Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [logic]

24 questions
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How much does Mathematical Logic relate to Statistics?

To wit, to what extent did statistics professors study Mathematical Logic ("ML" henceforth)? To what extent does Statistics use ML? How relevant is ML? I'm not referring to transitions or introductions to proofs like A Logical Introduction to…
NNOX Apps
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A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather than esoteric procedures?

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Repeated sampling principle: the frequentists of chapter 1 says the following: True frequentism states that…
The Pointer
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4
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Chicken and egg problem in determining the target feature

I have a large dataset of customers in an online shop, where many features regarding their history of buying behavior are recorded: who bought what, at which time, how often they entered the shop, at which points inside the shop the stood longest…
l7ll7
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Book or article recommendation about causality and counterfactuals

I'd like to assign undergraduate students with little to no math experience an article, short part of a book, or even a blog post about causality and counterfactual logic that is easy to understand. It seems that most articles and books are too…
firebird17139
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Relationship between categorical factors

I am not sure what this is called in English, but if we have two categorical factors, we can say that one of them (A) is finer than the other (B) if it holds true that if two observations belong to the same A group, then they'll also belong to the…
Mikiap
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1 answer

Multivariate normal distribution logic

From Introduction to Probability here (PDF page 348, book page 337) we are told: Definition 7.5.1 A $k$-dimensional random vector $X=(X_1, ..., X_k)$ is Multivariate Normal if every linear combination of the $X_j$ has a Normal distribution. That is,…
Arnold Davidson
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Why didn't $\Pr \left( A \rightarrow B \right)$ catch on?

Students are conditioned to thinking in terms of IF-THEN statements even before high school, and courses offered at the university level often lead to the formalization of material implication. Material implication is a function that two Boolean…
DifferentialPleiometry
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How to understand maximum likelihood estimation from an objective Bayesian paradigm?

I am trying to understand maximum likelihood estimation from an objective Bayesian/Jaynesian paradigm. My current understanding is that: There is a parametric family of functions f(x; theta) indexed by a tensor theta. And there is a mapping from the…
user297721
2
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0 answers

Deductive reasoning and artificial intelligence

AI has proven to be extraordinary effective for solving certain types of intellectual problems that we thought before only our brains could solve. The number of applications is tremendous: engineering, medicine, banking, law etc. Nevertheless the…
Alfred F.
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In the context of conjunctive boolean functions, what does "$\Rightarrow y$" mean?

This post gives an example to illustrate the size of a Hypothesis Space for discrete classification problems. A hypothesis is a function $f:\mathcal{X} \to \mathcal{Y}$, where $\mathcal{X}$ is the feature space (the set of all possible inputs) and…
fu DL
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Models that infer "high-level rules"

Are there any models that infer "high-level" rules? Consider for example the plot that represents data from a table with 3 entries: A $x$ and $y$ column of real-valued data and a label column with data *yellow",blue,magenta. Are there any models…
l7ll7
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A Logic based Problem with Probability of Failure

A lot of five identical batteries is life tested. The probability assignment is assumed to be $$ P(A)=\int_A\ (1/\lambda) * e^{-x/\lambda}dx\ $$ for any event A$\sqsubseteq[0,\infty)$, where $\lambda$>0 is a known constant. Thus the probability that…
J.Doe
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Is it always true that $P(X| Y \text{ OR } Z) \le P(X|Y)$?

Consider the following argument: If $(X| Y \ \text{OR} \ Z)$ is true, $(X| Y)$ must be true. For example, if $f(t)=10 $ when $ t=1 $ or $ \ t=0$ is true, then $f(t)=10 $ when $ t=1$ must be true as well. Therefore, the set of $X$ that make…
Dr. Who
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Can I merge multiple linear regressions into one regression?

I have a dataset of 48,000 records These records are divided equally into 4 groups Blue Group, Yellow Group, Green Group, and Red Group Each one of these groups has 12,000 records My study has resulted in 4 regression models Model 1 equation was…
asmgx
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Sum of individual parts not adding up to the whole

I am analyzing the WoW change in conversion rate (visitors who booked / visitors). Let's say the WoW change from week 1 to week 2 was -10% (dropped 10%). Now, I want to know what/where this drop in conversion rate came from. I have a hunch/business…
bp0308
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