The x-axis are group assignments and the y-axis is the corresponding probability.
$\alpha$ is the prior controlling how much you weigh previously selected groups when selecting a new group assignment.
As $\alpha$ gets smaller you weigh previously selected groups more heavily, hence for $\alpha=0.1$ only a few groups are selected. As $\alpha$ gets larger you weigh the previously selected groups less and less, hence the uniform distribution of groups for $\alpha=100$.
Note $\alpha=1$ corresponds to a uniform prior for the number of groups, but the resulting distribution will not be uniform. In general, larger $\alpha$ equals more groups, smaller $\alpha$ equals less groups.
Multinomial distribution is a discrete, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in \{0,1,\dots,n\}$ and $\sum_{i=1}^k x_i = n$. Dirichlet distribution is a continuous, multivariate distribution for $k$ variables $x_1,x_2,\dots,x_k$ where each $x_i \in (0,1)$ and $\sum_{i=1}^k x_i = 1$. In the first case, the support of the distribution is limited to a finite number of values, while in the second case, to the infinite number of values that fall into the unit interval are within the support.
Does Dirichlet distribution serves the same purpose as a multinomial
distribution?
No. Multinomial is a distribution for counts, while Dirichlet is usually used as a distribution over probabilities.
What are the advantages/disadvantages of using Dirichlet over
multinomial distributions?
They are different things, and as you can learn from the Can a Multinomial(1/n, ..., 1/n) be characterized as a discretized Dirichlet(1, .., 1)? thread, they behave differently in higher dimensions. You would almost never use them exchangeably.
The exception is that in some cases, you might want to use a continuous distribution to approximate the discrete distribution, e.g. as you can approximate binomial (for large $n$), or Poisson distribution (for large $\lambda$) with Gaussian.
What makes the Dirichlet distribution different from a multinomial
distribution?
They are continuous vs discrete distributions.
Best Answer
First, you need to put the data into a sensible form for
ggplot2:Then you can plot it by building up the components you can see in the plot (points and lineranges; faceting, axis control and facet borders):
Output: