVG files
  • How to import SVG files into SVG files
  • How to use LaTeX to label SVG y axes
  • How to edit SVG files using text editors such as Notepad
  • How to create collages with SVG files
  • How to re-scale SVG files to create scrollable stretched chart-paper type displays

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