similar to: Spline integration & Gaussian quadrature (was: gauss.quad.prob)

List: Thank you for the replies to my post yesterday. Gabor and Phil also gave useful replies on how to improve the function by relying on mapply rather than the explicit for loop. In general, I try and use the family of apply functions rather than the looping constructs such as for, while etc as a matter of practice. However, it seems the mapply function in this case is slower (in terms of CPU

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

I believe this may be more related to analysis than it is to R, per se. Suppose I have the following function that I wish to integrate: ff <- function(x) pnorm((x - m)/sigma) * dnorm(x, observed, sigma) Then, given the parameters: mu <- 300 sigma <- 50 m <- 250 target <- 200 sigma_i <- 50 I can use the function integrate as: > integrate(ff, lower= -Inf, upper=target)

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 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

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]]

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 everyone, My data consists of marked points and several covariates, whereby the marks are the time points of the observations. The problem is, that one of the covariates is hard to handle as an image. This covariate represents the type of roads. As there aren't roads at every location of the map, one cannot specify the value of the covariate at any point on a grid, which is necessary to

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

Hi all, Does anybody know any function that performs gaussian adapative quadrature integration of univariate functions? Thanks in advance, Regards, Caio __________________________________________________ [[alternative HTML version deleted]]

Can anyone help me on how to get the nodes and weights of the adaptive quadrature using R. Best wishes Boikanyo. ----- The University of Glasgow, charity number SC004401

Hi: I was wondering if someone could give me some examples of how to use the "integrate" function to perform multi-dimensional quadrature? I have a posterior density (up to a constant), for which I'd like to evaluate the normalizing constant. thanks for any help, Ravi.

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

I am using both nlminb and optim to get MLEs from a likelihood function I have developed. AFAIK, the model I has not been previously used in this way and so I am struggling a bit to unit test my code since I don't have another data set to compare this kind of estimation to. The likelihood I have is (in tex below) \begin{equation} \label{eqn:marginal} L(\beta) = \prod_{s=1}^N \int

Does anyone see why my code does not integrate to 1? library(statmod) mu <- 0 s <- 1 Q <- 5 qq <- gauss.quad(Q, kind='hermite') sum((1/(s*sqrt(2*pi))) * exp(-((qq$nodes-mu)^2/(2*s^2))) * qq$weights) ### This does what's it is supposed to myNorm <- function(theta) (1/(s*sqrt(2*pi))) * exp(-((theta-mu)^2/(2*s^2))) integrate(myNorm, -Inf, Inf)

Dear list, I'm seeking some advice regarding a particular numerical integration I wish to perform. The integrand f takes two real arguments x and y and returns a vector of constant length N. The range of integration is [0, infty) for x and [a,b] (finite) for y. Since the integrand has values in R^N I did not find a built-in function to perform numerical quadrature, so I wrote my own after

I have constructed the function mml2 (below) based on the likelihood function described in the minimal latex I have pasted below for anyone who wants to look at it. This function finds parameter estimates for a basic Rasch (IRT) model. Using the function without the gradient, using either nlminb or optim returns the correct parameter estimates and, in the case of optim, the correct standard

Hi R Users, I'm going to estimate via. ML the parameters in Poisson Lognormal model. The model is: x | lambda ~ Poisson(lambda) lambda ~ Lognormal(a,b) Unfortunately, I haven't found a useful package allowing for such estimation. I tried to use "poilog" package, but there is no equations and it's hard to understand what exactly this package really does. Using it I get the

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

A new version, 0.65-1, of glmmML is now on CRAN. It is a major rewrite of the inner structures, so frequent updates (bug fixes) may be expected for some time. News: * The Laplace and adaptive Gauss-Hermite approximations to the log likelihood function are fully implemented. The Laplace method is made the default. It should give results you can compare to the results from 'lmer' (for the