Monte-Carlo integration question

*To*: mathgroup at smc.vnet.net*Subject*: [mg66641] Monte-Carlo integration question*From*: "Yaroslav Bulatov" <yaroslavvb at gmail.com>*Date*: Thu, 25 May 2006 02:58:17 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

When I set MaxPoints to 10, I expect integration time complexity to not depend much on the number of dimensions. But the time taken seems to increase exponentially without bound, and a simple 50 dimensional integration problem (with MaxPoints=10) has been running for over a week, why such behaviour? << Statistics`MultinormalDistribution` (* Compute E[||X||] for d-dimensional Gaussian *) ev[d_] := Module[{ndist, params, pdf, intlimits, norm}, ndist = MultinormalDistribution[Table[0, {d}], IdentityMatrix[d]]; params = (Subscript[x, #1] & ) /@ Table[i, {i, 1, d}]; pdf = PDF[ndist, params]; intlimits = Sequence @@ ({Subscript[x, #1], -Infinity, Infinity} & ) /@ Table[i, {i, 1, d}]; norm = Sqrt[Plus @@ (#1^2 & ) /@ params]; NIntegrate[norm*pdf, Evaluate[intlimits], Method -> QuasiMonteCarlo, MaxPoints -> 10]] For[i = 1, i = 10, Print[{i, Timing[ev[i]]}]; i++] Yaroslav