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Does the following "approach" for integrating over the data space makes sense?

Suppose that we have the following posterior and prior distributions $p(\mu|x,m_{1}(x),s_{1}(x)) = Normal(\mu;m_{1}(x),s_{1}(x))$ and $p(\mu|m_{2},s_{2})$ The $m_{1}(x),s_{1}(x)$ indicate that the ...
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0 votes
0 answers
28 views

Are generalized estimating equations estimates affected by endogenous covariates (covariates correlated with model residuals)?

Are generalized estimating equations consistent or still okay with endogenous variables? The authors of GEE say here that their estimates remain consistent without any qualifications about endogeneity ...
0 votes
0 answers
13 views

Back transformation of mixed models

Need your help: I did my thesis about influence of parenteral nutrition on the liver with repeated measurements and missing data (retrospective aspect) so I used mixed models for statistical analysis. ...
3 votes
1 answer
59 views

Logistic regression: What are use cases for logistic regressions where $n \neq 1$, i.e., $n >1$? [duplicate]

NOTE: This question relates to Binomial logistic regression. Thus, the $n$ in the title, refers to the parameter of the Binomial distribution. Most real-world use cases of logistic regression ...
1 vote
1 answer
39 views

What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear

Why don't we consider nonlinear estimators for the parameters of linear regression models? says that LASSO is a non-linear estimator. I think LASSO has a solution via matrix multiplication. I don'...
0 votes
0 answers
19 views

Which regression models are appropriate for (ratios of) two different but dependent counts?

Consider a variable Y which is the ratio of the frequencies of two words/concepty (f,g) in a text: Y = f/g. Since the texts do not have equal length, the denominator when calculating the percentage of ...
0 votes
0 answers
23 views

Parameters in mlemodel in statsmodel

I am trying to run a TVP-VAR on statsmodel for a big data, but seems to run in a problem when I am trying to validate the vector matrix and the vector shape. Particularly, in the start and the update ...
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2 votes
1 answer
28 views

Why does the logistic model for binary logistic regression return the probability that the outcome was in class/category 1?

In the context of simple binary logistic regression (https://en.wikipedia.org/wiki/Logistic_regression) we have $p(x)=\frac{1}{ 1 + e^{\beta x}}$, where $p(x)$ is interpreted as the probability that ...
0 votes
0 answers
6 views

Weighting Ratio Data?

I am conducting an Interrupted Time Series Analysis on ratio data (number of applications refused/total number of applications). Data is modelled using a binomial logit regression (see below): ...
5 votes
3 answers
608 views

Alternatives to scatterplot for visualisation for large samples

I would like to visualise the following scatterplot in a different way that would make it more intuitive. The X axis is trading frequency and describes how many trades were conducted whereas the Yaxis ...
0 votes
0 answers
21 views

Tune threshold in hyperparameter tuning is giving worse results in MLR

First, I tried not tuning the hyperparameters without setting tune.threshold=TRUE. ...
2 votes
1 answer
37 views

Probability of sample minimum below a certain value

I have a list of 1000 songs with their bpm (beats per minute). If I were to sample 30 songs, is there a way to find the probability that the sample minimum is below a certain value like 100 bpm?
0 votes
0 answers
4 views

FCN model validation metrics oscilalte

I am doing FCN for semantic segmentation. Just based on the data below I am wondering if I should continue training the model if my validation accuracy and validation loss are oscillating like this. ...
5 votes
2 answers
86 views

Is there any intuitive meaning to $\beta^T A \beta=1$?

In a statistical paper, I found that $\beta^T A \beta=1$, where $\beta$ and $A$ are a vector and matrix of constants, respectively. In the paper, the author utilizes only the $\beta$ that satisfies $\...
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0 votes
0 answers
15 views

Difference in the results of qbinom() and sensR::findcr() in R

I try to understand the difference of +/-1 in the result of two functions using the binomial distribution. I need to know the critical value of a situation where I have n=9 tests, the probability of ...
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0 votes
0 answers
15 views

What is a perfect distribution to consider for the step increase/ decrease for the reversible jump MCMC

I am trying to understand the hyper parameters in the paper [1] for the model order selection with reversible jump MCMC (RJ-MCMC). There is a hyper parameter $\Lambda$ (The parameter of the Poisson ...
0 votes
0 answers
17 views

How to set up a monte carlo simulation for time-series, cross-sectional / panel data in R

I am looking for tips, pointers, explainers, blog posts, and the like, on how to set up a monte carlo simulation for a time-series, cross-sectional / panel data generating process in R. I would like ...
  • 407
1 vote
0 answers
18 views

Longitudinal data - formule

I have the following experimental design and I´m a bit lost: I have subgingival samples collected from 30 patients. Two samples were taken from each patient on a first visit (V1): A sample from a ...
0 votes
0 answers
13 views

I was trying to learn mathematics for Reinforcement Learning...Should i read the books Mathematics for ML or do online course like MIT Linear Algebra [closed]

I was trying to do research in RL so I need maths for it. I don't know whether i should read the book "Mathematics for Machine Learning" or do some course
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0 votes
0 answers
30 views

Largest possible area of a scaled normal distribution dominated by N(0,1)

I'm trying to understand and replicate a method for understanding stem distributions from 1955. However, replication in R indicates my understanding is wrong. This original work is available online (p....
1 vote
1 answer
15 views

Controlling for both time fixed effects and "entity invariant" variables

I have a question about a panel data regression model in general. I have firm-level data in a single country. Is it okay to control for both time fixed effects and entity-invariant variables, such as ...
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0 votes
0 answers
12 views

Using factor smooths as varying coefficients: Identifiability and identifiability constraints

I would like to use mgcv to build a model in which the effect of a covariable is modelled using a factor smooth as varying coefficient, i.e. the model ...
  • 1
0 votes
0 answers
19 views

How to evaluate stacked classifiers

I have 2 sets of classifiers, both trained on 2 different feature sets extracted from the same data. I would like to combine them using the "stacking" method, which I understand as follows: ...
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0 votes
0 answers
33 views

What exactly does the Box-Cox transformation do to a time series?

If I were to try and rephrase the argument in the original Box-Cox paper in my own words, I would say something like the following: given a model $$ y = x \beta , $$ if the residuals do not appear to ...
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0 votes
0 answers
11 views

How to interpret MSE RMSE in Randomforest and Xgboost regression [duplicate]

I apply Randomforest and Xgboost regression for my problem; data consist of 6236607. I feed the model the availability of machines, such as how many minutes the machine lasts at a practical start time....
0 votes
0 answers
15 views

metaSEM and casual mediation analysis

This is a multi-group study and my plan is Conduct casual mediation analysis ('mediation' package)separately for 4 groups and find a final mediator which is suitable for most groups. Apply meta-...
0 votes
0 answers
9 views

How to create a matrix with known number of signals for use in PCA testing

I'm looking for a way to create a matrix with a known number of signals and background error for use in PCA. The following example attempts this by combining signals of known amplitude, followed by ...
0 votes
0 answers
5 views

PCA on a matrix to produce a sequence

My dataset is organized as matrix with 6 variables (Each matrix shows a specific type of fault). I want to convert it to a sequence by applying PCA on matrix and choose the first principle component (...
1 vote
1 answer
39 views

Is this a known measure of "effective degrees of freedom" in regression?

Suppose $x,y$ are I.I.D random variables in $d$ dimensions. Consider the following quantity: $$R=\frac{(E\|x\|^2)^2}{E\langle x, y\rangle^2}$$ equivalently for empirical distribution with data matrix $...
0 votes
0 answers
21 views

Partial Correlation with Nominal/Categorical Variable

Is there a method to do a partial correlation with a nominal/categorical variable? If so: What is it called and how would you do it in R?
0 votes
0 answers
22 views

Marginal Likelihood Computation for Bayesian Linear Model

Given a simple Bayesian linear model with $N$ observations $y = X\beta + \varepsilon \quad \quad \varepsilon \sim \mathcal{N}(0, \Sigma)$ with known error variance-covariance matrix $\Sigma$ and ...
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0 votes
0 answers
9 views

Difference between margins and coefficients in Stata?

I read several explanation but I didn’t got it at all. What are the practical differences between margins and coefficients? To the background: I run a regression using an interaction Term ...
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0 votes
0 answers
11 views

Finding posterior with Ga prior, Exp likelihood

I'm using this 2017-2018 exam paper to pre-study for a module in Bayesian Statistics. It has a question, Assume that the waiting time, $t$, of a client in a bank can be modelled with an exponential ...
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0 votes
1 answer
18 views

Should I use standardised or unstandardised beta coefficient in this scenario?

I am running a regression on Tax payment and investment. Tax payment is numerical and investment is categorical like, number of projects carried out. When I run the regression the a unstandardised ...
0 votes
0 answers
18 views

AR(1) Process and Infinite Geometric Series

I'm doing an assignment and I've been told that ln(real consumption) has a unit root and is an I(1) process and that real consumption is given by: I've also been told that: Part A I need to derive ...
2 votes
2 answers
69 views

Why is $AUC=0.5$ and a 45-degree line for a ROC curve considered baseline performance?

$AUC=0.5$ and an ROC curve of a 45-degree line often are considered the baseline performance of a model, one that gets absolutely nothing from the features. If we predict the same (prior) probability ...
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0 votes
0 answers
7 views

Model performance graph is oscillating?

I've seen a fair amount of information online regarding the loss graph of a deep learning model oscillating, but not so much about the performance graph. In general, when I "properly" train ...
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2 votes
1 answer
82 views

How to *formalize mathematically* that a binary classifier has no predictive performance?

The objective of supervised learning is to induce a function $f_\theta$, where $f_\theta$ is from a family of functions $f_\theta \in F$, from a training set $D^{tr}=\{(x_0^{tr},y_0^{tr})\ldots, (x_n^...
1 vote
0 answers
20 views

Calculation of Sensitivity of the Outputs to the Inputs over Time in RNN

Alex Graves, author of Supervised Sequence Labelling with Recurrent Neural Networks, described how sensitivity of an output to the inputs is calculated as follows: /* The delta terms refer to the ...
0 votes
0 answers
10 views

Finding coefficients that maximize Spearman Rank Correlation [closed]

I have a sample of observations on stocks across say 5 factors , and I want to find the linear coefficients on these factors which when multiplied with the factors and summed produce a signal with the ...
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0 votes
1 answer
24 views

Analyzing data from a non-randomized sampling design (ecological monitoring)

I have 2 questions about analyzing data that was not randomly sampled from a population. I work with "ecological monitoring" data that involves repeatedly taking measurements from the same ...
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0 votes
0 answers
10 views

Impact heterogeinity in stata using psmatch2 [closed]

I am working on propensity score matching using stata, how can i get impact heterogeneity using psmatch2 (by variablename, sort:using teffects command)
0 votes
0 answers
17 views

In multiple testing, why FWER and FDR are the same if they the null hypothesis are all true?

For multivariate hypothesis testing, why are FWER and FDR the same when all null hypothesis are true? I know they both control for type 1 error, and FWER control is more strict one. But how can number ...
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6 votes
1 answer
28 views
+50

What do the terms "nearly-optimal rate", "near-minimax rate", "minimax optimal rate" and "minimax rate" mean in the context of posterior consistency?

Definition: A sequence $\epsilon_n$ is a posterior contraction rate at the parameter $θ_0$ if $$\Pi_n(θ: d(θ, θ_0) ≥ M_n \epsilon_n| X^{(n)}) → 0$$ in $P^{(n)}_{θ_0}$-probability, for every $M_n → ∞$. ...
0 votes
0 answers
5 views

Training / Testing Classifer on a data set - then predicting on same observation at a future point in time with new data

I am tasked with developing a leadscoring model for leads in a database. I plan to do this using a supervised learning binary classification algorithm. 'Good' lead will be false positives - those ...
4 votes
4 answers
628 views

Why is the probability of a set of outcomes possibly non-zero if each outcome's probability is zero in continuous probability? [duplicate]

In continuous probability, $\text{Pr}(X=x) = 0$ for all $x$. However, $\text{Pr}(a \leqslant X \leqslant b) >= 0$ given $b > a$. The $>$ is key here: each individual outcome has zero ...
1 vote
1 answer
37 views

Finding critical value for F statistic

I am performing a hypothesis test and therefore intersted in finding the F critical value for my F statistic. Below is the anova output when I compare two models. ...
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0 votes
0 answers
24 views

How can I predict a 2D array over time?

I've got a rectangular region that's composed of 1024 grid cells (32x32 cells). Each of these cells has an associated value, which then builds me a 2D array. For that 2D array, I've got 8 samples (...
0 votes
0 answers
4 views

Formula for weighted uniformity measure

Given three [n x m] floating point arrays all representing data about the same image: W - weight map F1 - with feature 1 information and F2 with feature 2 information I would like to calculate the ...
0 votes
1 answer
74 views

How to show for positive Borel functions $g, \int_{a}^{b} g(x)dF(x) = \int_{a}^{b} g(x)f(x)dx$

$\textbf{Problem:}$ Let $\mu$ be an absolutely continous probability distribution with distribution function $F(x)$ and density $f(x)$. For any Borel set $\Lambda$ and $a<b$, let $\nu\left(\Lambda \...

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