Questions tagged [computational-statistics]

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

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Fast top-n from samples of many different normal distributions

Let's say I have 1 million normal distributions, each with a different mean and stdev. I want to sample from each distribution and take the top 10 samples (for a Thompson sampling application.) Is ...
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Find the likelihood threshold for a Goodness-of-Fit test for multinomial data

Given a sample size $n \in \mathbb{N}$, a null hypothesis $H_0 = \langle p_1, p_2, \dots p_k\rangle$ which is an element of the $k$-dimensional probability simplex, and a significance threshold $\...
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Comparing the probabilities of 2 different completely separate models that predict different outcomes

You have 2 separate models, one is a binary classifier that predicts whether a customer will pay off their credit card balance on time and another binary classifier (separate model) whether a customer ...
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Simulating Iterated Brownian Motion

I was going through an interesting article (https://arxiv.org/pdf/1112.3776.pdf) while I was trying to read about subordinated processes. I wanted to simulate subordinated processes (in R or python) ...
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Why do we need a binary tree for this way of computing the two-sample Kolmogorov-Smirnov statistic?

In this paper, Detecting Change in Data Streams, section 5 Algorithms, the authors show a way to compute the two-sample Kolmogorov-Smirnov statistic over intervals and initial segments in $O(log(m_{1}+...
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Biplot interpretation

I'm quite confused as to interpreting results from a biplot. I am trying to find out which variable is negatively correlated with the variable Hue and which variable is uncorrelated with Hue. At this ...
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2 votes
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I have a group that contains zero data, and I want to know whether it is considered normally or not normally distributed.?

I have a group (group2) that contains zero data, and I want to know whether it is considered normal or not normally distributed. I used the SPSS software, and it showed this result. I also tried R, ...
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How do I solve skewness in a percentage difference calculation?

I have two variables I want to evaluate -- Planned Hours per project and Tracked Hours per project. Sometimes Planned Hours exceeds Tracked Hours, but often it's the reverse. I calculated the ...
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2 votes
1 answer
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Efficient storage of functional data

I have access to a sample (size $N$) of functional data. Each observation corresponds to $C$ functions. Each function $f_{n,c}$ is represented by $T_n$ points for $1\geq n \geq N, 1\geq c \geq C$. All ...
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What are some well-known unbiased estimator of regression coefficient besides OLS estimator?

Is there any other unbiased estimator of regression coefficient than OLS? For instance, one might consider using unbiased estimator with less computational cost (since OLS involves matrix inversion)?
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General way to describe dot product of N different random variables [duplicate]

I'm a novice to DS, so feel free to correct me. Imagine we have $N$ biased coins each with different probability of getting heads (which are known to us prior). What's the probability of getting $k$ ...
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Antithetic method for monte carlo when bounds of the integral are infinite

I wanted to apply Monte Carlo with antithetic variables to estimate $\int_{0}^{\infty} e^{-x} \,dx$ (equal to 1). I used this R code. ...
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What reasons beyond interpretability are there to use additive models over a complex, multivariate smoother?

Let's adopt for the second the notation from the R package mgcv. ...
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How to decompose multiple periodicities present in the data without specifying the period?

I am trying to decompose the periodicities present in a signal into its individual components. Say the following is my signal: You can reproduce the signal using the following code: ...
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Can I make Stata run lasso faster?

I am trying to run a lasso in Stata. I have 1.5 million observations and 1700 variables. Stata is running too slow. I am in 36th grid after 4 days. And get slower ever grid. I am using a 98GB Memory, ...
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KS-Test Mutual Independence Assumption Question

I am trying to test whether a distribution of data (intensities of a region in an image) follow a uniform distribution of the same range of value: ...
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Loadings of difference between two principal components?

I have a data set with 32 variables. Of those, I find two principal components. I then took the difference between principal components and I would like to find the loading of the difference between ...
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Are the distances on a hierarchical clustering dendrogram in the same units as the input distance matrix?

I use Aitchison distance as the input to a hierarchical clustering dendrogram. I started labeling and interpreting the dendrogram but wasn't sure about a few aspects: Are the vertical distances on ...
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Deriving the Newton-Raphson update for an MLE with two parameters

Suppose we use the Poisson process assumption given by Ni|bi1,bi2 ~ Poisson(λi) where λi = α1bi1 + α2bi2. The parameters of this model are α1 + α2 which represent rate. How do we derive the Newton-...
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An estimation method/algorithm for estimating the value of a specific parameter in a convex function

I am looking for an estimation/iteration process to estimate the value of a specific unobserved parameter of a convex function that fits the observed data of the other variables closely. Specifically, ...
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Understanding computational & statistical tradeoffs

Lots of people talk about computational vs statistical tradeoffs e.g. https://stat.mit.edu/research/statistical-and-computational-tradeoffs/. I have two questions. Can someone please provide some ...
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7 votes
2 answers
711 views

Can arbitrary precision calculations be useful for machine learning?

Regarding machine learning methods but dealing with arbitrary floating-point precision. It sounds cool to me but I am unsure if this would be of any use... Did anyone ever encountered cases where, for ...
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How many samples are needed to estimate quantiles for an unknown distribution?

I'm trying to evaluate performance of a metric learning model. The model that takes labelled image inputs and maps them to vectors on an N-dimensional unit sphere. The goal of the model is to map ...
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Do any standard copulas fit well these sampled bivariate data--exhibiting repulsive behavior--having uniform marginals

I'm currently developing a data set that consists of two $50 \times 50$ matrices, which I designate as q1 and Q1. I strongly believe (bordering on formal proof [cf. Corollary 1 in marginalinvariance]) ...
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Computing score for chess moves based on statistics

There are statistics available for the chess moves that can be played for various opening positions. These stats include the number of games played as well as the number of each of the outcomes (white/...
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1 answer
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Is best model selection by RSS equivalent to best model selection by R2 value?

I am trying to compare models using K-Fold-CV using the regsubsets function in R. By default, it states that the ideal model is determined by the $RSS$. I wished to ...
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Bootstrapping example ISL - pages 194-195

I'm currently learning about bootstrapping using the book Introduction to Statistical Learning, and am struggling to understand what the point of using the boot ...
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1 answer
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Is "controlling for variables" via multiple regression the same as feature importance, SHAP values with regression via xgboost?

There are a few posts going over the fact that "controlling for variables" in traditional stats involves building a regression model and including possible covariates in the model. An ...
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1 answer
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Simulation using the fundamental theorem of simulation (MATLAB)

I have a sub-task of an assignment about the parametric bootstrap method. The subtask is to, given a students t-distribution with $5$ degrees of freedom, sample $10000$ draws using the fundamental ...
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Rademacher Complexity of the family of constant-valued functions

Let $\mathcal{H}$ be a family of constant-valued functions with values in the closed interval $[a, b]$,how to calculate the rademacher complexity of $\mathcal{H}$? We know that the definition of ...
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9 votes
1 answer
315 views

Distribution of argmax of beta-distributed random variables

Let $x_i \sim \text{Beta}(\alpha_i, \beta_i)$ for $i \in I$. Let $j = \operatorname*{argmax}_{i \in I} x_i$ (ties broken arbitrarily). What is the distribution of $j$ in terms of $\alpha$ and $\beta$? ...
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Numerical evaluation of infinite sums

I am working with Skellam random variables and I would like to evaluate the CDF of the absolute value of a Skellam random variable in which both Poisson random variables have the same rate, $\lambda_1 ...
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How to compare the efficiency of a trained ML model over a non learning based approach for solving the same task or problem?

If a certain task T is solved by a non learning based method A (lets say, an optimization based approach). We now train a machine learning model B (lets say a neural network) that solves the same task ...
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1 vote
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Counting the Total Number of Local Minima for a Multivariate Function

Is it possible to count the total number of local minima for a scalar, multivariate function? We can assume the function is differentiable, but it is also non-convex and setting the gradient equal to ...
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How to cluster Multiple variables (11 numerical variables ) together into different buckets?

what's the best way to bucket multiple variables together? Below is my data which has 11 numerical variable. I tried with the maximum is two variable clustering and grouped them based on the clusters.....
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Computational discriminant analysis

I have objects come from 2 different groups GID. For each object I have 16 different parameters X. Matlab code to load the data: ...
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9 votes
1 answer
600 views

Is the ratio of two sums normally distributed?

I've encountered this problem and I'm not sure whether my logic is correct. Suppose I have a random sample of customer spending and I want to estimate the market share of a given store in a given ...
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1 vote
0 answers
10 views

Can Statistics help in reducing row-wise computation time on data.frames? [duplicate]

I have a data frame with 10,000 rows and 40 columns. I am trying to apply a function to each of these rows. For each row, I am expecting to return a scalar which is the value of the statistic I am ...
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0 votes
1 answer
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What model is best for the price change relationship between two stocks? python data analytics

I am kind of stuck with some stock price change investigation. My brain is about to be over-heated... What I want to know is, say there are two stocks in a market. Their price change in a minute wise ...
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5 votes
2 answers
1k views

Do deep neural networks learn slower with the addition of more hidden layers?

The number of hidden layers increases the number of weights, also increases the terms in the back-propagation algorithm, i.e. more derivatives, hence more computation. Can we say that neural networks ...
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2 votes
2 answers
144 views

Numerical MLE for Rayleigh distribution

I am given a rayleigh distribution described by, =$f\left(x|\theta\right)\:=\:\frac{x}{\theta ^2}e^{-\left(\frac{x^2}{2\theta ^2}\right)}$ I need to find a numerical estimate of the MLE of $\theta^2$ ...
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1 vote
0 answers
114 views

How to use statistics to speed up row-wise computations on a data.frame?

I have a data frame with 10,000 rows and 40 columns. I am trying to apply a function to each of these rows. For each row, I am expecting to return a scalar which is the value of the statistic I am ...
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2 votes
2 answers
132 views

How can I learn how to create a new statistic?

There are an infinitude of tutorials on how to use this and that statistic, but I can’t find anything at all about how to invent a statistic, and validate it. I can guess, from the papers: You make up ...
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1 vote
0 answers
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Assessing performance of entire nonlinear SUR in R?

I understand the McElroy's R-squared is used to assess the entire SUR system in Hamann & Henningsen's systemfit package in R. However, I've been running SURs ...
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1 vote
1 answer
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How to calculate errors of best value of parameters that obtained from MCMC method and observational data

I had a model and some observational data. I used MCMC method to obtain the best value of free parameters and used some coding to plot contours of 1 to 3 sigma confidence levels (as you see in the ...
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Choice of covariance matrices in Kalman filtering?

I am attempting to learn about Kalman filtering. I understand the state vector, call it $\mathbb{x}$, comes with a covariance matrix call it $P$. I can initially choose my $\mathbb{x}$ by my pre-...
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2 votes
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26 views

Preconditioning

Problem Statement Let $\pi(x)$ be my target distribution and suppose $\text{Var}_\pi[X] = \Sigma$. Suppose also that I have obtained samples $X^{1:N}\sim \pi$, computed their sample covariance matrix $...
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Probit Regression and Reverse Causality

In the context of my Master's Thesis, I am using cross-sectional data to investigate the impact of digitalisation and it's various tools on the propensity to adopt various sustainable behaviours for ...
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0 answers
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Comparing colors of digital and print (in cloth) images

I want to compare color histograms between a digital photo and its physically printed in cloth (like a tshirt) version. The process is simple: Printing a digital image (with good resolution) in a ...
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0 votes
1 answer
76 views

If $X_1, ..., X_n$ come from $\exp(5)$ using CLT, Calculate the probability $P(Z<z)$ [closed]

Please advise if the approach i am taking below is correct, I don't see how else to go about solving this problem. ...
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