# Questions tagged [philosophical]

For questions about PHILOSOPHY of statistics or probability: interpretations of probability, foundational issues with frequentist/Bayesian statistics, etc. Do not use this tag for generally speculative (aka "philosophical") questions.

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### Birnbaum's Theorem: Strong belief in a model $\implies$ the likelihood function must be used as a data reduction device?

Working through understanding section 6.3.2 (pg. 292-294) in Casella and Berger's Statistical Inference (2nd-ed). The following definitions and principles are given: Definition (Experiment): An ...
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### Help with completing a derivation of usefulness of cross-validation

This question is raised as a result of my attempt to answer this other question of mine. Let's refer to all our prior knowledge, both explicit and implicit, as $X_\text{true}$. Almost always, we are ...
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### Can an outcome variable be used twice in the same model?

When is it appropriate to use the same outcome variable in two likelihoods in the same model framework? Here is a specific example: ...
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### The rationale for when significance or null hypothesis testing is needed

Why do people sometimes claim that an effect is so huge and "obvious" that it does not warrant any inferential statistics calculation, even though the sample size is not large? This is ...
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### What is the role of determinism in stochastics?

What is the role of determinism in stochastics? In my opinion, determinism, much like the continuum, is merely a concept to describe an ideal world. In this idealized world we can calculate and argue. ...
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### Are “Data are fixed” in Bayesian viewpoint and “Data are random” in frequentist viewpoint talking about the same thing mathematically?

In my opinion, in BOTH Bayesian and Frequentist inferences, observational data $x$ are modelled as the observed value of a random variable $X$ which follows a certain probability distribution. ...
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### How would a Bayesian define a fair coin?

In the frequentist worldview, probabilities are long-run relative frequencies. Hence, a fair coin can be defined as a coin, for which the long run relative frequency of each of the sides approaches 0....
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### To a Bayesian, does a trick coin with two heads have 50% chance of flipping heads if they don't know that it has two heads?

And to expand on this idea, would uncertainty and complexity be the same thing to a Bayesian? For example, games with much randomness like poker and games that are more complexity based like chess -- ...
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### Why not conflating a distribution over distributions with a distribution?

This question is more like a philosophical one. I constantly find the notion of a distribution over distributions and redundant. Why don't we conflate that with the notion of a single distribution (by ...
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### Do testability and falsifiability have statistical definitions?

Psychology: the Core Concepts says Psychology differs from the pseudosciences in that it employs the scientific method to test its ideas empirically. The scientific method relies on ...
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### iid data (Bayesian) vs iid random variables (Frequentist)?

I've been pondering the differences in notation / language used in some of the resources I've read for statistics / machine learning. Warning: this might be embarrassingly obvious to any decent ...
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### Comparing scores on different dimensions in factor models

So I'm currently conducting some research where I'm using item response theory (IRT) to estimate the difficulty of school subjects in Norway. It turns out that a two-dimensional, simple-structure ...
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### What are some good books on the philosophy of statistics?

I am a PhD in biological sciences with some background in graduate-level probability. I am interested in questions like what does it mean for an event to have probability $x$ at a philosophical level. ...
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### What is the Statistical Method?

I apologize in advance for the possibly philosophical nature of the question, however I would like to get answers from this website rather than from Philosophy exchange at the moment. I also come from ...
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### How is Bayes Stats supposedly more "intuitive" when it requires us to think probabilistically which IS NOT intuitive for most folks? [closed]

People don’t naturally think in probabilistic ways, they often form priors through point estimates because it’s less cognitively taxing to reduce everything down to single numbers. So if the ...
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### Machine learning and empiricism: does prediction translate to evidence?

Let $X_1, ..., X_n$ be a series of idd random variables. Imagine we are training a machine learning classifier over these variables with the task of predicting a feature $F$. A typical scenario might ...
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### Does bayesians' critique to frequentists apply to themselves too?

I've been reading about bayesians versus frequentists, including articles in this forum (like this one). Key is of course the issue of "priors". The bayesian critique being that frequentists ...
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### What does "Parameters are fixed and data vary" in frequentists' term and "Parameters vary and data are fixed" in Bayesians' term exactly mean?

I hear the sentence in my question a lot, I kind of understand what it means but never have a clear picture of it. Hope to get the clear picture of what the sentence exactly mean.
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### Science practice: Where to introduce approximations?

In my work, I am using an algorithm which relies on estimates of the gradient of the log-posterior at a collection of Monte Carlo samples. Since this gradient is not available in closed form, I must ...
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### When is it okay to not use model selection

If I have a model in mind, to ask a very specific question, do I have to do some form of model/variable selection? There are many papers describing different ways to do model selection, why some are ...
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### Alternatives to the null hypothesis significance testing framework

How did academics support hypotheses before the null hypothesis significance testing (NHST) framework was, in part, introduced and democratized by Fisher/Neyman & Pearson? Suppose NHST was never a ...
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### Crossing Frequentism and Bayesian Analysis

Has anyone considered giving the posteriors of an analysis a sampling distribution and seeing where, methodologically, things could go from there? For details, check out: https://sdba-stats.weebly.com
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### Structural complexity versus ontological complexity

From the article https://en.wikipedia.org/wiki/Occam%27s_razor: Another contentious aspect of the razor is that a theory can become more complex in terms of its structure (or syntax), while its ...
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