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# 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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### What's the rationale behind a normality test followed by a $t$-test?

Correct me if I'm wrong, but from my understanding, the standard procedure of testing whether data from an unknown source have a specific mean is to (a) perform a normality test to see if the data are ...
42 views
+50

### Calibration with or without temporal structure

Setup I have a sensor which measures some air property outside. It outputs values on a continuous range. The sensor is expensive, so I want to replace it with multiple cheap sensors, which may give ...
50 views

### Two meanings of entropy?

In the world of physics, entropy seems to mean something different from stats + information theory world. So, I assumed that there are two definitions to the word entropy. Indeed, I looked up how ...
961 views

### Is it appropriate to use “time” as a causal variable in a DAG?

This question might be better suited for philosophy.SE, but I will post it here in the first instance, since it involves technical aspects that are best understood by users on this site. The title ...
35 views

### When computing MLE for linear regression, where does the uncertainty come from?

In my Machine Learning course, when computing MLE for a linear regression problem, we modeled the likelihood function as a Gaussian. I have trouble understanding why. Where does the uncertainty come ...
78 views

### Constructive mathematics and statistics [closed]

Usual non-constructive mathematics leads to some paradoxes (e.g. the Banach-Tarski paradox), which are directly related to the axiom of choice. In non-constructive mathematics, the axiom of choice (as ...
2k views

### What does Fisher mean by this quote?

I keep seeing this famous quote everywhere, but fail to understand the emphasized part every single time. A man who ‘rejects’ a hypothesis provisionally, as a matter of habitual practice, when ...
123 views

### Why don't people trade significance level for power?

As a convention, we have a lot of studies whose significance level is $0.05$ and a power of $0.8$. However, it is extremely rare to find a study whose $\alpha = 0.2$ with a power of $0.95$. From my ...
5k views

### When does Fisher's “go get more data” approach make sense?

Quoting gung's great answer Allegedly, a researcher once approached Fisher with 'non-significant' results, asking him what he should do, and Fisher said, 'go get more data'. From a Neyman-Pearson ...
86 views

### Do probabilities exist in reality? [closed]

I came across the seemingly interesting work of William Briggs in relation to probability and statistics. He make some bold claims, like the following: Probability does not exist as a thing, as a ...
627 views

### On George Box, Galit Shmueli and the scientific method?

(This question might seem like it is better suited for the Philosophy SE. I am hoping that statisticians can clarify my misconceptions about Box's and Shmueli's statements, hence I am posting it here)....
53 views

### What are the main approaches to the foundation of statistics without probability

The frequentist, likelihood and, to an even greater extent, Bayesian approaches to statistics are all based on probability. Without probability, it seems difficult to use a data sample ("seen" cases), ...
15 views

347 views

### What is the difference between Fisherian vs frequentist statistics? [closed]

I just read a research paper that said implicitly that there was a difference between the two. I thought that Fisherian statistics was another word for frequentist statistics.
57 views

### What are some basic principles to handle “none of the above” events in Bayesian statistics?

Suppose you want to assign a noninformative prior to the following event: The next tree that we will encounter is a: Spruce Pine None of the above We don't have any prior information, so we are ...
355 views

### Isn't the Solomonoff Universal Prior Biased Like Any Other?

The Solomonoff universal prior is fixed relative to a specific choice of universal Turing machine (UTM). Now, I understand that a UTM can simulate any other UTM, so that they assign a complexity to ...
73 views

### Is a frequentist approach to inference appropriate when working with non-repeatable data?

Jackman (2009) writes on p.xxxi-xxxii: Consider researchers analyzing cross-national data in economics, political science, or sociology, say, using national accounts data from the OECD. [...] ...
90 views

### Applying machine learning to dynamic complex systems (e.g. weather prediction)

Would it be correct to say that: Physics-based, domain specific models are more widely used and are more practical in (longer term) weather forecasts than pure machine learning approaches The reason ...
187 views

### Is testing model assumptions considered p-hacking/fishing?

"P-hacking", "fishing", and "garden of forking paths" as explained here and here describes an exploratory data analysis-like style of doing research that produces biased estimates. Does testing model ...
43 views

### Does it ever make sense to talk about the confidence (faith) in a probability value?

Let us suppose that we want to know what weather will be tomorrow. We ask two meteorologists and both give us an identical probabilistic answer: It will rain with probability of 30% It will snow ...
71 views

### What are the problems with existence of an “Omniscience Machine” within the constraints of collective human knowledge? [closed]

"If a machine can read and process written texts, manuscripts, journal articles and books, it would be able to predict results of new scientific experiments and construct new scientific theories." ...
47 views

### Why can scientists that refuse to bound the prior probability declare discoveries?

Summary: There appears to be scientists that refuse to put prior probabilities on some statements, such as the existence of the Higgs Boson. This is an understandable position. These scientists, ...
2k views

### Is everyday probability just a way of dealing with the unknown (not talking quantum physics here)?

It seems like in everyday probability (not quantum physics), probabilities are really just a substitute for an unknown. Take a coin flip for example. We say it's "random," a 50% change of head and a ...
374 views

### Is there an example of two causally dependent events being logically (probabilistically) independent?

Two events $A,B$ are independent when $P(A \cap B ) = P(A)P(B)$ I am trying to drill into this definition and to try to reconcile it with our intuitive idea of independence in the real world. I feel ...
174 views

### P-values and likelihood principle

This question came up in class: If we use p-values to evaluate hypotheses on an experiment, which part of the Likelihood Principle are we not obeying: Sufficiency or Conditionality? My intuition ...
128 views

### How important are interpretations of probability to the practice of statistics?

I know that the frequentist interpretation of probability is associated with classical statistics and maximum likelihood estimation, and that a subjective interpretation of probability is considered ...
Edits: I have added a simple example: inference of the mean of the $X_i$. I have also slightly clarified why the credible intervals not matching confidence intervals is bad. I, a fairly devout ...
The model of a HMM consists of a latent Markov chain with state $X$ and transition probabilities $P(X^t \mid X^{t-1})$, and observation variables $Y$ that depend on the current latent state via \$P(Y^t ...