Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
4k views

RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
6k views

Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
3k views

Computational Bayesian analysis in Mathematica: Any plans to develop MCMC?

Does anyone know if there are any plans to develop an MCMC capability in Mathematica? My reasoning for asking is that as it stands, I can't seem to find any 'out-of-the-box' functions/capabilities ...
872 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
5k views

Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. Attempt I wrote the ...
1k views

How to fit a linear model in the Bayesian way in Mathematica?

Basically, I'm looking for the Bayesian equivalent of LinearModelFit. As of the moment of writing, Mathematica has no real (documented) built-in functionality for ...
15k views

Estimate error on slope of linear regression given data with associated uncertainty

Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data? This is for a high school class, and so the normal ...
8k views

Showing the correlation of two variables using a plot

I have a list of $\{x_i,y_i\}$ pairs and I want to show that $x_i$'s and $y_i$'s have positive correlation. The result of ...
1k views

Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
3k views

Generate two random numbers with constraints

I want to generate two random numbers, $p$ and $q$, between $0.5$ and $1$. They are connected by the constraint $1/(2q) > p$. How do I generate $p$ and $q$?
4k views

Histograms with pre-counted data

I've got some large data sets which have been counted but not binned already - essentially, a list of pairs of values (not bins) and counts.* (Or, equivalently, it's been binned into too-small bins.) ...
977 views

Huge bug involving MultinormalDistribution?

Bug introduced in 8.0 or earlier and fixed in 11.1 I found a strange behavior regarding the CDF of the bivariate Normal distribution ...
4k views

Standard errors for maximum likelihood estimates in FindDistributionParameters

I am trying to fit a non-standard PDF to data and FindDistributionParameters works great, and gives me the parameters of the distribution back using maximum ...
1k views

Efficiently generating 2-D Gaussian random fields on the sphere

Context A couple of years ago I posted this question for an efficient code to generate an n-D Gaussian random field (sometimes called processes in other fields of research), which has applications in ...
469 views

Summer Solstice Spurious Correlations Challenge [closed]

I came across this hilarious web site that has charts of bizarre "correlations" between disparate categories. Results like this: In the spirit of my summer solstice shedding spuriously earned rep. ...
1k views

Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?

So, given some data, Mathematica 10.2 can now attempt to figure out what probability distribution might have produced it. Cool! But suppose that, instead of having data, we have something that is in ...
1k views

How to implement Markov Chain Monte Carlo with built-in functions?

These days I'm trying to conduct a model sensitivity test which is heavily based on the Markov Chain Monte Carlo simulation approach. And I find this 'MCMC' package that can perform Markov Chain ...
560 views

Unexpected behavior of confidence bands for data presenting two regions with uneven noise

Let's generate some noisy data with uneven noise. ...
2k views

Efficient way to simulate thousands of Markov chains

I am currently trying to simulate relaxation of a protein population while maintaining the stochastic properties of the system. For this, I used a Markov chain to describe the temporal evolution of ...
2k views

Are Easter days normally distributed?

How can Mathematica be used to check if Easter days are normally distributed? By definition, Easter day is the first Sunday after the first full moon after the spring equinox (so between March 23d ...
11k views

How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
1k views

Backtesting a Probability of Default (PD) model

Background PD models Financial institutions use Probability of Default (PD) models for various purposes such as client acceptance, provisioning and regulatory capital calculation as required by the ...
591 views

More efficient method to compute moments of the Johnson $S_B$ distribution

Here is a very specific feature request. I need Mean[JohnsonDistribution["SB", γ, δ, 0, 1]] When I issue e.g. ...
1k views

Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
479 views

Negative probability?

Bug introduced in 9.0.1 and fixed in 10.0.2 I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
928 views

How to efficiently find moments of a multinormal distribution?

Update: Starting from V10.0 the build-in Moment is fast enough for practical use. I have a multinormal distribution with covariance matrix $\sigma$ and zero mean. ...
1k views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and p(...
2k views

Using Mathematica to solve a probability problem

The problem is from Principles of Statistics by M.G. Bulmer: In a certain survey of the work of chemical research workers, it was found, on the basis of extensive data, that on average each man ...
1k views

Sisyphus Random Walk

A Sisyphus Random Walk evolves as follows: With probability (r) you advance the position of the walker by +1. With probability (1-r) the walker resets at x0 = 0. To simulate the probability of reset ...
954 views

Add a rug representation to plot

This question came to me when I read How convert list of numbers to list of points on x-axis? @Mr.W suggested Interlacing a single number into a long list for the question. @Artes provides a very ...
873 views

Visualization: elliptical insights into data sets…

I was recently reading the following paper on visualization techniques using ellipses to gain statistical insights. Elliptical visualization for looking at correlations has briefly been touched on ...
2k views

Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
282 views

HistogramList is much Slower in 10.2 vs 10.1

While I was running a code I wrote using version 10.1, I noticed that in version 10.2 the running time of the same code was more than twice as long. After some digging, I figured out the culprit is <...
1k views

What is the average of rolling two dice and only taking the value of the higher dice roll?

I am referencing to this question on mathunderflow: What is the average of rolling two dice and only taking the value of the higher dice roll? Now I tried: ...
246 views

Possible bug in OrderDistribution? [Update: Confirmed by Wolfram Research and enqueued.]

Bug Introduced in 11.3 or earlier Initial testing indicates this has been addressed in 12.0 Observe: ...
1k views

Does Mathematica have an implementation of the Poisson binomial distribution?

I need to work out the probability of having $k$ successful trials out of a total of $n$ when success probabilities are heterogeneous. This calculation relates to the Poisson Binomial Distribution. ...
3k views

Random letters: What is the chance that real words are generated?

Suppose that we are just typing random letters with our keyboards and we include space bar. We don't distinguish between capital and lowercase letters. If we do this for a long time, how many of the ...
9k views

Performing a chi-square goodness of fit test

How would I perform a chi-square goodness of fit test? I have tried the following, where my data consists of the observed values whilst the data pair contains the correct values. Then I use the ...
5k views

How to remove outliers from data

I have a data with noise which some times includes significant outliers. The position of the outliers are random. For example: ...
837 views

Measure a DensityHistogram[] pair similarity

I study human vision and more specifically eye-movements. "If we display 2 symmetrical patterns (20 min one after the other), will our gaze distribution be symmetric is my research question." The 2 ...
931 views

Simulate a simple spinner

I'm teaching some simple ideas in probability to students in grade 7. The "spinner" below works, but I'm wondering how I could make it just a bit more realistic by having it actually "spin" around a ...
1k views

How to compute the inverse CDF of HyperbolicDistribution properly?

Fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
393 views

Interfacing Mathematica with MINE using JLink

In last December's Science David N. Reshef, et al. proposed an interesting method to detect associations in data (Detecting Novel Associations in Large Data Sets, Science 334, 1518, 2011). Contrary to ...
469 views

Polynomial expectations of generic distributions

Summary Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
647 views

Solve this probability problem symbolically

Consider a unit square, Pick two points P and Q uniformly at random inside the square, What is the probability that |PQ|>1? I tried solve this problem ...
2k views

Bayesian Inference with Continuous prior distribution

Assume that we have a prior distribution for the probability of success as follows. p = BetaDistribution[6, 14] which we can graph as this ...
409 views

Estimating the probability distribution of a Brownian motion particle

I have system of hypothetical physics. A particle traverses a Brownian motion path in free space, and if it hits a boundary, in my case a box with an opening on one side, it teleports to an uniformly ...