All Questions
Tagged with simulation probability
133
questions
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How to compute Expected Squared Jump Distance (ESJD) of a Metropolis-Hastings algorithm
The Expected Squared Jump Distance (ESJD) seems to be defined slightly differently in various papers, which makes this very confusing. For instance, Definition 2.2 of Optimal Scaling of Random-Walk ...
- 2,236
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30
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Expected deviation between a theoretical discrete probability distribution and the simulated one resulting from a number of trials
Suppose we have seven colors, each associated with a theoretical probability to choose one of them. The probabilities are as follows:
red ______ 0.304761904761905
blue _____ 0.304761904761905
yellow ...
- 11
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2
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94
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Will this converge to origin?
Suppose you have a diffusion of 100 points with the following iteration:
$$(x_{n+1},y_{n+1}) \sim \mathcal{N}\left((x_n,y_n), \frac{x_n^2 + y_n^2}{2} I_{2 \times2}\right)$$
This will make a high ...
- 209
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102
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Auxiliary randomization and the generalized CDF inverse
I'm trying to solve Homework 4 from professor Ryan Tibshirani's class on "Advanced Topics in Statistical Learning" [pdf] at UC Berkeley. It deals with basic facts about CDFs and quantiles.
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3
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1
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3k
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How to generated skewed distribution with specific means and variances (in R)?
For teaching purposes I'm trying to generate some probability distributions that have varying amounts of skew but precisely controllable mean and variance. I'd like to plot these distributions and ...
- 327
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2
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179
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Simulate correlated Bernoulli variables where the sample distribution is exactly the same as the population distribution
Is there a way to generate two correlated variables with a Bernoulli distribution where the sample distribution is exactly the same as the population distribution?
I can easily generate a pair of ...
- 1,677
8
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2
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1k
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Simulation to estimate a conditional expectation
Let X and Y be independent and identical exponential random variables with parameter $\theta>0$. Compute $P[X \leq x | X+Y]$ for $x\geq0$.
I tried to solve this theoretically here (https://math....
- 211
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how do i empirically estimate variance of conditional normal distribution?
I've tried searching for this, but maybe I'm not using the correct search strings. suppose I have joint distribution $P(X_1,X_2)$ over 2 continuous random variables $X_1,X_2$ that I can sample from. ...
- 435
4
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323
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Why Can't We (Directly) Simulate Data From a Semi-Parametric Distribution?
I was reading this paper over here (https://journals.sagepub.com/doi/pdf/10.1177/1536867X1201200407). In the first paragraph on the second page, the authors write the following line:
"Furthermore,...
3
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2
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285
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Logistic regression simulation with respect to event occurrence (prevalence)
I am trying to simulate logistic regression data, but under the constraints of prevalence.
$$\text{logit}(y_i) = \beta_0 + \beta_1 X_1 + \beta_2X_2$$
For example, I want to create a dataset that has ...
- 313
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1
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1k
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Acceptance-Rejection Technique Theorem Proof
I am assigned to discuss the acceptance-rejection technique in our class. I have trouble understanding the last part of proving its theorem.
The theorem goes like this:
The acceptance-rejection ...
- 51
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161
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Simulating paths of stochastic process from density
I need yout help! I have a stochastic process $X_t$ and I know its density function $f(x,t)$, which is defined for $x>t$.
I'm looking for a code in R that simulates the paths of the process, so I ...
- 1
2
votes
1
answer
125
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Which distance to assess equality between discrete distributions?
I have approximated a discrete distribution via Monte Carlo in two different ways, which metric would you use to check the distance between the two distributions? I want to use it to diagnostic ...
- 31
6
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3
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871
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What is the probability of having all wealth concentrated into one single pocket after n trades?
On Joe Rogan's podcast #1769, Dr. Jordan Peterson said something like this:
Take a population of 10 people, each starting with 100 dollars.
They will "trade" based on a coin flip. Whoever &...
- 210
0
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1
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167
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product of log-normal variables
I'm trying to figure out some "paradox" that I don't understand.
I want to model the evolution of some quantity (eg price), my assumption is that from one time step to the next, I will ...
- 144