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Results tagged with pr.probability
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user 634
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
0
votes
Time integral of an Ornstein-Uhlenbeck process
I'm pretty sure the actual solution is given in Ornstein and Uhlenbeck 1930.
Since the O-U process is the velocity of a free particle undergoing Brownian motion, then you are asking for the the distr …
- 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
9
votes
1
answer
2k
views
Kullback-Leibler divergence of scaled non-central Student's T distribution
What is the Kullback-Leibler divergence of two Student's T distributions that have been shifted and scaled? That is, $\textrm{D}_{\textrm{KL}}(k_aA + t_a; k_bB + t_b)$ where $A$ and $B$ are Student's …
- 598
5
votes
Accepted
What can be said about an infinite linear chain of conjugate prior distributions?
Let's say that you have a distribution $F$ in the exponential family with density
\begin{align}
\newcommand{\mbx}{\mathbf x}
\newcommand{\btheta}{\boldsymbol{\theta}}
f(\mbx \mid \btheta) &= \exp\bigl …
- 598