# Tag Info

### Mini-Batch Gradient Descent - Why does sampling with replacement work?

It works (and we don’t care about sampling points multiple times) because it’s an unbiased estimator of the full gradient. Gradient distributes over summation (and expectation). The expected value of ...
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### What distribution to sample X from to get an uniform distribution in Y?

There is no need for absolute values around your sine function. f(x) = sin(x) is a perfectly fine pdf on the sample space [0, pi/2]. As schotti points out, you can create an RV with this pdf by taking ...
1 vote

### Formal definition of "sampling intensity" in terms of probability theory

The context for this definition is sampling of a population, which is modelled by considering some population values $X_1,...,X_N$ where $N$ is the population size. In the model-based approach to ...
• 94.4k

### Logistic regression simulation with respect to event occurrence (prevalence)

You have an array of explanatory variables $(x_1, x_2, \ldots, x_n)$ ($n=20000$) and a model that assigns a probability to each $x_i.$ You seek a subarray of these variables that has a mean ...
• 287k

### Logistic regression simulation with respect to event occurrence (prevalence)

Its going to be hard to simulate a with an exact proportion of 1s, but if you can get pretty close if you simulate a lot of data. Key thing to realize is that the intercept is the log odds of the ...
• 25.8k

### Choosing an equal number of samples from each strata - what is this called?

This would be a type of "disproportional sampling". In particular it would be "equal allocation". I've never tried it, but from this Stack Overflow question, https://stackoverflow....
• 1,477
1 vote

### What distribution to sample X from to get an uniform distribution in Y?

The question doesn't require a specific programming language, which is fine, but I noted that the OP's plot looks like the default style of matplotlib. @jbowman has given a useful r implementation. ...
• 3,402

### Can I take a random sample of my very large data set to overcome non-independence?

I will add a couple of points to Tim's answer, focussing on the original question, which was "My question is - is this valid? Am I missing anything here?". I think the approach can be valid, ...

### What distribution to sample X from to get an uniform distribution in Y?

I suspect the difficulty you are having is in the generation of $x$ from $f(x) \propto |\sin(x)|$. I have coded a very simple acceptance-rejection random number generator in R that will do the job: <...
• 32.7k

### What distribution to sample X from to get an uniform distribution in Y?

maybe i misunderstand your question, but why don't you sample from a uniform distribution and set X to the arccos of your samples? in R, this would be ...
• 391

### Why is random sampling good?

A non-random sample may be good for a particular purpose, or it may be bad. A random sample can be shown with high probability to be "good" for many purposes. In particular, in statistics, ...
• 610

### Why is random sampling good?

The Central Limit Theorem may be the theory you're looking for. It shows that random sample means follow a Normal distribution (even if the population isn't Normally distributed) and that allows us ...
• 139

### Why is random sampling good?

You seem to be conflating the idea of random sampling with the separate question of whether objects are sampled with our without replacement. The first method you describe is a simple-random-sample ...
• 94.4k
1 vote

### Markov Chain Monte Carlo with known normalisation

Another way of looking at the issue of approximating$$\mathfrak I = \sum_{x\in\mathfrak X} p(x)O(x)$$by stochastic techniques is to aim at adding primarily large values of $p(x)O(x)$. Assuming no ...
• 91.8k
Accepted

### Can I take a random sample of my very large data set to overcome non-independence?

If you downsample time-series data it would not remove the dependence, it would just dilute it. Say that your data follows the relationship $$y_{t+1} = f(y_{t}) + \varepsilon_{t+1}$$ so the current ...
• 113k
Accepted

### How to sample from a custom heavy tailed (e.g. custom Cauchy) distribution?

Because $Z$ is symmetric around $0$ and $|Z|$ has a generalized beta prime distribution, there is a simple algorithm to obtain random values of $Z$ efficiently: Step 1: Draw a random value $Y$ from a ...
• 287k

### Log-normal mean and standard deviation change after sampling

I did this in R and got very similar results to you, even when I tried sampling from the corresponding normal then exponentiating. The issue here is the scale of the values you're trying to sample. ...
• 131
1 vote
Accepted

If $X \sim \mathrm{N}(\mu, \sigma^2)$ and $Y=e^X$, then $Y \sim \mathrm{Lognormal}(\mu, \sigma^2)$. The random variable $Y$ has mean $m=\mathbb{E}(Y)=\exp(\mu+\sigma^2/2)$ and variance $v=\mathrm{Var}(... • 131 1 vote Accepted ### Showing that$E[\hat{\tau}_D] = P(n_D > 0)\tau_D$and$\vert E[\hat{\tau}_D] - \tau_D\vert \leq \tau_D(1-\frac{N_D}{N})^n$For (ii) I believe the idea is to get the upper estimate going from the usual Simple Random Sample to one with replacement where the inclusion events are i.i.d. Is the sample$S$drawn with or ... • 131 3 votes ### uniformly sample from gaussian distributed data It doesn't matter what the distribution of the data might be. You ask to create samples in which only the data values appear, yet are as uniformly distributed as possible. Remove any data not in the ... • 287k 1 vote ### Inverse transform sampling : comparing bias, variance and mse for an estimator Basically, what you are trying to do is evaluate the MSE :$\mathbb{E}(\hat{\theta} - \theta)^2\$ ,through Monte-Carlo simulations. That is, you evaluate the expectation (an integral here) through a ...
• 46
This works. Another way to view what you're doing is as $$\mu \sim U[0, 1] \quad \delta \sim \mathcal N(0, \sigma) \quad X = \mu + \delta .$$ The density of the sum of two variables is the ...