Questions tagged [randomness]

Randomness is the lack of pattern or predictability in events. Randomness is often modeled with probability distributions, but can also be generated by deterministic processes.

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Metric to quantify randomness

I have an $L \times L$ matrix representing a $2D$ region. Each entry of this matrix is a real number lying in the closed interval [0,1]. I want to quantify how different is this from a similar $L \...
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Stochastic modelling, distribution and ergodicity of a particular time series with a given finite history

Let $\Omega$ be a sample space. A stochastic process $\{Y_t\}$ is a function of both time $t \in \{1, 2, 3, \ldots\}$ and outcome $\omega \in \Omega$. For any time $t$, $Y_t$ is a random variable (i....
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Is using a fixed random seed in production okay?

I have a dataset and am trying to use GMM to cluster it. The algorithm works well but when I run it multiple times I get different results. While the clusters produced in each run are valid my users ...
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How to determine the randomness of coin tosses by its final position?

Suppose a circle is drawn on the floor, and a coin is tossed over it many times. If it jumped out of the circle, then we do not take it into account. How to determine from the statistics of coin end ...
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Chi Square Test?

Would I use a chi square test to solve the following: Use the attached data set for our company to address the following. ...
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Is there a term for this concept (Randomly Random)?

Let's say I have what appears to be a fair dice that over 10K fair throws it produces very close to 1/6 occurrences of each face value. But then one day it starts a string of throws where the 3 face ...
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Is anything inherently random?

Is anything inherently random? Or is all randomness observed in data either "errors in measurement" or "lack of understanding"? Assume we could measure everything with infinite ...
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Can we ever quantify the level of randomness within a (data collecting) experiment?

Can we ever quantify the level of randomness within a (data collecting) experiment? We all know that "randomness" is both directly and indirectly required on different levels for various ...
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Are randomness and probability really logically dependent notions?

Background Some have lamented that it is difficult to distinguish randomness from probability, but I seem to be having a contrary difficulty: are they even logically dependent notions? Probability ...
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Statistical Test for Randomness

just wanted to ask if it's possible to check whether a given sample of data is drawn from a random distribution? If so, can I use some statistical test like the Anderson-Darling test or Chi-squared ...
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measure if some binary events happen in random or are correlated

I have thousands of binary processes of uneven length like those below: ...
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Best practices for testing a coin-flip algorithm

I am uncertain what the best approach is to analyze a game's coin flip algorithm. A game that I play uses a coin flip algorithm to determine who goes first (on the play) or second (on the draw), but ...
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Why is randomness so useful?

Where by "why" I do not mean "list of use cases for randomness." If one has a quantitative question Q about topic X, it does not seem intuitive that values that by definition have ...
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Randomness generated by deterministic processes

The tag excerpt of randomness says: Randomness <...> can also be generated by deterministic processes. Is that not intrinsically contradictory? Or does it consider randomness epistemically ...
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Definition of model in the tag excerpt: random relationship(s) between variables

The tag excerpt of model says: A formalization of relationships between stochastically (randomly) related variables in the form of mathematical equations. This seems questionable to me. I guess ...
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Is random walk with drift is random?

I see everywhere in the web that lag-plot or acf are used to see if a time serie is random. If there is no structure in the lag plot then the data are random, and if autocorrelation = 0 then data is ...
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Why is a 100 heads run surprising? [closed]

Assume we have a fair coin. We flip it 100 times. The outcome is all heads. Why is it that all heads outcome is more surprising to us than a "more random looking" outcome with less ...
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Is there a way to determine if one picture is more random than another

I have two pictures. I only want to keep pictures that "display" randomness. Is there a way to distinguish more random from less? In these plots, time is the vertical axis. So, the second ...
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Why does k-NN algorithm produce different predictions with same model and data?

I have successfully created a model using Apple coremltools' KNearestNeighborsClassifierBuilder() and trained it. However, each time I run the algorithm, I get different predictions. Here are the ...
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How far from "even" is (or is not) significant?

If a six-sided die is rolled 600 times, an even distribution would be 100 rolls for each number. If I actually rolled 600 times and tallied the results... How far away from 100 would a count need to ...
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Frequency of mutants in a very large number of observations

During cellular division (generation of two cells from one) bacteria experience mutations, where a newly produced cell harbors altered genetic code. To measure the rate of this happening Max Delbrück ...
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The interpretation of a random variable

A variable is modelled as a random variable, without reference to the question whether it is truly random in reality. For example, when the outcome of a flip coin is modelled as a random variable, no ...
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Fixing random seed on inference

I will be deploying models into production and I'm wondering whether it is appropriate to fix the random number generator seed at inference time. Here's what I think: setting the seed will give ...
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How do you show a sequence of numbers is not random?

Let's say I take the following sequence of numbers: Obviously it's not random - each value is close to either .5, 1 or 2. What test would you use to show that it's not random?
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Test for random distribution of values in a sequence

I'm looking to measure the degree to which values in a column or list are ordered or pseudo-randomly aligned. In essence I'm trying to distinguish the following scenarios. Say we have a "sex" column ...
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Informational value of R squared and correlation? [closed]

Taleb has previously undermined the typical interpretation of correlation with regards to the informational value it carries, showing how the uncertainty is reduced in a non-linear fashion. With ...
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What are the necessary steps required for conducting a Wolfowitz runs test of randomness, given that I have all the necessary data?

I am writing a part in my thesis about the random-walk theory of price changes. I plan to set up a runs test of randomness to show whether the price changes do follow a particular random pattern. I ...
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How to spot/measure artifacts produced by several rotations of 2-dimensional data?

I am trying to transform dataset to mulitiply its size but preserve its initial random nature. I have 5-dimensional numerical dataset which represent particles in plane, produced by Monte Carlo ...
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I am drawing balls of three colours from an urn until it is empty. Is the sequence of colours random?

I have the following problem. I have an urn with n balls of k different colours. I draw balls without replacement until the urn is empty. This leads to a sequence of colours. I now want to show that ...
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Typo in Deepleariningbook.org or am I misunderstanding Bayesian stats?

This is on page 133 of the book: https://www.deeplearningbook.org/contents/ml.html#pf10 In the above, it says that the data set is directly observed and so is not random If that data we observe ...
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Why is Knuth's definition of random sequence (R4) too weak?

Knuth's $R4$ definition of a random sequence is called "too weak" and he presents an example of why --- second paragraph after the definition on the previous link. Definition $R4$. A $[0..1)$ ...
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My approach to deal with the effects of randomness in a ML model

I'm not a statistician, so please excuse a possibly wrong use of terminology here. My dataset has about 400 - 800 samples and about 800 features. The samples are ordered by time, although it is not a ...
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Need to randomize rank order,

I have a ranking of items, $X = (x_1, \ldots, x_n)$. I want to obtain a random sequence $\hat{X}$, which is a permutation of $x_i$, such that the expected rank-correlation (say, Kendall) between $X$ ...
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maximum randomness and non-randomness

Two questions about randomness of data-sequences: Using a variant of run test like Wald–Wolfowitz to check randomness hypothesis for a one-sample data sequence, which yields a P value denoting the ...
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Measure of randomness that maps well to "hard to guess"?

It was recently pointed out to me that entropy does not necessarily map well to "hard to guess". E.g.: consider a distribution where there's a very high (say, 90%) chance you select a single, ...
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Is there a way to check for sure that optimization was applied to the weights of NN?

Given the first or next steps of NN training, where weights were initially randomly sampled from some distribution, is there a reliable way to determine if some optimization was applied to the weights?...
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Classification accuracy heavily depends on random seed

I want to compare different classification methods and evaluate their prediction measures (such as accuracy etc). I first split the data into training and test set. With the training data I then ...
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LSTM - random and always-different time between data measurements?

I am working with a time series problem where the time between two data measurements is random, and I am trying, without luck, to find an LSTM architecture that can handle this. A very simplified ...
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Testing Randomness in day of year values

I have airline booking data (no. of bookings vs day of year). Day of year is a vector, taking values from 1 to 365, with stepwise increments of 1. We can have one data-set where booking exists for ...
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Stochastic vs Adversarial Multi-Armed Bandit Problems

I know that the multi-armed bandit can be formalised in multiple ways - two of them being the stochastic and adversarial ways. I am familiar with the fact that adversarial way is a game theoretic ...
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The assumptions regarding the t-test

The t-test has an assumption that the sample provided has to be random in nature. Do we test our sample for randomness before carrying out the t-test ?
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Explain the results of the 2-sample Kolmogorov-Smirnov test for two random Gaussian sets of numbers

Suppose I have two sets of random numbers drawn from the Gaussian distribution, $\mathbf{r_1}$ and $\mathbf{r_2}$. I then do a 2-sample Kolmogorov-Smirnov test (KS test) between the two to determine ...
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How do I prove one company is actually doing better than another?

Suppose I have the return information for two reverse logistic companies--See example data. For certain groups companies A and B each receive 50% of the work from a client, but for another group ...
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Random sampling at two different frequencies

In a production line, random samples are drawn to be tested for properties A and B. A has to be tested at a higher cadence than B and the assumption is that A and B have zero correlation. Since the ...
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Cross checking AI Selections vs Random Chance

Fifty Three Images AI Selects 20 images based on various criteria. I Select 20 images based on personal criteria. In a two group selection of all 53 items what is the likely overlap due to random ...
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How to do Monte Carlo with conditional input values?

Please apologise my likely ignorance of the correct terminology and notation. Any edits and suggestions to improve the question are very much appreciated. I want to perform a Monte Carlo simulation ...
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Check if a character string is not random

Background Let's say we have an alphabet of A,B, C, D, then we look through some data and find a "word" which is ...
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Is there a known PRNG that passes TestU01's BigCrunch but fails any test in NIST 800-22?

In other words, does TestU01 incorporate all statistical tests by NIST 800-22?
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What is the state of the art in statistics tests for distinguishing good from bad random number generators?

There are many packages out there. In particular, PractRand gives out an opinion on a number of them, but it's only an opinion. Is there conventional wisdom about which set of set of statistics ...
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Why are there different statistics tests in NIST SP 800-90B and NIST SP 800-22? [closed]

NIST SP 800-22 (published in 2010) lists out some statistical tests for telling good random bit generators from bad ones. NIST SP 800-90B (published in 2018) has apparently the same purpose but lists ...
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