# Main Page

**SFU Wiki**

## Group Meeting

- Future: Statistical Learning of Neuronal Functional Connectivity;
- Future:
- Future: Estimating the Quantile Function;
- April 19, 2017, Peijun
- April 5, 2017, Alex
- March 22, 2017, Yuping
- March 8, 2017, Yunlong
- Feb 22, 2017, Tianyu : A Statistical Perspective on Algorithmic Leveraging; The slides Slides ;
- Jan 23, 2017, Perry : Optimal Bayes Classifiers for Functional Data and Density Ratios; The slides Slides ;
- Dec 22, 2016, Tianyu : Functional principal component analysis of spatially correlated data; The slides Slides ;
- Dec 8, 2016, Yuping : Selecting the number of principal components: estimation of the true rank of a noisy matrix; The slides Slides
- Nov 24, 2016, Peijun : ￼Achieving near perfect classification for functional data;
- Nov 10, 2016, Yunlong : A DCM for resting state fMRI; Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers; Other reference
- Yuping: Global Optimization with Nonlinear Ordinary Differential Equations; The slides Slides
- Yunlong: Parametric Estimation of Ordinary Differential Equations With Orthogonality Conditions; The slides Slides
- Oct 27, 2016: Network Reconstruction From High Dimensional Ordinary Differential Equations; The slides HighODE
- Aug 11, 2016: Signal Compressing; The slides Sigmal Compressing
- Aug 11, 2016: Spatial Spline Regression Models; The slides Spatial Spline Regression
- Jun 30, 2016: Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes; The slides DirectionKrigging
- Jun 16, 2016: Functional Principal Component Regression and Partial Least Squares; The slides FPCR&FPLS
- May 26, 2016: Generalized Ordinary Differential Equation Models; The slides GODEM
- May 26, 2016: Fast Approximate Bayesian Computation for Estimating Parameters in Differential Equations; The slides FastABC.pdf
- May 26, 2016: Functional Regression - Annual Review of Statistics and its Applications
- Mar 17, 2016: [1]Spatiotemporal dynamics of random stimuli account for trial-to-trial variability in perceptual decision making; The slides Hame Park 2016
- Feb 25, 2016: [2]Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations; The slides Rue 2008
- Jan 21, 2016: A unifying review of linear gaussian models; ICA: A tutorial [http://www.stat.ucla.edu/~yuille/courses/Stat161-261-Spring14/HyvO00-icatut.pdf; The slides A unifying review of LGM
- Jan 14, 2016: Simon Wood's nature paper The supplementary files are downloaded from here http://www.nature.com/nature/journal/v466/n7310/full/nature09319.html The slides are here
- Dec 1, 2015: SFPCA Slides;
- nov 3, 2015: Bitcoin Slides; Bitcoin Stat. plos one ; Bayesian Regression Bitcoin ;
- Demonstration for ODE Parameter Estimation using Parameter Cascading Method
- October 20, 2015: Slides for Parameter Cascading Method; Jiguo's Thesis ;
- October 6, 2015: Sam's paper
- September 22, 2015: J. O. Ramsay, G. Hooker, D. Campbell, and J. Cao (2007), "Parameter estimation for differential equations: a generalized smoothing approach" (with discussion). Journal of the Royal Statistical Society, Series B 69,741-796. Jiguo lead the discussion. Talk slides
- July 15, 2015: Structured functional additive regression in reproducing kernel Hilbert spaces by Hongxiao Zhu, Fang Yao, and Hao Helen Zhang

## Differential Equations

https://cran.r-project.org/web/views/DifferentialEquations.html

Stochastic Differential Equations (SDEs)

In a stochastic differential equation, the unknown quantity is a stochastic process. The package sde provides functions for simulation and inference for stochastic differential equations. It is the accompanying package to the book by Iacus (2008). The package pomp contains functions for statistical inference for partially observed Markov processes. Packages adaptivetau and GillespieSSA implement Gillespie's "exact" stochastic simulation algorithm (direct method) and several approximate methods.

Ordinary Differential Equations (ODEs)

In an ODE, the unknown quantity is a function of a single independent variable. Several packages offer to solve ODEs. The "odesolve" package was the first to solve ordinary differential equations in R. It contains two integration methods. It is not actively maintained and has been replaced by the package deSolve. The package deSolve contains several solvers for solving ODEs. It can deal with stiff and nonstiff problems. The package deTestSet contains solvers designed for solving very stiff equations. The package odeintr generates and compiles C++ ODE solvers on the fly using Rcpp and Boost odeint . Delay Differential Equations (DDEs)

In a DDE, the derivative at a certain time is a function of the variable value at a previous time. The package PBSddesolve (originally published as "ddesolve") includes a solver for non-stiff DDE problems. Functions in the package deSolve can solve both stiff and non-stiff DDE problems. Partial Differential Equations (PDEs)

PDEs are differential equations in which the unknown quantity is a function of multiple independent variables. A common classification is into elliptic (time-independent), hyperbolic (time-dependent and wavelike), and parabolic (time-dependent and diffusive) equations. One way to solve them is to rewrite the PDEs as a set of coupled ODEs, and then use an efficient solver.
The R-package ReacTran provides functions for converting the PDEs into a set of ODEs. Its main target is in the field of *reactive transport* modelling, but it can be used to solve PDEs of the three main types. It provides functions for discretising PDEs on cartesian, polar, cylindrical and spherical grids.
The package deSolve contains dedicated solvers for 1-D, 2-D and 3-D time-varying ODE problems as generated from PDEs (e.g. by ReacTran).
Solvers for 1-D time varying problems can also be found in the package deTestSet.
The package rootSolve contains optimized solvers for 1-D, 2-D and 3-D algebraic problems generated from (time-invariant) PDEs. It can thus be used for solving elliptic equations.
Note that, to date, PDEs in R can only be solved using finite differences. At some point, we hope that finite element and spectral methods will become available.
Differential Algebraic Equations (DAEs)

Differential algebraic equations comprise both differential and algebraic terms. An important feature of a DAE is its differentiation index; the higher this index, the more difficult to solve the DAE. The package deSolve provides two solvers, that can handle DAEs up to index 3. Three more DAE solvers are in the package deTestSet. Boundary Value Problems (BVPs)

BVPs have solutions and/or derivative conditions specified at the boundaries of the independent variable. Package bvpSolve deals only with this type of equations. The package ReacTran can solve BVPs that belong to the class of reactive transport equations.

Other

The simecol package provides an interactive environment to implement and simulate dynamic models. Next to DE models, it also provides functions for grid-oriented, individual-based, and particle diffusion models. Package scaRabee offers frameworks for simulation and optimization of Pharmacokinetic-Pharmacodynamic Models. In the package FME are functions for inverse modelling (fitting to data), sensitivity analysis, identifiability and Monte Carlo Analysis of DE models. The packages nlmeODE and PSM have functions for mixed-effects modelling using differential equations. mkin provides routines for fitting kinetic models with one or more state variables to chemical degradation data. The package CollocInfer implements collocation-inference for continuous-time and discrete-time stochastic processes. Root finding, equilibrium and steady-state analysis of ODEs can be done with the package rootSolve. The deTestSet package contains many test problems for differential equations. Package pracma contains solvers for ODEs, as pure R scripts, useful as a learning tool. The PBSmodelling package adds GUI functions to models. Package ecolMod contains the figures, data sets and examples from a book on ecological modelling (Soetaert and Herman, 2009). primer is a support package for the book of Stevens (2009).

## Things to learn

- October 22, 2015: Estimation of Stochastic Differential Equations with Sim.DiffProc Package Version 2.9
- October 9, 2015: Haocheng Li mentioned to me that ECME algorithm by Joseph L. Schafer is very good for estimating linear mixed model. He also mentioned that the mixed effect model may be hard to estimate when the number of random effects are large. This can be a good problem to explore.
- July 7, 2015 Functional Regression
- Theory of functional differential equations by Hale, Jack K Applied mathematical sciences, 1977, [2d ed.]. --

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