It's a bit simplistic to speak only about migrants.

In the case of Islamic terrorism, I've heard it commented that recruits come from the children of migrants rather than the migrants themselves. This certainly seemed to borne out by the London 7/7 bombers and the Charlie Hebdo attackers to name two cases.

Prison populations in western countries also seem to have disproportionate numbers of ethnic minorities.

I also heard that Canada refuses to break down crime figures by ethnicity/race as a matter of public policy. If that is true it seems that there is a fear that the figures might look bad for minorities.

In the interests of community harmony, authorities commonly seem to want to accentuate the positive and sweep any negativity under the rug.