numerical integration - NProbability failing to converge

I would like to numerically calculate the probability of an event involving a random vector. Specifically:

NProbability[(t + e > (t + u)/(t + v)), {t, e, u, v} \[Distributed] 
  MultinormalDistribution[{0, 0, 0, 0}, {{1/2, 0, 0, 0}, {0, 1/2, 0, 0}, {0, 0, 1/2, 0}, {0, 0, 0, 1/2}}]]

When entering the above code, the output tells me that

"Increasing the value of the GlobalAdaptive option MaxErrorIncreases might lead to a convergent numerical integration"

However, NProbability does not seem to allow me higher MaxErrorIncreases (e.g. Method -> {GlobalAdaptive, MaxErrorIncreases -> 10000} is not accepted as valid input).

Answer

direct simulation, of course I suppose this is doing the same as NProbability without the convergence check..

n = 10^6; 
Count[RandomVariate[
    MultinormalDistribution[{0, 0, 0, 

      0}, {{1/2, 0, 0, 0}, {0, 1/2, 0, 0}, {0, 0, 1/2, 0}, {0, 0, 0, 
       1/2}}], n], {t_, e_, u_, v_} /; (t + e > (t + u)/(t + v))]/n //
  N

0.408513

p vs log10(n):

Comments

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