Wrzlprmft
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Do we need hypothesis testing when we have all the population?
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20 votes

To illustrate my points, I will assume that everybody has been asked whether they prefer Star Trek or Doctor Who and has to choose one of them (there is no neutral option). To keep things simple, let’...

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Why is a random walk not a stationary process?
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14 votes

For stationarity, the entire distribution of $p_t$ has to be constant over time, not only its mean. And while the mean of $p_t$ is indeed constant, e.g., it’s standard deviation isn’t. The larger $t$, ...

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Are all simulation methods some form of Monte Carlo?
13 votes

All simulation methods involve substituting random numbers into the function to find a range of values for the function. I have never heard of that definition of simulation. For example, Wikipedia’s ...

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Intuitive explanation of stationarity
12 votes

First of all, it is important to note that stationarity is a property of a process, not of a time series. You consider the ensemble of all time series generated by a process. If the statistical ...

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How to test statistically whether my network (graph) is a "small-world" network or not?
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10 votes

TL;DR: You can’t. What is typically done The current “state of the art” in determining whether a network is a small world uses the following approach: Calculate the mean shortest path length $L$ ...

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Explain "Curse of dimensionality" to a child
10 votes

The curse of dimensionality is somewhat fuzzy in definition as it describes different but related things in different disciplines. The following illustrates machine learning’s curse of dimensionality: ...

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Test if two samples of binomial distributions comply with the same p
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7 votes

The test statistics $p(k_2)$ is that of Fisher’s Exact Test. Since $$\sum_{k_2}^{n_2} \frac{1}{n_1+n_2+1}\binom{n_1}{k_1}\binom{n_2}{k_2}\binom{n_1+n_2}{k_1+k_2}^{-1} = \frac{1}{n_1+n_2+1},$$ ...

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Are time series methods only good for forecasting?
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6 votes

Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible ...

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How to understand mutual Granger causality
5 votes

Consider the following examples: Your time series are the gross domestic products (GDP) of France and Germany. As the two country’s economics are strongly interacting, a strong French economy is ...

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“t-tests are too fundamental for academia”
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4 votes

Different statistical tests answer different questions. The $t$ test comes in many flavours, but the most simple one answers the question whether the mean of a population is different from zero¹. The ...

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Surrogate Time Series using Fourier Transform
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4 votes

You need to use the Fourier transform (and inverse transform) for real time series, i.e., rfft and irfft, respectively. This way you ensure that your surrogate is real. You can do this by replacing ...

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Difference between real and random graphs in bipartite networks
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3 votes

What you need is a test that compares two distributions based on samples, such as the Kolmogorow–Smirnov test. In your case, you can compare the degree distribution of your original network to each ...

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How to generate random networks for comparison with my network?
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3 votes

In most cases it depends on what exactly you mean by random, i.e., which null hypothesis you want to test. This again depends on your application, network acquisition, and underlying question. Two ...

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Forecasting vs Classification
3 votes

I feel like classification is simply projecting the outcome of a certain data set onto a predefined group of outcomes, which sounds similar to forecasting. After all you may forecast ...

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Distribution of White Noise in Time Series
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3 votes

Is there any approximation theory in statistics that support this assumption (CLT?)? As already noted, white noise does not need to be normally distributed and I would assume that you find deviations ...

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Analysis of irregularly sampled time series
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3 votes

A non-linear time series is a time series which is generated by a non-linear process. For an regularly sampled time series $x_0, …, x_n$, this corresponds to a non-linear dependence of $x_t$ on $x_{t-...

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Why do we use the class mark in calculating the mean in grouped data?
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2 votes

In an ideal world (for your purpose), the class mark is identical to the class’s mean, i.e., $$ x_i = \frac{1}{f_i}\sum_{j=1}^{f_i} y_{ij} = \frac{\sum\limits_{j=1}^{f_i} y_{ij}}{\sum\limits_{j=1}^{...

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Why is removing instationarities a good thing when trying to forecast a time series?
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2 votes

[…] de-trend and de-seasonalize a time series first so that it becomes stationary. First of all, this does not necessarily make the time series stationary. There are many other forms of ...

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Is this a nonlinear time series?
2 votes

Showing that an observed time series is non-linear is notoriously difficult. Briefly, you would have to find a measure indicating nonlinearity (e.g., a positive Lyapunov exponent or a non-integer ...

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Bootstrapping Time Series Data
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2 votes

If your time series has no autocorrelation, this indicates that the time information is irrelevant. To be on the safe side, you can confirm this using other methods such as the fourier transform or by ...

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Variance and autocorrelation with missing and/or unevenly spaced data in time series
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2 votes

Does the varying window size (measured in points) adversely affect these statistics somehow? Strictly speaking, variance is a property of the distribution of your data points and all you can do is to ...

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Estimate statistical significance of a feature in a time series
2 votes

To evaluate the significance of the peak you have to formulate your a priori knowledge on the individual time series you are measuring as a null hypothesis. A likely null hypothesis would be that your ...

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Is a time series the same as a stochastic process?
2 votes

The difference between a stochastic process and a time series is somewhat like the difference between a cat on a keyboard and an answer on Stack Exchange: Cats on keyboards can produce answers, but ...

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Counterintuitive result when comparing two groups of time series
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2 votes

Regarding 1. and 2. It can very well be that other features of your time series (than you want to measure) lead to higher cross-correlations. To give an illustrative example (that does not exactly ...

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What is the difference between local efficiency and betweenness centrality in network analysis?
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1 votes

Yes, if you look into the definitions, there will be obvious differences. I won’t do this here since there is no commonly agreed upon definition of local efficiency to begin with and what you write is ...

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"Multi-level" social network analysis?
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1 votes

If I understand your data and setup correctly, you have what is called a bipartite graph (or bipartite network). This kind of network is defined by the following properties: There are two types of ...

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To test for small-world property, does the random graph generated has to be completely connected?
1 votes

You use Erdős–Rényi networks as instances of a null model for your real data. Thus the answer to your question depends on what null model is appropriate to your situation. Are disconnected networks ...

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Finding out frequency of peaks using the Fourier transform
1 votes

You seem to conflate the following two concepts typically denoted as frequency: The inverse of the period of a periodic signal or component. I refer to this as frequency in the following. The number ...

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Hypothesis testing for higher density in subsets of a network/graph
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1 votes

Just looking at the global weight density or weight distribution, respectively, corresponds to the null hypothesis that there is no structure in the network whatsoever and edges are assigned randomly. ...

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Can I smooth every time series using Moving Average?
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1 votes

Can these issues cause any problems while applying the MA? Yes, if you want to communicate the changing variance, the moving average usually will cause that feature to be lost. Just think about what ...

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