Questions tagged [logic]

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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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1answer
92 views

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 ...
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4answers
303 views

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. ...
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1answer
67 views

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, ...
2
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1answer
141 views

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 ...
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0answers
27 views

Is ther any logic that migth help while you create a Neural Network? [duplicate]

I am a newbie in Tensorflow and Keras and for the first moment I ask me the same few questions while I am creating my Neural Network. Even searching for some explanation of how to estructure, train, ...
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0answers
62 views

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 ...
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1answer
61 views

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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2answers
337 views

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 ...
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0answers
19 views

what is the distance metric for Hierarchical clustering of logical data in R?

I want to perform clustering based on 20 logical columns that all have TRUE/FALSE as field values. I'm using the cluster package stats (hclust) and Cluster (agnes) and both use Euclidian distance but ...
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4answers
1k views

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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3answers
99 views

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?
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43 views

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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1answer
109 views

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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0answers
481 views

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,...
2
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1answer
147 views

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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4answers
605 views

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 ...
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1answer
27 views

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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3answers
463 views

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. ...
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0answers
25 views

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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1answer
133 views

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 $\lambda$...
2
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1answer
232 views

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 ...
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2answers
42 views

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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1answer
645 views

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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0answers
24 views

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 ...