Combining probabilities with Bayes' Theorem, especially as used for conditional inference.

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I have a problem with bayes and train lines

I have this problem which I can't fully understand it: Assume you have entered in a foreign city of unknown size. At entrance you see a tramcar with number $100$. Let us assume that the tramcar ...
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33 views

Variational inference engines

After doing some research on the topic, I have noticed a surprising deficit of inference packages and libraries that rely on message-passing or optimization methods for Python and R. To the best of ...
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48 views

What is the difference between these two probabilities?

I am working on a word sense disambiguation task and I have a dataset consisting of labelled sentences for two meanings of the word 'line'. I am trying to find 'trigger' words that are good at ...
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28 views

Does smoothing of Bayes classifier will increase precision?

I have implemented Bayes multinominal and Bernoulli's model and my question is does the smoothing have any impact of the performance of both models (Laplace’s law of succession or add one smoothing)?
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29 views

Calculation of a time until the absorbing state given chemicals are initially separate

Biochemist from Siberia has just patented a new super genome formed by amalgamating genome X and genome Y. These genomes are harmless when separate, but when mixed there is a 45% chance of an ...
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33 views

Solve discriminant functions to get decision boundary in R

I am trying to solve the discriminant functions in R for two, 2-D gaussian distributions and trying to find the decision boundary. The discriminant function is given by, $g(x) = -.5x'\sigma^{-1}x + ...
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41 views

Is it possible for a bayesian model to “forget” about some points?

Say you are doing some online bayesian inference over observations. You want to infer $\mu, \sigma$ for $X$, with a model $X \sim \mathcal{N}(\mu, \sigma)$. Now everytime you observe a $X_i$, you ...
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42 views

Expected value of posterior vs. success probability

Context Suppose I have two models, $H_1$ and $H_2$ for which I know the prior probabilities $p(H_1)$ and $p(H_2)$. Furthermore, I know the class-conditional distributions $p(x|H_1)$ and $p(x|H_2)$ of ...
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78 views

Randomly given a coin from an unfair set of 6 coins, how can I determine which coin I was given?

Suppose I have 6 different coins that have wildly different increasing chances of flipping a heads, and I know the chances of flipping a heads for each. (ie. Coin 1: 1/280 chance of heads ... Coin 6: ...
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18 views

Applications of bayesian inference to external ballistics?

I'm reading "The theory that would not die" by Sharon Bertsch McGrayne (Fine book. Strongly recommended to everyone). The author says that bayesian inference has been used for ballistics applications ...
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2answers
74 views

Bayes factor calculation

I am a newbie to Bayesian stats...I came across an article for calculating Bayes factor by rounder etal.. In this article how am I supposed to put t value..n scale r on effect size parameters. If you ...
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186 views

Laplace smoothing and Dirichlet prior

On the wikipedia article of Laplace smoothing (or additive smoothing), it is said that from a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a ...
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1answer
48 views

Bayesian references [duplicate]

Any good places to start getting into Bayesian statistics? I'm a graduate student in social sciences, with a decent amount of stats classes under my belt, but I'm far from fluent. Any references would ...
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2answers
102 views

Long-run behavior in coin tossing experiment

I have read the following information on this site and I am not sure if it is actually true (or if I misinterpret it): Events that are random are not perfectly predictable, but they have long-term ...
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1answer
85 views

The Conjugate Beta Prior proof

Hello. I'm having a problem with trying to figure out this proof that shows the beta distribution is conjugate to the binomial distribution (picture attached). I understand it until the third row, ...
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2answers
82 views

Using Naive Bayes to calculate the probability of user presence based on the presence of her belongings

Alice, Bob, and Charlie work for a company and each of them has a cell phone and a car. They drive to work and they have their cell phones with them when they show up at work. The company has ...
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60 views

Clarification on LDA and the multivariate Gaussian

From my understanding, to calculate the posterior probability of a sample $x$ belonging to a class $k$ using Linear Discriminant Analysis you would first calculate the eigenvector matrix $W$ required ...
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230 views

Why did Thomas Bayes find Bayes' theorem so challenging?

This is more of a history of science question, but I hope it's on-topic here. I've read that Thomas Bayes only managed to discover Bayes' theorem for the special case of a uniform prior, and even ...
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66 views

Small conditional probabilies textbook question

I have an example from a book I am working through (car starting problem, with fuel & dirty spark plugs), but need a little help please. We have probabilities: P(NS) = 0.016, P(NF) = 0.001, P(F) ...
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73 views

Use of expectation propagation for model inference

I have a joint probability distribution as given in the figure: In this figure, variables in circles are random variables and variables in squares are constants. So, I can write the joint ...
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1answer
58 views

Conditional distribution of a discrete random variable given a continuous one

I can´t solve a conditional distribution problem using the simple Bayes´ Theorem for PDFs. The thing is, I know that X|Y ~ Poisson(Y) and that ...
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60 views

I have a question on conditional P with multiple events

I'm following this "Modeling and Reasoning with bayesian networks book's problems and Im stuck in this: ...
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80 views
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30 views

Mean of Posterior distribution

If $X1..Xn$ be iid $\sim N(\theta,\sigma^2)$, and let $\theta$ has double exponential distribution, $\pi(\theta) =\frac{e^{-|\theta|/a}}{2a}$, a known. Find mean of the posterior distribution. My ...
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28 views

Posterior distribution as a distribution for a new random variable?

So in Bayesian framework one uses observed data $X=\{x_1,...x_n\}$ to update the prior $p(\theta)$. My question is it justified to say that $p(\theta|x_1,...,x_n)$ corresponds to a new random variable ...
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Apply Bayes to multiple conditions

I am trying to simulate a process of selection without replacement. The process is one in which the system places a set of items in a specific order, and then the user selects N items in whatever ...
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155 views

Flaw in a conditional probability argument

Imagine an experiment where you roll two fair, six-sided dice. Someone peeks at the dice, and (truthfully) tells you that "at least one of the dice is a 4". What is the probability that the total of ...
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59 views

Can posterior distribution for a continuous variable be greater than one?

I already asked this question here, but I am not sure where would be better to ask it? This might sound a dumb question but I am really confused about it. According to Bayes' rule we do have the ...
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32 views

How to compute the probability that there is no difference between matched pairs

I am looking for a way to find the probability that there is no difference between a matched pair of binary data. I don't want to know whether the difference is statistically significant, I want to ...
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1answer
105 views

Prove/counter example: A minimax decision rule is always Bayes wrt some proper prior

Not sure whether the claim is true or false. If claim is true, intuitively, it might have something to do with "least favorable priors", but am not able to figure out the connection. If claim is ...
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256 views

How do you derive the Success-Run Theorem from the traditional form of Bayes Theorem?

In my industry it is common to test a sample of 20-30 and then use that data to draw conclusions about the reliability of the product with a certain confidence. We have tables for such things but it ...
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55 views

Bayes Theorem for Continuous Value Attributes

I need any solved example/data set which explain how to apply Bayes Theorem for continuous value attributes. I read the book (Machine Learning by Tom Mitchell) and found this equation. But I need some ...
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113 views

What is the difference between probability and fuzzy logic?

I have been working with fuzzy logic (FL) for years and I know there are differences between FL and probability specially concerning the way FL deals with uncertainty. However, I would like to ask ...
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37 views

Bayesian Expected Loss for mean F1-score loss function

So I have a multi-label classification problem where the exact number of labels in each test set example is unknown. The loss function is mean F1-score which is where p is the precision and r is ...
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113 views

Randomized Results Sampling

I'm taking a look at randomized results and have a question about an end case. Specifically, suppose my scheme is as follows: 1) I want to ask question Q_A. The probability of answering Q_A in the ...
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219 views

Bayes' Rule - Law of Conditional Probability

A market research firms conducts studies regarding the success of new products. The company is not always perfect in predicting the success. Suppose that there is a 50% chance that any new product ...
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276 views

Why does Bayes' Theorem work graphically?

From a mathematical standpoint Bayes' Theorem makes perfect sense to me (i.e., deriving and proving), but what I do not know is whether or not there is a nice geometric or graphical argument that can ...
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49 views

Error in an article with a conditional probability?

I’ve recently read the article "Visual Tracking of Human Visitors under Variable-Lighting Conditions for a Responsive Audio Art Installation," A. Godbehere, A. Matsukawa, K. Goldberg, American Control ...
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161 views

Locomotive problem with various size companies

I'm working through Think Bayes (free here: http://www.greenteapress.com/thinkbayes/) and I'm on exercise 3.1. Here's a summary of the problem: "A railroad numbers its locomotives in order 1..N. One ...
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134 views

Computing Bayes Factor using “Bayesfactor” package

For the purpose of model selection, I am using the Bayes' factor to compare different combinations of predictors in a linear regression model. I have used the function ...
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54 views

Priors on matrix determinant

I have a positive semi definite matrix (covariance matrix). Was wondering are there any distributions that can place a prior on the determinant? Something along lines of $$\exp(-k|X|)$$ Note that ...
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36 views

Error with syntax for BayesGLM in R with Gaussian family

I am trying to fit a Bayes glm model with an inverse Gaussian family and link="identity". However, I'm getting the following messsage: ...
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Bayes theorem example - Is a conversion rate the same as a user's probability to convert?

In web analytics we often calculate conversion rates for groups of users (number of users who bought / number of users). If we turn this around and a new user lands on a site I believe that this ...
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1answer
336 views

eBayes() lmFit()

I am using the golub data set from R with the labels. labelgb <- factor(c(rep("ALL",27),rep("AML",11))) names(golub) <- labelgb I need to use the ...
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127 views

Need help with some surprising classifications by naiveBayes

We are trying to do a POC on using NaiveBayes to classify an establishment by the category. We loaded the following training set in R. ...
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1answer
34 views

Confusion related to derivation of the probability distribution

I was reading a paper where they showed that when $\mathbf{X}$ and $\mathbf{Z}$ are two multidimensional variables $$p(z_{nk}=1|\mathbf{X}, \mathbf{Z}_{\neg nk})\propto ...
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74 views

Connection between PDFs/PMFs and Bayes Theorem

UPDATE Original question was confused and poorly worded. I thought about it more and don't think I have a question any longer. After thinking a bit more I came up with: For a distribution, such as ...
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Bayesian Meta Regression how to weight covariates

I want to perform a Bayesian Meta-Regression using Pearson correlations as covariates. Should I transform them in to "z"? How can I weight them?
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48 views

Simple Bayes network

Given the following Bayes network: with $p(k=t)=.2$ $p(o=t)=.1$ $p(s=t|k=f,o=f)=.0$ $p(s=t|k=f,o=t)=.2$ $p(s=t|k=t,o=f)=.5$ $p(s=t|k=t,o=t)=.95$ how would I calculate $p(s=t|o=t)$ and ...
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How can posterior be persisted and reconstituted as future prior?

Suppose I model a data generating process as a hierarchal model and have made some training observation from the process. To learn about the process, with the observations I run the bayesian ...