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Results tagged with st.statistics
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user 634
Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.
2
votes
Accepted
Estimate gaussian (mixture) density from a set of weighted samples
The usual EM algorithm can be modified for weighted inputs. Following along the Wikipedia presentation, you would use these formulas instead:
$a_i = \frac{\sum_{j=1}^N w_j y_{i,j}}{\sum_{j=1}^{N}w_j …
- 598
0
votes
What is the probabilistic counterpart of weighted K-Means
Are you looking for a GMM with weighted samples? Please see my answer
- 598
1
vote
statistical approach to multinomial distribution
The conjugate prior of the multinomial distribution is Dirichlet -- it is a distribution over the parameters (the probabilities of outcomes) of the multinomial.
Define
D = Dirichlet(X + 1)
(the 1 …
- 598
3
votes
2
answers
2k
views
Why is Beta the maximum entropy distribution over Bernoulli's parameter?
Why is Beta(1,1) the maximum entropy distribution over the bias of a coin expressed as a probability given that:
If we express the bias as odds (which is over the support $[0, \infty)$), then Beta-p …
- 598
3
votes
Peakedness of multimodal distributions
What about information entropy? The smaller it is, the more mass is in peaks.
- 598
17
votes
1
answer
10k
views
Conjugate prior of the Dirichlet distribution?
What is the conjugate prior distribution of the Dirichlet distribution?
Edit: Since I asked this question many years ago, I've written a Python library for working with exponential families. Maximum …
- 598
2
votes
0
answers
1k
views
Estimating Wiener process parameters
Consider a Wiener process with zero drift, infintesimal variance $\sigma^2$, and an unknown starting value $\nu$. That is,
\begin{align}
Y_t \sim \mathcal{N}(\nu, t\sigma^2).
\end{align}
Now, su …
- 598