Unanswered Questions
3,433 questions with no upvoted or accepted answers
17
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0
answers
2k
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Rademacher complexity of logistic regression
Consider logistic regression. We have the logistic loss function,
$\phi: R\rightarrow [0,1], \phi(u)=\log(1+\exp(-u))$, which is Lipschitz, and we have the linear function class $F=\{f_w:R^d \...
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12
votes
0
answers
1k
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Why we really need the concept of "Local" Rademacher complexity?
Recently, I have been studying High-Dimensional Statistics: A Non-Asymptotic Viewpoint written by Martin J. Wainwright. In this book, the author uses a special complexity measure which is called Local ...
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11
votes
1
answer
521
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Queuing theory for elevators
It's been a while since I had my probability course based on Sheldon Ross' book "Probability Models", and while I never went into econometrics, I was very interested in the queuing theory section. I ...
CommunityBot
- 1
10
votes
3
answers
232
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How to guess the size of a set?
Assume we have a set of unique words and draw a number $n$ of them using simple-random-sampling without replacement independently in each round. We have several rounds and try to guess the set size ...
CommunityBot
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9
votes
0
answers
137
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Intuitively, why do flushes overtake straights as the number of cards in hand increases?
A 5-card poker hand is more likely to be a straight than a flush.
But a 13-card bridge hand is more likely to contain a 5-card flush than a 5-card straight (source: I read it online somewhere).
What ...
- 4,199
9
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0
answers
521
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Distribution/expected length of the shortest path in infinite random geometric graphs
Consider an infinite random geometric graph $G(\rho,d)$ in which vertices are uniformly and independently scattered over the 2D plane with density $\rho$ and edges connect the vertices that are closer ...
- 135k
8
votes
0
answers
311
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Time evolution of a Bayesian posterior
I have a question regarding the time evolution of a quantity related to a Bayesian posterior.
Suppose we have binary parameter space $\{ s_1, s_2 \}$ with prior $(p, 1-p)$,
The data generating ...
- 1,533
8
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0
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Exercise on Borel Cantelli Lemma ($\limsup X_n/ \ln(n) =1$ a.s.) help required to rigorously write the statement
I hope this question is within the scope of this site. Please note that I have solved this Exercise, I do have doubts about my presentation though and about how to rigorously empathize on the ...
- 12.3k
8
votes
0
answers
301
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Cox's Theorem: ignorance, objective priors, and the Mind Projection Fallacy
I've been trying to understand Cox's Theorem and the problems surrounding it. There's so much information on this topic that I've become confused as to the exact state of the theorem. I've gathered ...
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8
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0
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398
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Dynamics of birth-death process with discouraged arrivals (alternatively, M/M/1 queue with balking customers)
Take a continuous-time birth-death process, where $k \in \{0,1,\ldots\}$ is the count and
the arrival rate of death is $\mu \geq 0$ for $k = 1, 2, \ldots$
the arrival rate of births is $\alpha_k > ...
- 84k
8
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0
answers
647
views
Sum of absolute values of T random variables
Where X is a r.v. following a symmetric T distribution with 0 mean and tail parameter $\alpha$.
I am looking for the distribution of the n-summed variable $ \sum_{1 \leq i \leq n}|x_i|$.
$Y=|X|$ ...
- 84k
8
votes
0
answers
439
views
Conditional probability update for correlated Poisson variables
Some background:
I am trying to estimate the number of failures in two related machine populations. I model machine failures in a year as a correlated Poisson process as such:
$Y_0,\ Y_1$ and $Y_2$ ...
- 32.1k
7
votes
1
answer
199
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Posterior consistency for scale-mixture shrinkage priors in low dimension?
Consider the model [1]
$$y_n=X_n\beta_n+\epsilon_n$$
$$\beta_i|\sigma^2,v_i \sim \mathcal{N}(0,\sigma^2 v_i), i=1,\ldots,p$$
$$v_i \sim \beta^\prime(a,b)$$
$$\sigma^2 \sim \mathcal{IG}(c,d)$$
where $\...
- 90.8k
7
votes
1
answer
780
views
Probabilities arising from permutations
Certain interesting probability functions can arise from permutations. For example, permutations that are sorted or permutations that form a cycle.
Inspired by the so-called von Neumann schema given ...
CommunityBot
- 1
7
votes
0
answers
166
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How many sides and what are the probabilities of each side for an unfair die?
Problem
I would like to run an inference that predicts from a series of die rolls, how many sides the die has, and what is the probability of landing on each side.
Example
For example, imagine a die ...
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