Non-numerical values errors as NIntegrate

Here is my code: 1. Define a Gaussian Mixture Model

SuperModel[w1_?NumericQ, w2_?NumericQ, w3_?NumericQ, w4_?NumericQ,
w5_?NumericQ, m1_?NumericQ, m2_?NumericQ, m3_?NumericQ,
m4_?NumericQ, m5_?NumericQ, m6_?NumericQ, m7_?NumericQ,
m8_?NumericQ, m9_?NumericQ, m10_?NumericQ, sigma1_?NumericQ,
sigma2_?NumericQ, sigma3_?NumericQ, sigma4_?NumericQ,
sigma5_?NumericQ] =
MixtureDistribution[{w1, w2, w3, w4,
w5}, {MultinormalDistribution[{m1, m2},
IdentityMatrix[2]* sigma1],
MultinormalDistribution[{m3, m4}, IdentityMatrix[2]*sigma2],
MultinormalDistribution[{m5, m6}, IdentityMatrix[2]*sigma3],
MultinormalDistribution[{m7, m8}, IdentityMatrix[2]*sigma4],
MultinormalDistribution[{m9, m10}, IdentityMatrix[2]*sigma5]}]

1. Integral over the product of the PDF
NIntegrate[
Product[PDF[
SuperModel[w1, w2, w3, w4, 1 - (w1 + w2 + w3 + w4), m1, m2, m3, m4,
m5, sigma1, sigma2, sigma3, sigma4, sigma5],
Part[ListY, j]], {j, n}], {m1, -1, 1}, {m2, -1, 1},  {m3, -1,
1}, {m4, -1, 1}, {m5, -1, 1}, {sigma1, 4, 16}, {sigma2, 4,
16}, {sigma3, 4, 16}, {sigma4, 4, 16}, {sigma5, 4,
16}, {w1, w2, w3, w4} \[Element]
RegionIntersection[
ImplicitRegion[w1 + w2 + w3 + w4 <= 1, {w1, w2, w3, w4}],
ImplicitRegion[w1 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w2 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w3 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w4 >= 0, {w1, w2, w3, w4}]]]


Then it gives me following error code: I'm curious what's wrong with the part of product of PDF?

Supplementary:

1. ListY: the list of $$\{Y_i\}$$, contain $$n$$ $$Y_i$$ generated from a specific Gaussian Mixture Model. For instance, let $$n = 5$$, then ListY could be:
{{0.574953, -3.92776}, {1.15219, -2.60178}, {-0.851673, -2.08292},
{-5.36409, 0.645265}, {0.560418, 3.89104}}

1. If I replace Product[...] with only a real number, it works:
NIntegrate[1, {m1, -1, 1}, {m2, -1, 1},  {m3, -1, 1}, {m4, -1,
1}, {m5, -1, 1}, {sigma1, 4, 16}, {sigma2, 4, 16}, {sigma3, 4,
16}, {sigma4, 4, 16}, {sigma5, 4, 16}, {w1, w2, w3, w4} \[Element]
RegionIntersection[
ImplicitRegion[w1 + w2 + w3 + w4 <= 1, {w1, w2, w3, w4}],
ImplicitRegion[w1 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w2 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w3 >= 0, {w1, w2, w3, w4}],
ImplicitRegion[w4 >= 0, {w1, w2, w3, w4}]]]


• What happens when you evaluate the integrand at a point in the domain? Do you get a number? – Michael E2 Jan 14 at 1:09
• What is ListY?. – OkkesDulgerci Jan 14 at 1:11
• Seems I found one of the mistake in my codes.... – 0o0o0o0 Jan 14 at 2:49