Questions tagged [logic]
The logic tag has no usage guidance.
32
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If we know A is independent of B, why isn't P(A|B,C) = P(A|C) necessarily true?
Let's say we know that A is independent of B, or mathematically:
$$P(A|B) = P(A)$$
Then how come we can't say the following is necessarily true:
$$P(A|B,C) = P(A|C)$$
If the outcome of B doesn't have ...
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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 ...
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1
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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 ...
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4
votes
4
answers
681
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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 ...
- 1,275
4
votes
0
answers
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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,...
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4
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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. ...
- 8,502
3
votes
3
answers
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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.
...
3
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2
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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 ...
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1
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"Successful projects share the same 5 keys qualities. In each quality our project achieves over average score". What can we conclude about this?
I'm not sure if this is a statistical problem, but I suppose it's a frequent problem involving using statistics, so I ask here anyway. Hope it's on-topic.
From the book Smart Pricing: How Google, ...
- 329
3
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1
answer
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Probability of two equivalent statements
Let A and B be two statements such that A is satisfied if, and only if, B is satisfied. Can we then say Pr{A} = Pr{B}?
- 31
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1
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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 ...
- 97
2
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1
answer
230
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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 ...
user297721
2
votes
1
answer
107
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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 ...
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1
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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 ...
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1
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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 $\lambda$...
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1
answer
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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 ...
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3
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Why is inference different in logic and statistics?
In Bayesian Inference, the term "inference" means learning parameters. In logic, inference means deducing something. Why are these two terms different?
1
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3
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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 ...
- 291
1
vote
1
answer
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Symbolic knowledge (First-order Logic) as priors in the Bayesian deep learning
In Bayesian learning, priors play an important role. As per my understanding, most of the priors are statistical, and they used mean and variance value as prior. Then deep learning model uses the ...
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Logical disjunction OR between two independent random variables
Consider the Bernouilli experiment of tossing a coin $2$ consecutive times, with the probability of getting "heads" of $p=0,8$
The base space can be described as follows $\Omega=\{HH,TT,HT,...
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Answer Set Programming - Make a Fact INVALID [closed]
I have a question regarding Answer Set Programming on how to make an existing fact invalid, when there is already (also) a default statement present in the Knowledge Base.
For example, there are two ...
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1
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Symbol for 'equally likely/probable'
I'm looking for the 'mathematical' symbol, if it exists, that denotes 'equally likely'. For example, one has two potential outcomes from a present state, both of which are equally likely (or probable)....
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3
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Relationship between logical implication arrows and causal diagram arrows
I am reading some of Pearl's more recent work on causal diagrams. It is fun to read but I am struggling to make some connections. Does anyone have intuitive (or precise) knowledge of the relationship ...
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Likelihood in Bayesian inference: p(x|theta, I) = p(x| I)?
In page 164 of the book “Probability theory: the logic of science” the author says that:
$$
p(D|\theta I) = \prod_{i=1}^{n} p(x_i|\theta I) = \theta^r(1-\theta)^{n-r}
$$
$ \theta $, in this equation, ...
user297721
0
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2
answers
2k
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Ordinal Logical Regression in R using polr interpretation
I'm using the polr package to do a ordinal logistic regression on my data. We did a survey for university students asking them a bunch of questions. To analyse the results i want to do an ordinal ...
0
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1
answer
698
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How to design a fitness function for binary logic network?
Assume we have a directed graph of connected nodes, where each node represents a logical operator. Input for this logic operator are values on all edges leading to the node and the result is outputted ...
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0
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49
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Softened logical implication using statistics
In a machine learning application, I have the following boolean implications $$\forall\,x,y:I_b(x,y)\rightarrow E_b(x,y),$$ where $I_b(x,y)$ being true means $x$ and $y$ are isomorphic, and $E_b(x,y)$ ...
0
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0
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Which groups/time periods to compare in staggered Difference in Difference (DiD) with unit and time fixed effect logistic regression model?
I am trying to build a logistic regression with staggered DiD (for not yet treated) that incoporates unit and time fixed effect.
I am stuck with the logic of building the model as I am trying to ...
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0
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In a specifically ordered set of binary data (ones and zeros), how can you organize them in patterns and from there build a probabilistic network? [duplicate]
So I have a set of 1s and 0s. They are listed in a column on excel. They are listed in a specific order. I do not wish to change their order.
So they appear as (1, 0, 1, 0, 0, 1 and so on... 0).
Here ...
0
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0
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A question about the interpretation of a certain probability about bounds of polynomials
Consider a polynomial $p(z)= \sum_0^n a_i z^i.$ In the literature there are numerous bounds about the roots of $p(z)$.Now once we prescribe certain dsitribution to the coefficients ,the bound itself ...
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0
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Independence, correlation and logical implication [duplicate]
Two random independent variables ($P$: "two variables are independent") are uncorrelated ($Q$: "two variables - the same two involved in sentence $P$ - are uncorrelated"), or using ...
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Are these logical variables for predicting among train/test sets?
I'm wondering if the following makes sense for a model.
I have a training and a test set. I want to predict whether a website visitor is a bot or a human, based on several visits. The data has been ...
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