Questions tagged [computational-statistics]

Refers to the interface of statistics and computing; the use of algorithms and software for statistical purposes.

227 questions with no upvoted or accepted answers
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7
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2answers
6k views

Is it ok to get negative Cosine Similarity using LSA?

I am getting negative cosine similarity value between two documents in Latent Semantic analysis. How should it be treated?
7
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1answer
5k views

Unscented Kalman filter-negative covariance matrix

I have recently started working on the unscented Kalman filter. I coded the numerically stable version (i.e., square root Kalman filter) and used MATLAB for implementing. In the final update step, ...
6
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0answers
36 views

Simulate correlate random variables with given marginal distribution where one is always larger

Is it possible to simulate pairs of random variables with a given marginal distribution and population correlation where one random variable is larger than the other? More formally, I need to simulate ...
6
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0answers
157 views

Is this problem Bayesian? And can I use variational approximation?

Suppose there are $N$ samples of observations $\mathbf X(n)$ ($n=1,\cdots,N$), which are given by probability distribution $p(\mathbf X(n)|\mathbf Z(n))$ with their conditions are given by hidden ...
5
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0answers
267 views

Consistency of variable selection based on Lasso estimator for high-dimensional data

According to this paper by Meinshausen and Bühlmann (2006) the variable subset selection coming out of a Lasso is not always consistent in high-dimensional cases. It is bounded by the neighbourhood ...
5
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0answers
910 views

Measure of similarity between two multivariate samples

I have two samples from a multivariate distribution. One is approximate and the other is exact. My aim is to measure the similarity between the approximate sample and the exact sample. In particular, ...
5
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0answers
1k views

Kurtosis, bias, unbiased and statistics

I apologize ahead of time if this is too vague or meta to be a valid question. I've been looking at Algorithms (Sedgewick & Wayne). They define a class stdstats. In that they define min, max, ...
4
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0answers
90 views

Dynamic panel data model with AR(2) process in the errors

I set up the following dynamic panel data model: $$y_{it}=\alpha y_{it-1}+x_{it}^T\beta+v_{it}$$ Additionally, I have the process in the errors: $$v_{it}=\rho_1u_{it-1}+\rho_2u_{it-2}+\epsilon_{it}$$ ...
4
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1answer
76 views

Looking for a recursive formula for asymptotic variance of importance sampling estimator (self-normalized)

Looking for a recursive formula to approximate variance of importance sampling estimator $Var_q\big[\delta_{IS}\big]\approx\sum_{i=1}^n\tilde w(X_i)^2\big[h(X_i)-\delta_{IS}\big]^2$. This is an ...
4
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0answers
932 views

Simulated Annealing Parameter Tuning

My question concerns parameter tuning for simulated annealing (SA). I've the following toy equation $$ y = (x^2+x) \times cos(2x) + 20 \text{ if } x \in (-10, 10) $$ My problem is that the solution ...
4
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0answers
61 views

Metrics to identify the presence of more than one circle in a set of (x,y) coordinates

I have a set of $(x,y)$ coordinates that represent any number of circles in a plane. What I am trying to do is determine whether there is 1 or more circles present in the data set. This would normally ...
4
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0answers
121 views

What is the feasibility to run linear model for large amount of data?

I am looking for empirical approximations and guidelines on how many operations are required to run a linear model on a given amount of data, or if it's even feasible. Let's assume we use QR ...
4
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1answer
61 views

Need some OLS model help

I need some help with calculating a OLS regression model. The model is $sales = b_{0} + quantity^{b_{1}}$, and the objective is to find the own-price elasticity calculated at the means, $\frac{\delta ...
4
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0answers
973 views

Faster computation of high-dimensional multivariate normal probabilities

My goal is to find a faster way to calculate something like mvtnorm::pmvnorm(upper = rep(1,100)) that is, the tail probability of multivariate normal distribution ...
4
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0answers
291 views

How to visually show the convergence of a process?

I have some set of measurements that I have represented as vectors $x^t$ for $t \in \{ 1, 2, ...\}$. I want to test "convergence" of the process (visually) in some sense. I thought maybe I could run ...
4
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0answers
147 views

How to estimate the given function using Rao Blackwellization approach?

I have a function $X$ which is lognormal (0,1) and then another function $\log Y = 4 + 2 \log(X) + \epsilon$ where $\epsilon \sim \mathcal N(0,1)$ I want to estimate $E(Y|X)$ as a Rao Blackwellized ...
4
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0answers
558 views

How to compute the weight matrix for WLS estimation of a multi-group ordinal CFA model

I am attempting to perform a two-group confirmatory factor analysis (CFA) of one continuous factor on six ordinal predictors in OpenMx (...
3
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2answers
82 views

Is my logistic regression model correct?

I have a factorial design 2*2 (A and B). Both variables with two responses high (coded as 1) and low (coded as 0) and I have a response variable $y$, my logistic model include interaction between A ...
3
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0answers
21 views

Statistical inference for morphogenesis models

I work developing morphogenetic models of plant tissues. In short, a typical model of this kind would be a single starting cell that grows and divide, while exchanging molecules with other cell based ...
3
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1answer
343 views

Running SMOTE on very large class imbalanced datasets - batched or subsampled implementations

There is a theoretical and computational aspect to this question. I was trying to use SMOTE to reduce class imbalance in a rather large dataset--about 8 million rows. The data has a binary outcome ...
3
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1answer
58 views

Computing Wassertein Distance

For two probability measures $\mu$ and $\nu$, the Wassertein Distance is defined as $$W_p (\mu , \nu) = \left[ \inf\limits_{\gamma \in \Gamma} |x-y|^p \, d\gamma (x,y) \right] ^{\frac{1}{p}} \, , $$ ...
3
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0answers
93 views

Computing the CDF of the minimum of particular dependent random variables

For each $i=1,\dots,n$ let $Z_i\sim\text{Poisson}(\lambda_i)$, and suppose $\{Z_i\}$ are independent. Also for each $i=1,\dots,n$, let $\{Y_{ij}\}_{j\in\mathbb{N}}$ be an infinite sequence of iid ...
3
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0answers
417 views

Importance sampling: what is this bias?

I am experiencing what seems to be a bias in importance sampling, which, given that it's an unbiased procedure, should not be there. Consider linear regression $$ y = X\beta+\epsilon $$ where there ...
3
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0answers
2k views

Finding correlations in a large dataset

My main objective is to find correlations between process parameters and their impact (more specifically: the amount of wear measured) on specific sections of equipment used in the process. I've ...
3
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0answers
58 views

Which formula for Pearson $r$ would you use in computational practice?

Considering that you have to compute (large) correlation matrix between variables x, y, z,...etc, via matrix multiplications, will you prefer $\frac{cov_{xy}}{\sqrt{\sigma_x^2 \sigma_y^2}}$ or $\frac{...
3
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0answers
69 views

Statistical image analysis

I am working on analyzing a set of high resolution images and I was wondering what would be the most statistically valid method to test, whether the object 'x' is in the centre of the circle (diamond ...
3
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1answer
94 views

What is your configuration to do statistical analysis on large data sets?

The stat packages which I've been using are not very well suited for working with large data sets, i.e. more than 1 billion records. They all tend to try loading all into memory, and install one one ...
3
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0answers
348 views

Is this simple paired-sample permutation test valid?

I have about 10 pairs of scores, $(x_1, y_1),~ ...,~(x_{10}, y_{10})$, with all $x_i$ and $y_i$ being between 0.0 and 1.0. I'm interested in testing whether the mean difference over pairs is ...
3
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0answers
73 views

differences between fake computer-generated data & real data

generally, is there a/some formula(s) or algorithm(s) to prove that a data set is a fake one generated using computer and not by field work? more specific, recently I got a research questionnaire data ...
3
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0answers
149 views

Aggregate variance for ordinary least squares?

I am writing some MapReduce code to calculate ordinary least squares from a sample of data. I'd like to include standard error, but I am running into a problem in calculating the variance of the noise....
3
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0answers
2k views

What do the dip test output parameters mean?

This may sound like a silly question, but I'm not a statistician, mathematician, or programmer, really. I did quite a bit of googling, including looking into Stack Exchange, but couldn't find a clear ...
3
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0answers
113 views

Is there an efficient algorithm for sampling from the negative hypergeometric distribution?

I'm writing a small statistics library currently. One of the algorithms I'm implementing has two variants: one that samples the hypergeometric distribution and one that samples the negative ...
3
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0answers
270 views

Changepoint Analysis in R for Time Series Data

I'm new to R and statistics in general. My background is in Software Development, and I've tasked myself to solve a problem in a 3rd party application. This application is a Game, and I'd like to ...
3
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0answers
802 views

EM algorithm for mixture of Negative Binomial distributions

I am trying to derive the EM-algorithm of mixtures of negative binomial distribution $Neg\;Bin(r,p)$. I have the updating equations for updating the E-step as well as $p$ and the mixing coefficients $\...
3
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0answers
137 views

Coefficient of variation to compare running time of two algorithms

I have developed two new sorting techniques using C language. I need to compare the performance of the both sorting techniques, to see which one is better than another. To do this, I used different ...
3
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0answers
33 views

Computing values of the Lilliefors c.d.f

How up-to-date is the assertion in this Wikipedia article that tables of the Lilliefors distribution have been computed only by Monte Carlo methods? (It would seem preferable to use deterministic ...
2
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0answers
43 views

Computationally estimate $E[f(\hat \beta_1 X)]$ where $\hat \beta_1$ is the estimated coefficient obtained by ordinary least squares regression?

Let $(X_1,Y_1),(X_2,Y_2),\dots,(X_5,Y_5)$ be i.i.d samples and consider the regression model $$ Y_i = \beta_0 + \beta_1 X_i + \varepsilon_i, \quad \quad \text{for} \ i \in \{1,2,\dots,5\}, $$ where $\...
2
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0answers
11 views

Reference Request: Ratio of Computational Complexity to Predictive Quality

I remember coming across a "performance metric" which was the ratio between the MSE and the computational time. However, I can't seem to recall the name of this metric or a reference. Does anyone ...
2
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1answer
75 views

Which statistic is this 'overlap between sets/sections' - if any?

I’m sure someone in history already invented the following formula before. Does anyone know if so and what it’s called? Let’s say there is a set of number pairs, such that the second number in each ...
2
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1answer
70 views

Orthonormalization to use closed form Lasso solution

Given the Lasso problem $$ min_\beta (Y-X\beta)^\top(Y-X\beta) \quad s.t. \|\beta\|_1\leq\lambda, $$ and assuming that X is orthonormal such that $X^\top X=I$, we know that the closed form solution ...
2
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0answers
83 views

Computational time of a (fairly complex) GAM with ARMA structure in brms

I am fitting a model for time-series analysis of Wikipedia views with STAN through the brms package. I came up with a pretty good distributional model, which ...
2
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1answer
271 views

LDA/NMF Topic Modeling vs Topic Modeling using “skip gram” approach

I am having a little friendly debate with my coworker on how to properly/optimally do topic modeling. I am just using the regular traditional nmf/lda approach and he decided to do it using "skip grams"...
2
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0answers
48 views

Downsample a stochastic process without losing correlation statistics?

I have a stochastic variable $X(t)$ which changes at a discrete set of random times $t_1, t_2, \dots$. I can simulate this stochastic process to obtain a series $X(t_1), X(t_2),\dots$ However, the ...
2
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0answers
41 views

Using Markov random field spatial weights to account for spatial autocorrelation

I am looking at the relationship between life expectancy and smoking rate within the London boroughs. I thus created a bayesx spatial regression model including a term which assigns spatial ...
2
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0answers
31 views

Simulation - problem of maximization inside a circle

I am doing some projects related to statistics simulation using R based on "Introduction to Scientific Programming and Simulation Using R". In the Students projects session (chapter 24), I am doing ...
2
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0answers
126 views

Machine Learning - Predicting Multiple Response Variables (Clothing Sizes)

For context, when a retailer buys in a clothing item they have to stock it in various sizes. The ratio of stock for each size is referred to as the "size ratio" of the product. E.g. S=0.2, M=0.5, L=...
2
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0answers
80 views

Edgeworth Expansion of Discrete Random Variable

Background Consider a random variable $Z$ given by $$ Z=\sum_{i=1}^nX_i,$$ where the $X_i$ are iid random variables which are linear combinations (with both positive and negative coefficients) of ...
2
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0answers
39 views

Selection of differentially expressed genes

I don't have any statistical background. Have some questions. I see in some research papers they select differentially expressed genes based on fold change and p.value. And in some other papers I ...
2
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0answers
64 views

Why matrix inverse is not numerical stable?

I was told by many people, many times, Never explicitly compute matrix inverse, because it is not numerical stable. Instead, use LU, QR, SVD decomposition to solve the linear system. But why? Is ...
2
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0answers
96 views

Stability of maximum likelihood algorithm with indeterminate forms

Assume that I want to estimate a copula model, where the copula has a single parameter, $\theta$. When this parameter takes a specific value, say $\theta_I$, this copula converges to the Independence ...

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