Racial Profiling in the US

"In 2013, of the approximately 660,000 crimes of interracial violence that involved blacks and whites, blacks were the perpetrators 85 percent of the time. This meant a black person was 27 times more likely to attack a white person than vice versa. A Hispanic was eight times more likely to attack a white person than vice versa."
(see paragraph 10 for Citation)
It's common to assume that blacks are frequently targeted by police, this claim might mean that black Americans are arrested for crimes that are committed by other people, or that other people commit crimes at the same rate but aren't caught as often, or that the police aim to enforce all petty offenses against blacks and ignore severe offenses in other groups. There is significant data to undercut the view that black Americans are being unjustly targeted by law enforcement generally:
"...the annual National Crime Victimization Survey (NCVS). In 2013, 90,630 households and 160,040 people were interviewed for the NCVS about their experiences as crime victims—whether reported to the police or not... In crimes that involve direct contact with victims and in which race of offender can therefore be clearly identified, black arrest rates are below reported offender rates. For example, blacks were identified as 73 percent of robbery offenders but accounted for only 59 percent of robbery arrests. When crimes from all categories are aggregated, black offenders were 14 percent less likely than non-blacks offenders to be arrested. This suggests that police do not show anti-black bias, but make arrests that closely match the proportions at which people of different races commit crime."

Another point is "multiples." Multiples refers to statistics regarding how many times more or less likely one demographic is to commit a given type of crime than another; white Americans are used the baseline here because this is the group that is supposed to be systemically favored by police.
Police officers have the most leeway to harass (i.e. "target") citizens for minor crimes, if there was a systemic racial bias, one would expect almost every white man who spits on someone else's shoes to be ignored and almost every black man who commits any minor infraction to be targeted. With this assumption of police maliciously enforcing every possible law against blacks, it would be expected that the black multiple of the white rate of misdemeanor criminal mischief, or firearms violations to be much higher relative to the black multiple of white shootings or felony assault, as individual cops have the leeway to ignore a white man slapping someone (misdemeanor assault), but not beating another man almost to death (felony assault). The actual rate of multiples entirely contradicts what we would expect with the assumption of police bias: https://i.imgur.com/GvAk68k.png

The above chart shows that blacks were only 2.7 times more likely to be arrested for criminal misdemeanor mischief in NYC in 2014, and 14.6 times more likely to be arrested for the crime of robbery. This data is incompatible with the expectations one would hold with an assumption of blacks being targeted by police and imprisoned whenever possible. In fact, if police thought that blacks were more likely to resist arrest (as the statistics show that they are, on average), and thought them more likely to be a potential physical threat, this would fit well with the data, which shows that police officers go out of their way not to arrest blacks for minor crimes. The data supports a view that police do not go out of their way to arrest blacks for all possible crimes, no matter how minor, but do make arrests when a situation has escalated to the point that they are obligated to take action.
Source for the above two quotes and chart (which is itself based on government statistics): https://www.amren.com/the-color-of-crime/

Other dubious evidence of police bias are studies that reference self-reporting on drug use, these studies claim that blacks and whites report at similar rates, but blacks are more likely to be arrested for drug offenses, therefore there is obviously police bias; at least that's how the argument is presented.
Here's an example of a mainstream outlet repeating this line of thought:
"Over their lifetimes, black and white Americans use illicit drugs at similar rates, according to federal data. But black adults were more than 2½ times as likely to be arrested for drug possession." https://www.washingtonpost.com/news/wonk/wp/2016/10/12/police-arrest-more-people-for-marijuana-use-than-for-all-violent-crimes-combined/?utm_term=.977329e451e5

True, blacks comprise 31.7% of all drug arrests (https://ucr.fbi.gov/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-43), but they also comprise 30.7% of all emergency room visits for overdosing on illegal drugs (https://www.samhsa.gov/data/sites/default/files/DAWN2k11ED/DAWN2k11ED/DAWN2k11ED.pdf). Their disproportionate rate of drug arrests almost perfectly mirror their disproportionate rate of overdosing on illegal drugs, but we don't have to rely on this alone to prove that self-reporting is inaccurate.

And there are multiple studies that have shown blacks are more likely to fail to accurately report their own drug usage:
https://www.researchgate.net/publication/232439635_Drug_Use_among_Juvenile_Arrestees_A_Comparison_of_Self-Report_Urinalysis_and_Hair_Assay
http://www.tandfonline.com/doi/abs/10.3109/10826087709027235#.VezHPBHBzRY
http://corescholar.libraries.wright.edu/aids/21/
Credit to below source for compiling the links in the two previous paragraphs:
http://thealternativehypothesis.org/index.php/2016/04/15/white-privilege-cops-and-courts/

White Americans take fewer risks in acquiring illegal drugs than black Americans:
"Using trivariate probit regression with demographic, drug use, and drug market covariates, analyses reveal that African Americans are nearly twice as likely to buy outdoors (0.31 versus 0.14), three times more likely to buy from a stranger (0.30 versus 0.09), and significantly more likely to buy away from their homes (0.61 versus 0.48). These results provide an additional explanation for the differential in arrest rates between African Americans and Whites."
https://www.ncbi.nlm.nih.gov/pubmed/16600529
Any study based merely on self-reporting of drug usage is not valid, given the racial discrepancies in means of acquiring drugs, and honesty in self-reporting.

To close with a final fact, according to the FBI's Uniform Crime Reporting (UCR) Program (http://archive.is/uP3Yp) black Americans committed 51.1% of all murders in the US in 2015 despite being only 13.16% of the population of the US as of June, 2016 (https://www.census.gov/quickfacts/fact/table/US/PST045216). Black Americans as a demographic are much more likely to be involved in violent crime than other groups, and it should therefore be no surprise to anyone that they are also more likely to be involved in lethal altercations with the police. Black Americans, according to UCR data, also committed 53.5% of all robberies in the US in 2015.