All Questions
Tagged with dirichlet-distribution maximum-likelihood
9
questions
1
vote
1
answer
2k
views
Maximum a posteriori on Multinomial distribution with a Dirichlet prior can result in negative probabilities?
I am doing a maximum a posteriori (MAP) estimation of a Multinomial distribution $M(c_1,\dots,c_n|p_1,\dots,p_n)$ with a Dirichlet prior $D(p_1,\dots,p_n|\alpha_1,\dots,\alpha_n)$. The experimental ...
- 113
1
vote
1
answer
2k
views
Maximum likelihood estimation of a Dirichlet distribution multivariate parameters
Is it necessary to find the 'maximum likelihood estimates' of prior dirichlet parameters after finding their initial values through the 'method of moments ' to find posterior probabilities through ...
1
vote
1
answer
340
views
What is the mode of Dirichlet-Multinomial (Polya) distribution?
What is the ML estimate of the parameter $e_i$ for the Dirichlet-Multinomial (Polya) distribution defined below?
$p(\mathbf{x}|\mathbf{e}) = \frac{N!}{\prod_i^d x_i!}\frac{\Gamma(A)}{\Gamma(N+A)}\...
- 135
3
votes
0
answers
479
views
What is the mode of the Dirichlet distribution when some $\alpha_i < 1$
Suppose $X \sim \mathcal D(\alpha_1, \ldots, \alpha_p)$, and suppose $\alpha_i < 1$ for some $\alpha_i$. In this case, the density is unbounded, and so no proper "mode" can exist.
On the other ...
- 8,962
7
votes
1
answer
4k
views
Maximum Likelihood Estimation of Dirichlet Mean
Consider the problem of computing a Maximum-Likelihood estimate of the parameters to a finite Dirichlet distribution, given a set of multinomial observations (probability vectors) assumed to have been ...
- 338
1
vote
0
answers
759
views
Dealing with 0 values when calculating the mle for a Dirichlet distribution
I have $N$ pmfs, and for each each $L$ samples. Each sample has a variable amount of $x$ values, but the $x$ values that they have can be matched. So for example:
$$sample_1 \rightarrow\ x_1 = 0, x_2 ...
- 287
3
votes
1
answer
1k
views
Can log-likelihood function calculated value (M-step) be smaller after 1 EM-iteration?
I am applying a MAP log-likelihood approach in order to fit a Markov mixture model, where objective function to be maximized is given by the formula:
$$
L(X|\Theta _K)=\sum_{i=1}^{n}f(X_i|\Theta_K)+\...
- 779
0
votes
0
answers
538
views
can Dirichlet prior distribution be larger than 1?
This question is related to my quest of clustering the sequences using mixture Markov modeling.
I have trouble understanding Dirichlet priors in the context of MAP-estimate (Mixture Markov Models). ...
- 779
1
vote
1
answer
1k
views
How to use prior probability in inferencing from HMM for activity recognition?
I am interested in modelling human activities using sensor data with HMMs and would like to incorporate prior knowledge during inference. The normal procedure is to model K different activities with K ...
- 33