# All Questions

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### Does the following pmf belong to the exponential family?

I recently saw a pmf: $f(y)=\frac{\mu^y}{(y!)^\theta z(\mu,\theta)}$, where $z(\mu,\theta) = \sum_{i=0}^{\infty}\frac{\mu^i}{(i!)^\theta}$. I am wondering if this belongs to the exponential family? ...
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### Are there situations in which we want to model/estimate the *independent* variable?

Parametric regression approaches can be characterized in the following way: Assume our dependent-variable comes from a particular distribution (e.g., the normal distribution). Estimate the effect(s) ...
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### How to find confidence interval for the mean of a variable between two different factors in SPSS?

I have data that outlines tumor sizes in patients and whether or not they are male or female. I would like to find the 95% confidence interval for the difference in mean tumor size between male and ...
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### Given Pivotal Quantities Find Confidence Limits

Based on the pivotal quantities below $Q_{1} = \frac{ \hat{\theta_{1}} - \theta_{1}}{ \hat{\theta_{2}}} , Q_{2} = \begin{pmatrix} \frac{\hat{\theta_{2}}}{\theta_{2}}\end{pmatrix}^{-1}$ derive ...
12 views

### Sample mean and sample variance

The sample mean is $\sum_{i=1}^n X_i$ and the sample variance is $S^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \bar X)^2$ Can someone please explain how the sample mean and sample variance are ...
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### Verifying and/or changing priors assumptions on Bayesian ANOVA

I am performing a Bayesian analysis of around 1500 data, divided into 2 factors, one that I am interested x1, and the id-variable for the paired/within-subject x2. x1 has 15 levels, and x2 around 100 ...
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### Standard Errors NaN ARMA and ARIMA with R

I'm working with a time series of 59 elements, and i'm just wondering why the R function, ARIMA, throws an NaN for the standard errors of some parameters. I'm trying to model the residuals of a ...
6 views

### Comparing and evaluating win probabilities in sports from different settings

Background I'm trying to predict the probability that the home teams wins a certain sports game, for each minute of the game. Taking these win probabilities together produces a nice visual of the ...
12 views

### Gibbs entropy and Shannon entropy

The two formulations seem identical to me: $H(x) = \sum p(x) log(1/p(x))$ why would the equation be attributed to Shannon rather than Gibbs (in the context of information)?
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### Playing with Continuous uncertainty in Decision Trees

Classically, for decision trees we define a split or various "buckets" to transform continuous data into discrete data. The data I am currently processing has uncertainty associated with it (each ...
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### repeated cross validation generalized additive model

i used the below code for repeated cross validation of generalized additive model (GAM): fitControl <- train(y ~ x0 + x1 + x2 + x3 + x4 +x5 +x6 +x7 data = data, method = "gam", ...
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### forecasting with ratio

i have daily data about revenue and number of push notification sends. I am trying to predict revenue/sends by day. there is a day of week effect also and days may have different sends. For example ...
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### ANOVAS and Planned Comparisons

I'm fairly new to stats and we have been asked to conduct our own one way ANOVA's for class. Our first hypothesis is that gender will effect exercise. Our second is more one tailed, Men will ...
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### Is unbiased maximum likelihood estimator always the best unbiased estimator?

I know for regular problems, if we have a best regular unbiased estimator, it must be the maximum likelihood estimator (MLE). But generally, if we have an unbiased MLE, would it also be the best ...
9 views

### determine break point [on hold]

Please tell me break points for each graph. Thank you.
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### Ordinal Logistic Regression

My dataset looks like this: ...
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### Hierarchical Multivariate Multiple Regression

I have a data set with four predictors and five criteria, and the literature says there are consistent gender differences in the predictors. I'd like to run a hierarchical regression and enter gender ...
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### Measure heterogeneity among multiple samples and scale variables

I would like to know what are the available statistical measures for quantifying heterogeneity on data that look like this... ...
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### Proportion Sample Size Estimation? Finite Population

I was asked by someone running a food drive to help with the following problem: Food is being collected in bins, which hold about 1,500 lbs of food each. They are looking to collect about 500-600 ...
15 views

### Volatility of investment (/w currency hedging)

I´ve been trying to compute volatility of investment with currency hedging, and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
14 views

### Does non-response bias affect the validity of a statistical model?

I want to build a (generalised linear mixed) model on some survey data. The PROC GENMOD command in SAS doesn't admit weighting in the sense of survey weights. I am not interested in population-level ...
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### How to treat the group variable as continuous in boxplot() in R? [on hold]

If I understand correctly, boxplot() treats numerical group variable values as discrete values and spaces the boxes evenly on the plot. What can I do to produce a ...
14 views

### What comes first: outlier detection or model selection?

I'm fitting a GLMM (mixed logistic regression) in R. I have five covariates. For model selection, I'm using glmmLasso() (in R) to determine which of the five covariates and their interactions should ...
10 views

### Using VAR in R to estimate the effect of oil prices on stock returns [on hold]

I am having some problems with estimating a VAR in R. I am trying to replicate a study from Park and Ratti 2008 Using a time period from January 1997 to February 2016, I have been able to perform ...
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### one sample t test for clustered data in R

How shall I do one sample t test for clustered data? For instance, I have N = 100 number of observations, which are obtained from 5 different regions. I'd like to test whether the outcome y is ...
6 views

### Interpretation of interaction b/w two dummy variables and purpose of it

Suppose we have the model: Y = a + bX + cZ where X and Z both are dummy variables, and a, b & c are coefficients. What might be the purpose of adding an interaction term between both dummy ...
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### Applying filters learned from convolutional neural networks

I have a neural network that I trained on 32 * 32 px size images. Can I use these filters learned from the network on larger images not used in training the network such as a 600 * 800 px image? Or ...
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### how can we calculate the mean return time from state i to state j of markov chain in R?

I have calculated the mean state time from state i to i which is the reciprocal of stationary distribution E=1/pi where pi is stationary distribution in R can use the function ...
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### Is it possible that my 200 boostrap samples have better performance that my original data?

When I check the performance of 200 bootstrap samples, all of them have better scores than my original data. (I am not asking about the learning technique because it is a conceptual question, but it ...
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### Is there a common recommendation on product lifetime declarations in terms of Reliability function?

I mean: if I read on the label that a specific product (car, household appliance, whatever...) is declared to have a lifetime of N years, does it actually mean that the Reliability function R(t), ...
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### Do two test statistics at the same $\alpha$ value give the same TYPE 1 error rate and same decision?

Do two test statistics at the same $\alpha$ value give the same TYPE 1 error rate and same decision? I think it is clear that they do give the same TYPE 1 error rate by definition, but do they always ...
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### How to combine statistical moments at different orders?

I am performing a number of simulations involving the estimation of statistical moments at different orders (lets say, from the 1st till the 3rd order). For certain case studies, I have useful ...
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### Minimum sample size for multiple choice question

I have a question about minimum sample sizes for a multiple choice survey. I have searched around this site and the internet, but haven't found a 100% clear answer yet. What if someone a survey was ...
12 views

### Multiple linear regression interactions

When plotting the effects of two factors on the dependent variable, why do parallel lines like the ones illustrated in figure 44 show that there is no interaction between factor (i) and factor (j)? ...
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### Interpretation of Regression coefficient

I have 5 variable regression equation. If I added any constant (Fix value, say 100) in all the observation of variable A, another (Or same) fix value in variable B. While rest of three variables are ...
36 views

### Why doesn't standardization work in the linear regression?

I have a matrix containing the attributes of the item and their corresponding rating. All of the attributes are in the range of (0,1) and the rating is in [1,5]. I transform the range of rating to ...
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### Confidence interval for fitted lambda from Possion distrubtion

So my question is: you are given a set of data and you know the distribution is Possion with parameter lamda > 0. I figure out xbar is 4.06, and the z value we are using is 1.96 and n=50? But how can ...
2 views

### finding and comparing temporal and location-specific pass patterns in a soccer game

I have data on several soccer matches, where ball passes have been recorded in terms of XY-location where the pass starts, XY location where the pass ends, the team making the pass, the player making ...
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### Do I still need ergodicity if I have multiple/infinite time series of the same data generating process?

The main reason we need ergodicity (and therefore stationarity) is, as Shalizi puts it: The ergodic theorem is important, because it tells us that a single long time series becomes ...
14 views

### determine which of the populations is “larger” with Wilcoxon/MannWhitney test

when using Wilcoxon test in Python - I get that one population is significantly different (greater) than the other. Where in the output do I get which population is actually the "larger" one? would ...
5 views

### Train softmax temperature during function optimisation

Instead of simply choosing a softmax temperature, does anyone include this parameter during function optimisation? e.g. in the last layer of a neural network during backprop? Does it make sense to ...
12 views

### Three-level partially nested model

I am modeling change over time in group psychotherapy subjects using R and lme4. My data have the following structure: subject (id) time (code 1-10 for equally spaced repeated measures) outcome (for ...
26 views

### Logistic Regression Probabilities

I have performed a logistic regression on some data, and the function is: $p(x,y) = \frac{\exp(4.5 + 3.5x - 0.1y)}{1+\exp(4.5 + 3.5x - 0.1y)}$ This also gives you the probability of observing some ...
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### What is the difference between R2 and variance score in Scikit-learn?

I was reading about regression metrics in the python scikit-learn manual and even though each one of them has its own formula, I cannot tell intuitively what is the difference between R2 and variance ...
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### What is 'E' embedding matrix in “Show, Attend and Tell” paper? [on hold]

I'm reading this paper Show, Attend and Tell: Neural Image Caption Generation with Visual Attention I couldn't understand what exactly the embedding matrix E is and how is it learnt ? Also what are ...
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### true negative is 0% whereas true positive is 100% correctly classified

I used Naive Bayes from Spark's MlLib to train a model and test it on the data (in the form of an RDD). The results were confusing. the data and results are as follows: The problem is a binary ...
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### Convolutional Neural Network for 3D point cloud?

Can Convolutional Neural Networks or Deep Architectures be used for generating 3D point clouds ?
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### Mahalanobis Distance and feature scaling

I've been using Mahalanobis distance to look for outliers. This link: https://www.cs.princeton.edu/courses/archive/fall08/cos436/Duda/PR_Mahal/M_metric.htm says that feature scaling is addressed in ...
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### Interpreting interaction term that only includes some of the variables in the model

I have a multinomial regression model with 5 variables (forced to enter the model), and all 2 way interactions between those variables (forward stepwise). The variables are: age, education level, ...

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