All Questions
Tagged with statistics stochastic-processes
712
questions
2
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0
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32
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Characteristic function of Dirichlet Process
Suppose $P \sim \text{DP}(\alpha,G) $ where $G \sim N(0,1)$ is the base measure and $\alpha > 0$ is the concentration parameter. The stick breaking representation says that $P$ can be expressed as \...
- 21
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Probability brainteaser [closed]
Normal 52 card deck. Cards are dealt one-by-one. You get to say when to stop. After you say stop you win a dollar if the next card is red, lose a dollar if the next is black. Assuming you use the ...
- 103
1
vote
1
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99
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Pure Birth Process. Finding the probability we are state n after time t, in general (David Kendall 1949)
Hi, I'm stuck understanding a paper by David G Kendall (Stochastic Processes and Population Growth, 1949). The paper demonstrates how to derive $p_n(t) = \mathbb{P}(X_t = n)$ for a pure birth process ...
- 11.3k
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56
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$UCB-\alpha$ policy for multi-armed bandit - conditions on UCB indices for picking suboptimal arm
While reading the optimality proof for the $UCB-\alpha$ policy for the multi-armed bandit problem , I came across a claim which I couldn't understand the logic of.
Notations:
$I_{i}(t) = \hat{\mu}_{i}(...
- 23
1
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0
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30
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Characterization of purely nondeterministic discrete parameter $L^2$-processes
In the characterization of purely nondeterministic processes, more precisely at proposition 2.2.7 of "Topics in Stochastic Processes", Ash, Gardner et al., after having defined, given $\{X(t)...
- 4,624
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56
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Computing the Variance of a Gaussian Random Variable (follow-up question)
This is a follow-up question on Computing the Covariance of a Gaussian Process. The user @Kurt G. confirmed my result there, but there must be a mistake in my computations. Therefore, I want to share ...
- 439
3
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35
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Name for this type of Markov process?
I'm experimenting with this type of stochastic process and I'm wondering if there is a specific name for it. So far I've described it as a discrete-time continuous-state Markov process but curious to ...
- 45.7k
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2
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79
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How to understand that each random variable $X_t$ of a random process is defined on the same probability space?
According to the definition of random process, for a random process$\{X_t,t\in T\}$ each $X_t$ is defined on the same probability space $\{ \Omega,F,P\}$.
Consider the process of rolling a six-sided ...
- 170k
0
votes
1
answer
58
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Bound on the expected time of first success in a series of Bernoulli RVs
Given an infinite series of Bernoulli RVs $X_1,X_2,...$ (which may be differently distributed and mutually dependent), we are given that for every $n>0$, $$\mathbb{E}\left[\sum_{t=1}^{n}(1-X_t)\...
- 47
1
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1
answer
46
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How to get the two above conditional distribution?
Random variables X and N have joint distribution, defined up to a constant of proportionality,
$f(x,n) \propto \frac{e^{-3x}x^n}{n!}$ for $n=0,1,2,...$ and $x>0$. Note that X is continuous and N is ...
- 12.6k
1
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2
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146
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Recurrence of a state in an infinite state space for discrete markov chains
Question
Let $(X_n)_{n\ge0}$ be a Markov Chain with stochastic matrix $P$, determine whether or not the state $0$ is recurrent when $p_1=p_2<0.5$ and $\gamma >0$. The stochastic matrix P is ...
- 4,331
2
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1
answer
144
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Brownian motion (Wiener process) as a random function
In many articles concerned with functional data analysis, it is considered a regressor $X$ which is a random variable valued in some infinite dimensional set $F$ equipped with (semi/pseudo) metric $d$...
- 2,325
4
votes
1
answer
117
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How long does it take for a two-site wait activation?
Consider two sites, linked as sketched
Initially, both sites are off (red). However, each activates (turns green) at a constant rate $f$. Once activated, a site remains activated. If one activates, ...
- 102k
0
votes
1
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64
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Given the pdf for one variable, how can I transform this into the pdf of another variable
I am considering the diffusion of a particle in 1-D subject to a potential. I have been able to compute the average position $<x> = f(t)$ of the particle as a function of time $t$ as well as the ...
- 13
2
votes
1
answer
524
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Negative values in Poisson process
I'm trying to make some sense of the following definition:
A collection of random variables $\{ N_t \}$$_{t \geq 0}$ is called a Poisson process with rate parameter $\lambda > 0$ if
$N_0 = 0$
$N_{...
- 159k