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The sample space of an experiment is the set of all possible outcomes of that experiment. For example, if you toss a die two times, the sample space of this experiment would be $$ \Omega = \{ (1, 1), (1, 2), (1, 3), ..., (1, 6), (2, 1), (2, 2), ..., (6, 1), (6, 2), ... (6, 6) \} $$ In the example with guessing the numbers, the experiment is to choose 4 ...


4

$\theta$ is a common variable in statistics. We usually see $\theta$ as an angle in trig and physics long before we see its use in statistics, but $\theta$ is just the variable of choice in statistics for an unknown parameter. $$\theta_0 = b$$ $$\theta_1 = m$$ The interpretations of the intercept and slope parameters are different, hence the different ...


2

Specifically, Naive Bayes assumes conditional independence of features (conditioned on classes), not statistical independence. And, informally speaking, despite strong assumptions, it works pretty ok in practice. An obvious reason of using naive assumption is that the number of parameters needed in the model is linear with increasing number of features. ...


2

On "Deep Learning with Python" by F. Chollet (https://www.manning.com/books/deep-learning-with-python) he uses the "Boston Housing Price" dataset for an introductory example in regression. In Python you can easily import the data using: from keras.datasets import boston_housing


2

There are two answers. The first one is, YES YOU CAN! The second answer is You may not need it. First answer. Yes, you can use the 5x2cv paired test for regression. The only issue is that for each of the 10 test sets, you need a SUMMARY of the error of the regression for that test set. So you may use average regression error, or similar measures. You will ...


1

Often finding the distribution that fits the data is not an endpoint, but a starting point. By knowing the distribution (whether it is "true" or just an approximation), you can say something about the likelihood of a new observation. For example, you found your observations fits well to N(0,1). Next you observe x=3.1 (the value you've never observed), whose ...


1

The entirety of statistical inference is based upon assuming that a variable of interest: 1) Has a probability distribution; and 2) The parameters of the assumed probability distribution can be estimated form the data. You never know the true probability distribution of a variable (except perhaps in contrived or very unusual circumstances). If you did, ...


1

I use the repeats as I have a small dataset (<200) and would like tighter bounds on my model performance for significance testing. Repetitions of $k$-fold cross validation allow you to measure model instability, and the uncertainty related to that source of variance will go down if you average repetitions. But it doesn't do anything about the actual ...


1

If I understand correctly, you have some $p \in (0,1)$ and you would like to add some error $\epsilon$ to it such that $p+\epsilon \in (0,1)$. The problem being, how to chose $\epsilon$ such that we don't escape the bounds $(0,1)$. One solution may be to sample $\epsilon$ from any distribution with support over $\mathbb{R}$ (e.g Normal distribution), and ...


1

I dont understand how this can be overfitting. For me overfitting occurs when you cannot generalize anymore. Here you test-rmse keeps decreasing which means that you have not overfitted yet. Increase the capacity of the model and increase the boosting rounds until you have seen test-rmse decrease and then increase. This is the behaviour you should spot


1

You asked: in the case where 𝑛 is 10's of millions does Gaussian process regression still work? Not in the standard sense of constructing and inverting a large matrix. You have two options: 1)choose a different model or 2) make an approximation. 1) Some GP-based models can be scaled to very large data sets, such as the Bayesian committee machine linked ...


1

No matter how you slice it, this is effectively a different question - instead of looking for a value Y(X), you're asking about the parameters of a distribution with a mean of Y(X) and variance/standard deviation E(X, deltaT). I see two broad approaches here: 1) The simpler implementation is to run your current model on some historical data, tweak the lag, ...


1

I do not quite understand what you mean by “optimistic”. Training on a balanced set and testing on an imbalanced set is fine to me, as long as the test set model the real distribution of the data well and the classifier performs well. However, if you want to estimate the precision on the imbalanced set based on the performance on the training set, that will ...


1

Your question rightly acknowledges that throwing away cases can lose useful information and power. It doesn't, however, acknowledge the danger in using regression as the alternative: what if your regression model is incorrect? Are you sure that the log-odds of outcome are linearly related to treatment and to the covariate values as they are entered into ...


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