'non-finite-function value' Error when call 'integrate' with 'maxLik' function

Question

I want to use the maximum likelihood method to estimate the parameters of a function which involves integration. However, when i tried to run it, i got a message that "non-finite function value".

Here are the codes:

library("maxLik")

integrand <− function(x,para) 
{
  # print(para)
  
  # dv, dv_T, dn, dn_T are the actual input data, here only gives one set of value for easy debugging
  dv <- -1.4527280  
  dv_T <- 0.2038909 
  dn <- 17.5174383 
  dn_T <- 26.6993828
  
  beta10 = para[1];
  beta11 = para[2];
  beta12 = para[3];
  alpha1 = para[4];
  beta20 = para[5];
  beta21 = para[6];
  beta22 = para[7];
  alpha2 = para[8];
  
  U_Cur = exp(beta10 + beta11*dv + beta12*dn + alpha1*x);
  U_Tgt = exp(beta20 + beta21*dv_T + beta22*dn_T + alpha2*x);
  
# Update Start - 03/10/2021

   if (is.infinite(U_Cur))
      {
        if (U_Cur<0)   
        {U_Cur=-2^1000}
        else
        {U_Cur=2^1000}
      }

 if (is.infinite(U_Tgt))
      {
        if (U_Tgt <0)   
        {U_Tgt =-2^1000}
        else
        {U_Tgt =2^1000}
      }

# Update End - 03/10/2021

  # print(U_Cur)
  # print(U_Tgt)
  
  P <- (U_Cur/(U_Cur+U_Tgt))
  
  # print(P)
  
  return(P)
}


integrand2 <− function(para1) {integrate( integrand, lower = -2 , upper = 2, para=para1)$value }

MLE<-maxLik(logLik=integrand2,start=c(0.5, 0.2, 0.1, 0.3, -0.5, 0.2, 0.1, 0.6))

After debug, i find the reason of the error is the value of U_Cur or U_Tgt sometimes may be 0 or Inf.

I have no idea about how to deal with that, I really appreciate any related proposal.

===================================

EDIT:

I have update the value of U_Cur, U_Tgt, if they are (-)infinite, set their value as (-)2^1000 (the code is added in the function body above, between “# Update - 03/10/2021”).

Answer 1

I could be misreading your code, but it looks like you are maximizing the following (log)likelihood:

LL = int^2_{-2} exp(5+x+theta) dx = exp(5+theta)int^2_{-2} exp(x) dx.

That likelihood will be maximized by sending theta to infinity. Is that the log likelihood you want?