# Tag Info

### Can someone give a simple guide of Dirichlet process clustering?

What is the difference between (Dirichlet) distribution and (Dirichlet) process? The difference between a Dirichlet distribution and a Dirichlet process is perhaps easier to understand when you ...

### Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters

To demonstrate a solution to this hyperprior problem, I implemented an hierarchical gamma-Dirichlet-multinomial model in PyMC3. The gamma prior for the Dirichlet is specified and sampled per Ted ...
• 61

### Understanding and Implementing a Dirichlet Process model

What is the difference between DP and CRP? The Chinese Restaurant Process (CRP) is a distribution over partitions of integers. The connection to the Dirichlet Process (DP) exists thanks to De Finetti'...
Accepted

### What does $\in$ mean vs $=$ in probability? What does $d\phi$ mean?

This is indeed rather confusing: the notation $d\phi$ stands for an infinitesimal measurable set located around $\phi$. As in standard measure theory settings with Leibniz's $dx$. It can thus be used ...
• 94.5k
Accepted

### How can we convert values proportional to probabilities to Bernoulli probabilities?

Since $p(1)=p$ and $p(0)=1-p$ are both proportional to a known expression* (the unscaled probabilities, $u(i)=c.p(i)$, with the same unknown constant of proportionality, $c$) and you know the $p(i)$ ...
• 264k
Accepted

### Predictive Density for Dirichlet Multinomial

The first slide applies the general result of the second slide to a case when $$y=\overbrace{(0,\ldots,0,1,0,\ldots,0)}^{1\text{ at }\kappa\text{th position}}$$ with different notations, since [in the ...
• 94.5k
Accepted

• 8,102

### Dirichlet process mixture modelling for a Gaussian likelihood

Chinese restaurant process Let's define this problem using the Chinese Restaurant Process (CRP) formulation of the Dirichlet Process (DP), which can be summarized as follows (from Gershman et al., ...
• 3,172
Accepted

• 8,102

### Polya Urn - formulas

I find the notion of $\alpha G_0(x)$ initial balls of color $x$ confusing and potentially misleading. I like another version of the urn better, similar to the one described on Wikipedia. Let's assume ...
• 156

### Frequency distribution of Chinese Restaurant Process?

Your data {500,100,40,30,12} implies that 500+100+40+30+12 customers chose to sit at a new table, 100+40+30+12 customers chose to sit at a table that had exactly 1 customer at the time, 40+30+12 chose ...
Accepted

### Dirichlet Process with known mean

One approach would be to use the centered Dirichlet process described in the paper "Semiparametric Bayes hierarchical models with mean and variance constraints" http://ftp.stat.duke.edu/...
• 86

### Posterior of parameter for Chinese Restaurant Process

Mike West wrote a method for this. The summary is that looked at in the right way, the posterior can be modelled as $p(α|k, n) ≈ G(a + k − 1, b + γ + log(n))$ Where $a,b$ are priors, $k$ is the ...
• 4,041
Yes, I think your interpretation is correct. An important point is that the parameter vector $\pi$ in the model is assumed to follow a Dirichlet distribution. These parameters represents the ...