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GAM model warning message: step failure in theta estimation

When running and gam model and this warning message pops up, what does this mean and what is advised? A simple increase in knots (even by 1) seems to remove this warning message. "Warning message:...
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The kernel estimation of conditional density seems to be largely driven by the value of bandwidth. What's wrong with the interpretation?

Suppose I have data $\{Z_{1i},Z_{2i}\}_{i=1}^N$, and I want to estimate the conditional density $f(z1|z2)$ using the nonparametric kernel estimator: $\widehat{f}_{h}(z1|z2)=\frac{\sum_{i=1}^{N}\frac{1}...
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  • 1,682
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How to determine the number of pixel from a warped image from a region proposal RCNN

I am learning R-CNN with this slides. On slide 63 one warped image region is specified by 224x224 pixel. Is this just a random value or from where is the value coming from? I cannot see any ...
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goodness of fit test for model

I did GLMM with negative binomial family. After checking goodness of fit using the equation "1-pchisq(summary(model4)$deviance,summary(model4)$df.residual)" it gives the value zero. what it ...
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Find pdf of X+Y

Let X ∼ Exp(λ) and Y ∼ Exp(μ) be two independent exponential random variables, where λ, μ > 0. Find the probability density function of X + Y if λ ̸= μ. I have successfully find ans if λ = μ, but ...
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Why does selective search algorithm for R-CNN extract approximately 2000 region proposals?

What would happen for example if we would extract instead of 2000 region proposals 1000 or 4000 region proposals?
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1 answer
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How does the dynamic regression component from TBATS differ from the one in SARIMAX?

Both TBATS and SARIMAX support the modeling of long-term seasonality by using dynamic regression. Dynamic regression in this case involves the use of sin and cos terms to model seasonal components. In ...
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1 vote
1 answer
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Estimate at which point a linear model hits a certain value (including probabilities)

I have a simple 1D set of datapoints with a trend, I want to estimate at which point $X_t$ (i.e., at which point in the future) the model will hit a certain threshold $Y_t$: I can fit a trendline to ...
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Penny's game probablity

Independent flips of a biased coin that lands on heads with probability 0.8 are made. Each of two players, A and B, had chosen one out of the eight triplets: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} ...
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1 vote
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Seasonal and trend adjustment for irregularly spaced time series

I know of different methods that exist to remove seasonality and trend in the data to make it stationary. However, that exists only for regular time series; that is, a series that follows a fixed ...
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Difference between cross validation vs model accuracy measures

I have a time series ARIMA model and I want to validate the accuracy my prediction. But I dont understand the difference of using cross validation vs model accuracy measures such as MAPE, MAE, MSE and ...
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is it good to have 100% accuracy on validation?

i'm still new in machine learning. currently i'm creating an anomaly detection for flight data. it is a multivariate time series data that include timestamp, latitude, longitude, velocity and altitude ...
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Two-Sample Rank Statistics

Assume we got two models, either regression or RF or whatever. I'm trying to observe the relative importance of each feature by using ranks. That is, if we look at a regression model, we have a t-test ...
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  • 2,351
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Different Meanings of "Clusters" in Statistics

Typically, I have always come across the term "cluster" within statistics as reference to "clustering" - that is, for example the "K Means Clustering" algorithm. Recently,...
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-1 votes
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Energy imported from Russia

from this spreadsheet: https://ec.europa.eu/eurostat/statistics-explained/images/2/24/EnergyMixDependencyImports_25-03-2022.xlsx it appears that Italy imports 73.5% of energy from the world, while ...
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Jackknife estimation and testing

I'm using jacknife method to get the uncertainty of my estimation. My estimation restricted to (0,1) and some can be very small. For example, the jackknife estimate for variable A is 0.0000503 and ...
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1 vote
1 answer
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power and sample size estimation

For a one-sided test: $$H_0: \mu_1 \leq \mu_2 \ H_1: \mu_1 >\mu2$$ $$\alpha=0.025,\beta=0.1$$ How to calculate the sample size needed? Is this information enough to calculate the sample size?
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No previous information in a clinical trial

I'm conducting a clinical trial with a treatment group and a placebo group and calculated the sample size based on a previous study. However, I would like to add two more new placebo groups with ...
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2 votes
0 answers
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Finding the MVUE of the center of a circle of unknown location

Is there a known analytic solution for finding the minimum variance unbiased estimator of a disk of an unknown location given that a sample of $n$ points was drawn uniformly and randomly from the disk ...
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  • 7,062
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How can I compute rectangular confidence regions for parameters using R?

Simultaneous confidence regions for multivariate parameters (say, a confidence region for multivariate mean, or for regression parameters) usually find an elliptical region when the parameters' ...
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  • 1,033
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6 views

Principal component analysis (PCA) vs. Partial Least Squares (PLS)

I know the the difference between PLS and PCA estimation procedures.But what is the main output in terms of dimensionality reduction for PCA and PLS?
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Measuring value of free users

I was wondering if the following scenario had a word for it (eg. Survival analysis...). Suppose we have a company that has pro users (pay $10/ month) and free users. I want to calculate the worth of ...
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GLS vs. OLS with sandwich (or GEE with sandwich?) - repeated data (no covariates!)

Let's assume I have a series of repeated observations at time t0..t3. I want to test the difference at each time point vs. t0. When doing a set of independent comparisons "vs. control" (...
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5 views

Sampling from a Poisson Process

I am trying to simulate a one dimension correlated random walk. In this algorithm, the direction of a particle’s next step is correlated with the direction of it’s previous step. The particle’s step ...
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Caret: ordinal models with VGAM library

I started to look into the students performance dataset: https://archive.ics.uci.edu/ml/datasets/Higher+Education+Students+Performance+Evaluation+Dataset I would like to train two models with caret ...
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1 vote
1 answer
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Can I convert a typical reinforcement learning problem to a supervised learning problem?

I'm not sure if I've understood correctly the whole point of reinforcement learning. In my point of view, the whole goal of RL is learning a policy that maps states to actions. Let us suppose that I ...
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  • 410
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6 views

The expected value of point product of matrices

I have two random binary matrices of the same size m*n. let's call them A, B I know r_i which is the row sums of A, and c_j which are the column sums of B what is the expected value of C_ij = A_ij*...
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  • 551
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Proper way to report on Confidence Intervals for 2 Proportions means

Disclaimer: Stat noob Context: I'm trying to figure out the best way to report CI to a non-data/stat/math savy audience. I'm performing a two proportion z test for an experiment. Control: 0.3097 ...
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9 views

forward stepwise AIC approach

I am learning about performing stepwise model selection by AIC and I have 2 questions here: 1.Regarding to stepwise AIC, what is contribution (effectiveness) of the number of parameters in the model ...
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  • 41
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13 views

Correlation of multivariate distributions without "slope"

Wikipedia has this image showing different correlations: It says: The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (...
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  • 547
0 votes
2 answers
27 views

Why adjustment is needed when calculating Skewness and Kurtosis?

Some packages such as Mathlab, Minitab and SigmaXL caluclate adjustment for skewness and kurtosis. For example at: https://octave.org/doc/v4.0.1/Descriptive-Statistics.html it is suggested that ...
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1 vote
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Fitted ARIMA on new time series

Based on the accepted answer from this post: How to use a fitted model parameters for forecasting other time series, it is possible to use a fitted ARIMA model for forecasting another time series. ...
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How does attention add expressive power to encoder-decoders?

I am learning about the attention mechanism for the first time, and the context in which it has been introduced (watching Lecture 8 of Stanford's CS224N) is that of language translation using seq2seq ...
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Summing confidence intervals, given $[a_0, a_1]$ and $[b_0,b_1]$, and $c=a+b$, is $[c_0, c_1]$ where $c_0 = a_0+b_0$?

How can you sum confidence intervals? Basically the title: Given $[a_0, a_1]$ and $[b_0,b_1]$, and $c=a+b$, is $[c_0, c_1]$ where $c_0 = a_0+b_0$? These are 95% CI's. How can you show this? Given ...
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Interpreting interaction effect with ln(time) in Cox regression

I am fitting a Cox proportional hazards model with the interaction effect dummy:ln(time). How would you interpret the result? Is it a simple exp(x)-1)*100 to receive the percentage increase in y? Coef:...
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  • 11
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1 answer
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Multilevel model for education data, if individuals within cluster change (school) between time points

If I am wanting to fit a multilevel model across two time points and the first time point is Primary (uk education system, age 7-11 - keystage 2) but the second time point is secondary education (uk - ...
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  • 115
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Multinomial Logistic Regression get predicted probabilities without using predict_proba()

I have a 5 class multinomial logistic regression using sklearn and I would like to achieve the same output as model.predict_prob() just using the coefficients and ...
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  • 11
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0 answers
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Multiclass classification on top of given probability distribution from previous model

I have a multiclass classification problem that has multiple steps. Firstly, I am given a probability distribution over the classes by a base model for each sample. The task is to create a new model ...
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1 vote
1 answer
21 views

Building a bootstrapped distribution to test reliability of empirical data

I have data from a study where subjects (considered as "generations" in a Telephone-like game) sang short melodies from one to the next, starting from a randomly-generated melody (seed) ...
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  • 1,560
0 votes
1 answer
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Two Sample Independent Test for Proportions (z test or t test)

Context: I have two independent samples that I want to compare for equality through an AB test. The metric being evaluated is binary: user clicks or not (proportions). Question: I keep reading that z ...
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2 votes
1 answer
55 views

Linear regression's (OLS) coefficient interpretation with heteroscedasticity

To use OLS for inference, is it necessary in all cases that the premise of homoscedasticity is met? I need to check the influence of some features (eg age, income...) on a variable y (whether or not I ...
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  • 39
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Common Trend Assumption in Difference-in-differences

I'm running a DiD analysis on whether the introduction of a spinoff NFT (non-fungible token) collection affects the prices of the parent NFT collection. First thing that I did is to visually test ...
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2 votes
1 answer
120 views

How to assess normality under the OLS assumptions?

When we have a multivariate regression function, which assumption has to hold so that the OLS assumptions are not violated: ...
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0 votes
1 answer
19 views

Finding the non-zero region of a marginal

Basic question but: what happens to the region on which a pdf is non-zero when a bivariate is integrated to get a marginal? The example I'm working on (course problem booklet for a mathematics BSc ...
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  • 265
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Why does the IV estimator fail to attenuate the EIV bias in a two-stage FM regression?

In Jegadeesh et al. (2019), they proposed to use the instrumental variables (IVs) estimation approach to attenuate the errors-in-variables (EIV) bias, which is inherent to a two-stage Fama-MacBeth (FM,...
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0 answers
6 views

How truncation works when applying BERT tokenizer on the batch of sentence pairs in HuggingFace? [closed]

Say, I have three sample sentences: ...
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1 vote
1 answer
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Neural networks - calculating output manually if $x_1=x_2=0$ . Should this be easy to do?

This is a problem question I'm trying to make sure I understand from a past paper (with no solutions). The R output is below. ...
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Interpreting Shapley Values on Breast Cancer

I was analyzing Shapley Values on the Wisconsin breast cancer data set (binary classification). I applied it on Random Forest and on Ridge and Lasso Regression. However the summary plot seems to be ...
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  • 1
0 votes
0 answers
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knitting rmarkdown throws error printing result of contour() [migrated]

I want to knit the following code into an html document. The code runs fine in Rstudio but fails when I attempt to knit - what am I missing here? ...
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1 vote
1 answer
22 views

Calculate sample size for clinical trial without raw data

Usually, we calculate the sample size needed for a clinical trial based on a former clinical trial which shows there is a significant effect. What if there is no such a trial? What if there is no ...
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