similar to: functions for high dimensional integral

I find the one-dimensional "integrate" very helpful, but often enough I stumble into problems that require two (or more)-dimensional integrals. I suppose there are no R functions that can do this for me, "directly"? The ideal thing would be to be able to define say f <- function(x) { x1 <- x[1] x2 <- x[2] sin(x1*x2)*exp(x1-x2) } and then write say integrate(f,

I've written a series of functions that evaluates an integral from -inf to a or b to +inf using equally spaced quadrature points along a normal distribution from -10 to +10 moving in increments of .01. These functions are working and give very good approximations, but I think they are computationally wasteful as I am evaluating the function at *many* points. Instead, I would prefer to use

Dear R community, I wrote and someone else helped me type a 5-page R-info in Chinese, covering the most basic information on how to get and install and start using R on Wintel PC. This could serve those not fluent in/intimidated by English but want to start using R. (I met a lot of those in China) <http://www.ms.uky.edu/~mai/ZhongWen.htm> also a MSword version of the same (may print

I have an R function defined as: f<-function(x){ return(dchisq(x,9,77)*((13.5/x)^5)*exp(-13.5/x)) } Numerically integrating this function, I observed a couple of things: A) Integrating the function f over the entire positive real line gives an error: > integrate(f,0,Inf) Error in integrate(f, 0, Inf) : the integral is probably divergent B) Increasing the interval of integration

Hi there, I am using SAS Proc NLMIXED to maximize a likelihood with multivariate normal random effects. An example is the two part random effects model for repeated measures semi-continous data with a cluster at 0. I use the "model y ~ general(loglike)" statement in Proc NLMIXED, so I can specify a general log likelihood function constructed by SAS programming statements. Then the

Hello all, I'm hoping to find a way to evaluate the following sort of integral in R. \int_a^b \int_{g(y)}^Inf f(x,y) dx dy. The integral has no closed form and so must be evaluated numerically. The "adapt" package provides for multidimensional integration but does not appear to allow the limits of integration to be a function. I need to evaluate a number of integrals of this

Dear All, I wonder if there is a way to fit a generalized linear mixed models (for repeated binomial data) via a direct Maximum Likelihood Approach. The "glmm" in the "repeated" package (Lindsey), the "glmmPQL" in the "MASS" package (Ripley) and "glmmGIBBS" (Myle and Calyton) are not using the full maximum likelihood as I understand. The

Hi, anyone knows about any functions in R can get multidimensional integration not over a multidimensional rectangle (not adapt). For example, I tried the following function f(x,n)=x^n/n! phi.fun<-function(x,n) { if (n==1) { x }else{ integrate(phi.fun, lower=0, upper=x, n=n-1)$value } } I could get f(4,2)=4^2/2!=8, but failed in f(4,3)=4^3/3! Thanks Best, Lynette

Hi, I would like to solve a double integral of the form \int_0^1 \int_0^1 x*y dx dy using Gauss Quadrature. I know that I can use R's integrate function to calculate it: integrate(function(y) { sapply(y, function(y) { integrate(function(x) x*y, 0, 1)$value }) }, 0, 1) but I would like to use Gauss Quadrature to do it. I have written the following code (using R's statmod package)

Hi R users, I have a couple of questions about some problems that I am facing with regard to numerical integration and optimization of likelihood functions. Let me provide a little background information: I am trying to do maximum likelihood estimation of an econometric model that I have developed recently. I estimate the parameters of the model using the monthly US unemployment rate series

Dear R-users I would like to integrate something like \int_k^\infty (1 - F(x)) dx, where F(.) is a cumulative distribution function. As mentioned in the "integrate" help-page: integrate(dnorm,0,20000) ## fails on many systems. This does not happen for an adaptive Simpson or Lobatto quadrature (cf. Matlab). Even though I am hardly familiar with numerical integration the implementation

Hi All, I am trying to use A Gaussian quadrature over the interval (-infty,infty) with weighting function W(x)=exp(-(x-mu)^2/sigma) to estimate an integral. Is there a way to do it in R? Is there a function already implemented which uses such weighting function. I have been searching in the statmode package and I found the function "gauss.quad(100, kind="hermite")" which uses

Hello to all, I am having trouble with intregrating a complicated uni-dimensional function of the following form Phi(x-a_1)*Phi(x-a_2)*...*Phi(x-a_{n-1})*phi(x-a_n). Here n is about 5000, Phi is the cumulative distribution function of standard normal, phi is the density function of standard normal, and x ranges over (-infty,infty). My idea is to to use quadrature to handle this integral. But

Dear R list I am looking for a function in R that computes the integration of a discrete curve, such as a power spectrum, in a specified interval (in my case, that would be 'power in a certain frequency band'). I found only functions, such as 'integrate', that perform adaptive quadrature on analytic functions, and not on a curve specified as a set of (x,y) pairs. I have the

Hi folks, I am having a question about efficiently finding the integrals of a list of functions. To be specific, here is a simple example showing my question. Suppose we have a function f defined by f<-function(x,y,z) c(x,y^2,z^3) Thus, f is actually corresponding to three uni-dimensional functions f_1(x)=x, f_2(y)=y^2 and f_3(z)=z^3. What I am looking for are the integrals of these three

Spencer Thanks for your thoughts on this. I did a bit of work and did end up with a method (more a trick), but it did work. I am certain there are better ways to do this, but here is how I resolved the issue. The integral I need to evaluate is \begin{equation} \frac{\int_c^{\infty} p(x|\theta)f(\theta)d\theta} {\int_{-\infty}^{\infty} p(x|\theta)f(\theta)d\theta} \end{equation} Where

In co-operation with Markus Hegland and myself, Zhongwen Ding has written a package, based partly on Markus Hegland's code, that provides a parallel processing interface to a remote multi-processsor system. Pyro (Python Remote Objects) and R must both be installed, both on the client machine and on the remote server. The system uses rsync, with an ssh protocol, to handle file transfer. Once

I am trying to test out several mgcv::gam models in a scalar-on-function regression analysis. The following is the 'hierarchy' of models I would like to test: (1) Y_i = a + integral[ X_i(t)*Beta(t) dt ] (2) Y_i = a + integral[ F{X_i(t)}*Beta(t) dt ] (3) Y_i = a + integral[ F{X_i(t),t} dt ] equivalents for discrete data might be: 1) Y_i = a + sum_t[ L_t * X_it * Beta_t ] (2) Y_i

Hello, I want to know if there are some functions or packages to solve differential and integral equation using R. Thanks. Shao chunxuan. [[alternative HTML version deleted]]

Hi all, We know that Hermite polynomial is for Gaussian, Laguerre polynomial for Exponential distribution, Legendre polynomial for uniform distribution, Jacobi polynomial for Beta distribution. Does anyone know which kind of polynomial deals with the log-normal, Student抯 t, Inverse gamma and Fisher抯 F distribution? Thank you in advance! David [[alternative HTML version deleted]]