Beta distribution on discrete data Suppose that my data $y \in \{0,0.1,\ldots,1\}$. What are the consequences of modeling that data as continuous, i.e., as if $y \in [0,1]$, by using the beta distribution? Is there a version of the beta distribution that can account for this? 
 A: You could model the variable $10Y \sim {\rm BetaBinomial}(n = 10, a, b)$.  Specifically, if $X \sim {\rm BetaBinomial}(n, a, b)$, then $$\Pr[X = x] = \frac{\Gamma (b+1) \Gamma (a+n) \Gamma (n+x) \Gamma (a+b-x)}{\Gamma (a) \Gamma (n) \Gamma (x+1) \Gamma (b-x+1) \Gamma (a+b+n)}.$$  The only restriction on the parameters $a,b$ is that they be positive; $n$ must be a nonnegative integer; and $x \in \{0, 1, \ldots, n\}$.  This PMF has many nice properties:  see http://en.wikipedia.org/wiki/Beta-binomial_distribution
A: It is rather easy to create a discrete version of the beta distribution, and in its standard interval from zero to unity. In your case the support is $Y \in \{0,0.1,\ldots,1\}$.  So consider the probability mass function, with $j=\{0,1,...,10\}$
$$P(Y=j/10;\alpha;\beta) = \frac{(j/10)^{\alpha-1}[1-(j/10)]^{\beta -1}}{ \sum_{j=0}^k(j/10)^{\alpha-1}[1-(j/10)]^{\beta -1}} $$
but with $\alpha \ge 1,\;\; \beta \ge 1$, and using $0^0 \equiv 1$.
It is characterized by the same flexibility in shape than the continuous version (bar the "U-shape" which would require parameters smaller than unity).
