All Questions
Tagged with expected-value sampling
41
questions
2
votes
2
answers
77
views
Estimate number of bad actors
This might be a silly question, but it's got me stumped. I am trying to estimate the number of bad actors in a system.
Let's suppose we have 100 users, and some percentage of them are bad actors. In ...
1
vote
0
answers
83
views
Estimating expected value with respect to posterior
I have a neural network and I need to calculate the following:
$$\mathbb{E}_{P(\theta|D)}[f(\theta)]=\frac{\sum_\theta P(D|\theta)P(\theta)f(\theta)}{\sum_\theta P(D|\theta)P(\theta)}$$
Where $f$, ...
- 197
2
votes
1
answer
246
views
Monte-Carlo integration with importance-sampling
I came across a paper, where (section 3.2) importance sampling is used to estimate an integral. I think I understand what importance sampling is but I don't understand how they got the solution.
The ...
- 23
0
votes
1
answer
92
views
Estimating the integral $\int_{0}^\infty x^4 e^{-2x}\,dx$
We have been given a random variable having a Gamma distribution as shown below:
Using the accept-reject algorithm, we are supposed to sample from the Gamma distribution using exponential as the ...
9
votes
2
answers
730
views
Mean of the log and variance of the log
I am struggling to derive the following identities:
$$
\mathbb{E}[\log Z]=2\log(\mathbb{E}[Z])-\frac12\log(\mathbb{E}[Z^2])
$$
$$
\mathrm{Var}[\log Z]=\log(\mathbb{E}[Z^2])-2\log(\mathbb{E}[Z])
$$
...
- 245
2
votes
1
answer
354
views
Average Error vs. Aggregate Error
I was reading this paper on the history of Bagging Estimators (https://www.stat.berkeley.edu/~breiman/bagging.pdf) and came across the following section:
I am having difficulty understanding the ...
6
votes
1
answer
697
views
Sample without replacement from 1 to N and stop when the value is less than the previous one
I came across a question as below
Assume a series includes integer from 1 to N. Every time one samples an integer without replacement from the series. The process continues if $X_{n}$ >= $X_{n-1}$, ...
- 713
1
vote
2
answers
929
views
Average count of overlap between random samples
If I randomly sample n numbers from 1..m, x times, what would be the average count of ...
- 13
2
votes
1
answer
55
views
Why is the expected value of any data point in the sample equal to population mean?
Suppose we have a distribution of heights of all males in a country.
Let population size = N.
Now, I take a sample of 100 males = {h1,h2,h3,....h100}
How is the expected value of any data point, i.e., ...
0
votes
2
answers
61
views
Expected value of $x$ given $x = f(h)$ and $h$ is a random sample of some normal distribution
Let's say we have random variable $H \sim\cal N(0, 1)$. We take 1000 samples of this distribution. Then, for each $h$, we calculate $x=f(h)$. ($f$ is some complicated function). How can I calculate ...
- 3
1
vote
1
answer
176
views
Consistency of likelihood importance sampling estimator
In a lecture recently our lecturer described a method for approximating the expectation of a function over a posterior distribution using likelihood importance sampling. That is:
$$ \mathbb{E}_{p(x|D)}...
- 13
1
vote
1
answer
147
views
Expected value of a "sample unit"
This is within the context of "survey sampling".
Let $P = \{1,...,N\}$ be the target population, and $S = \{s_1,...,s_n\}$ a sample from P. P and S are identified by the corresponding values of the ...
- 1,511
1
vote
1
answer
191
views
Intuition behind probabilities for sampling without replacement
I am not understanding the explanation here in regards to expectations and probabilities for sampling without replacement. I am not seeing why we don't treat each draw as a unique random variable. ...
- 3,273
0
votes
1
answer
68
views
Likes/Retweets in Twitter data depends on time of extraction
Currently I scheduled a task to extract twitter data of a week (every sunday) to predict the stock market for the following days.
The number of likes of a tweet is not static and changes over time. ...
- 106
3
votes
0
answers
349
views
Why do we use the log-derivative trick before Monte Carlo?
I still don't understand how we can approximate the gradient of an expected value... Indeed it's impossible to sample points and then to average the gradients of them as we have only samples... (How ...
- 399