# All Questions

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### Can "Curve Fitting" be seen as an Alternative to Numerical Differentiation?

For a long time, the following point always confused me: If the "Fundamental Theorem of Calculus" tells us that all real and continuous functions are differentiable (i.e. have derivatives) - ...
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### How to use siamese network in binary classification - inference mode

Siamese network consists of two identical networks. Networks share the same weights. The general workflow is as follows (taken from here): Suppose that I have 10 images of apples, 10 images of ...
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### How to change/adapt loss function while using "class" incremental learning

As a beginner on class incremental learning and trying to understand the general concept. In class incremental learning, we have a model that can make a classification between classes A, B, and C. By ...
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### Fitting two lines to convoluted data [duplicate]

Assume you are provided with data derived from two linear equations + noise, such as that below. How would you go about deconvoluting the lines, and obtaining their slopes/biases? Colab link for ...
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### Two sample hypothesis tests for functional (curve) data

Suppose I have two samples of functional data or curves $x_i(t), i \in \{1,\dots,n_1\}$ and $y_i(t)\in\{1,\dots,n_2\}$ for $t\in\{1,\dots,T\}$. What tests are suitable for testing the null hypothesis ...
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### What is the distribution of $\Lambda$?

As in Likelihood ratio test for $H_0:(\mu_1,\mu_2)=(0,0)$ vs $H_1:(\mu_1,\mu_2) \neq (0,0)$, There are $X_1, X_2$ where $X_i \sim N(\mu_i,1), i=1,2$. They are independent. The question is Find the ...
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### Why I cannot find suitable ARIMA model for the dataset?

I have a monthly dataset. I applied ADF test and saw that this dataset is stationary. Also, Canova-Hansen test is applied to see if there is stochastic or deterministic seasonality. As you see below ...
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### Why is my highest coefficient not significant but lower ones are? (Poisson regression)

I'm looking to see if income level affects the number of pets a person has, controlling for number of children. I have run a GLM (Poisson family) model, and found that if a person is categorised as '...
16 views

### How are Judea Pearl's Bayesian Nets different from Google's Causal Impact?

At a high level, how are these two approaches, similar and different? I understand that both use Bayes rule, however, I'm unclear on how they differ. Causal Impact uses structural time series to ...
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### Combining several granger causality tests

I have two time series and I am testing them with gragner. The problem is that it's not continuous, one timeseries is constant while the other one has half of the time data. Example: yes = has data, ...
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### When do we REALLY need to distinguish interval from ratio measurement levels?

This question is specifically aimed toward the practice of statistics and data science and toward statistics educators (particularly introductory level statistics). In brief, ¿when do we really need ...
12 views

### Do SVM's find the minimal number of support vectors in the case of redundancy?

Consider the case where more than the minimal number of vectors lie on the lines (or hyperplanes in higher dimensions) defined by the margin found by the SVM algorithm. For example, see the image ...
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### MLE - CDF vs PDF as the likelihood-function?

Would maximum-likelihood estimation: with the cumulative-distribution function as the likelihood-function and the probability-density function as the likelihood-function, yield the same/equal ...
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### Can I do Bayesian Logistic Regression of multiple categorical variables one by one?

My main background knowledge about Bayesian analysis comes from Doing Bayesian Data Analysis by John K. Kruschke. I have a dataset with observations y (success, fail) and several categorical variables ...
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### For Friedman Test, what are the pros and cons of different post hoc comparison method?

scikit_posthocs lists some post hoc pairwise comparison methods if significant results of the Friedman’s test are obtained. How do I decide which one to use? In my case, the toy dataset ...
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### Which distribution family for generalized linear-mixed model based on the plots?

I have a repeated measure study with continuous and two categorical predictors (time for repeated and group for control/experiment group. I checked the assumptions, and realized that there may be some ...
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### Emmeans treat NA coefficent differently for lm and glm regressions

I specified two regressions lm(y~factor1 * factor2 + covariates) ...
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### Does empirical cumulative distribution function (ECDF) has its Akaike information criterion (AIC)?

Working on multivariate distribution fitting, and right now I have marginal univariate transform models and a copula model. Was thinking if I pick ECDF for marginals, do I still have meaningful AIC? ...
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### Variance of Jacobian in backpropagation

Glorot and Bengio introduced the Glorot uniform initialisation in their 2010 publication. My question concerns some details in the derivation, specifically how equation (2) leads to equation (6). I ...
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### What exactly is the history of Dynamic Time Warping? Where can I find information?

I am writing a thesis comparing some methods of time series classification, part of which is DTW combined with K-NN algorithm. I'd love to know (and write, backed by reliable references) something ...
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### Normalize binary variable in MCDM?

I have some data with a couple of binary but also continous variables. For MCDM, there are different normalization techniques such as Max, Max-Min or Vector Normalization. However, I'm wondering if it ...
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### Residuals of GAM models not improving with poisson or ziplss, but better with negative binomial (help with high values)

I am running GAM models on species counts with lots of zeros and high values or high counts. Residuals under poisson family have a s-like curve on qq line with models not predicting lower and higher ...
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### Are there classifiers with infinite number of classes?

I am writing something about time series classification. I wrote this sequence: A classifier is a function that for given input $x_1, ..., x_n$ (in this case representing data stored in audio file) ...
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### Mixed effects possion model in R [closed]

Is there a function in R that enables you to carry out mixed effects poisson model?
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### How to prove the following properties about $\chi_1^2$?

Given two independent r.v. $X\sim N(\mu_1, 1)$ and $Y\sim N(\mu_2, 1)$. What is $$f(x)=P(\min\{X^2, Y^2\}>\chi_1^2(0.05))$$ provided $\mu_1=x, \mu_2=0$, where $\chi_1^2(\alpha)$ is the $1-\alpha$ ...
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### Can Grad-CAM be used for CNNs with a flatten layer?

I would like to visualize CNNs with a flatten layer. I looked into Grad-CAM, which is one of the most popular visualization methods for CNNs, but I thought it could only be used for CNNs with a global ...
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### Are ALL "Loss Functions" in Statistical and Machine Learning Models Fundamentally "Noisy"?

I am trying to better understand the meaning of "noise" with regards to function optimization. Up until now, I always thought of "noise" from a signal processing standpoint: for ...
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### Is it necessary to preprocess the data before doing sentiment analysis using Veder, TextBlob and Corenlp?

I want to perform unsupervised sentiment analysis using Veder, TextBlob and CoreNlp. Is it ...
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### Bottleneck Layer VAE - values centred around 0 with small standard deviations

As the title states, I'm curious as possible theoretical explanations for why might VAE bottleneck layer have values more or less centred around 0 with small standard deviations. I have found this out ...
17 views

### Mean squared error of estimator - calculus of a concrete case [closed]

it's been some years since I last did some Statistics and I need some help to find the solution $z$ of the following problem: $X_{1}, \ldots, X_{(19)}$ are independent identically distributed under ...
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### Examples in the Real World where Evolutionary Algorithms/Genetic Algorithms Outperform other Classes of Optimization Algorithms

I have been trying to do some research to find out if there are certain industries/types of problems or even specific examples in applied research paper where Evolutionary Algorithms (e.g. Genetic ...
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### what is the probability of sample variance when true variance and true mean is unknown?

Sample Variance by definition is $s^2 =\frac{1}{n-1} \sum{(x_i-\bar{x})^2}$ When the population distribution is normal and true variance $\sigma^2$ is known, Sample Variance follows the chisq ...
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### unable to load shared object 'TMB.so' [closed]

I installed broom.mixed package via conda conda install -c conda-forge r-broom.mixed, however, it doesn't import and shows error message: ...
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### B-Splines with R: plot a first and second derivative on curve fit [closed]

I'm using R to fit a set of data to a B-spline, to plot the data together with the fitted curve and show the lines for the 1st and 2nd derivatives on the graph. ...
129 views

### Probability that the absolute value of a normal distribution is greater than another

Greatly appreciate anyone that is willing to Help. I am thinking about the question of comparing the absolute value of normal distributions. Given $a > b$, $X$ ~ $N(0,a)$ and $Y$ ~ $N(0,b)$, what ...
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### Would this be modelled as a GLM or an LM? [duplicate]

I am fairly new to stats so apologies if this is a stupid question! If I am looking to test if income (categories: middle income, high income, low income) predicts the number of pets a person has, ...
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### White-Test: Use F-Statistic or LM-statistic?

to interpret the White-Test, it is recommended to use the LM-statistic = N*R-squared of the auxiliary regression which follows a Chi-squared distribution with df = number of restrictions. But I ...
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### R -non central chi squared distribution samples [closed]

In R, how could I take random samples from the non-central chi squared distribution, defined as: 𝑓(𝑥) = ∑𝑝(𝑦)𝑔(𝑥|𝑦) where 𝑔(𝑥|𝑦) ~$χ^2_{n+2y}$ and 𝑝(𝑦) = 𝑃(𝑌 = 𝑦|𝑌~𝑃(𝜆/2)) where ~𝑃(...
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### Comparing properties of networks of different sizes

I want to compare some network properties such as density, average path and modularity among groups of sizes ranging from 100 to 4000. How can I correctly compare these networks? Considering the ...
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### How to sample from a distribution approximated by a Neural Network?

There are a few models already that approximate distributions with a neural network i.e.: energy models define a density function $f(x)= e^{S(x,w)}/Z$ where $S$ is a neural network and $Z$ is a ...
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### Lme4 Crossed Effects Mixed Model w/ Interaction Terms

Greetings Statisticians! I am trying to create a crossed effects mixed model w/ interaction terms in lme4 to describe a regional analysis of MRI data in mouse brains w/ genotype, treatment, and time ...
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### Random samples from custom distribution with rejection method

Could you please suggest a method (in R) to produce random numbers from: $P(X=x)= -\frac{1}{log(1-p)} \frac{p^x}{x}$ 𝜃 ≡ 𝑝 ∈ Θ = (0,1), 𝑥 = 1,2... I am very new to this and completely lost..
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### Can fixed effects models be validated with out-of-sample data?

Suppose I have a 2-way unit and time fixed effects model: $$y_{it} = a_i + b_t +X_{it}\beta + \epsilon$$ I collect data on a set of units $A$ and $B$, where $A$ and $B$ are disjoint. The data was ...
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### Principles in experiment design for functional data analysis

The goal or objective of "standard"$^†$ experiment design is to design a data collection scheme (for a finite budget) such that linear models$^†$ can be applied and inference results can be ...
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### How to test for the endogeneity between variables? which tests i should use?

my thesis is about measuring the impact of population growth on the economic growth in my country. However, i should test for the endogeneity between the variables chosen. for the dependent variable i ...