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

learn more… | top users | synonyms

1
vote
1answer
42 views

Bayes in English

I am not a statistician or mathematician but am trying to learn. My question: In Bayes Theorem, $p(C|X)=p(X|C)p(C)/p(X)$, what are the English terms for $p(X|C)$ and $p(C)/p(X)$? In other words, is ...
0
votes
0answers
13 views

What is the empirical Bayes estimator for a gamma-Poisson with more than 1 observation for each Poisson parameter?

I am looking at the Wikipedia entry for empirical Bayes, but it's a bit confusing - it seems to me the solution must apply only to the case in which there's only $n=1$ sample $y$ for each $\theta$ and ...
0
votes
0answers
6 views

Rearranging 2 discriminant function to solve for 1 parameter (to derive a decision boundary)

I have a task where I want to classify patterns from 2 classes where the samples are drawn from a bivariate Gaussian distribution. I use the 2 discriminant functions ($g_1$ and $g_2$) to classify the ...
0
votes
0answers
25 views

Performance comparsion study on real data in MATLAB (machine learning)

I need to compare performance using 2-class classifiers–an LDA classifier and Exact Bayes in MATLAB. I have to use this dataset. Can anyone give me any advice how to do that (at least the steps of the ...
2
votes
0answers
81 views

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 ...
2
votes
0answers
34 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 ...
0
votes
1answer
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 ...
0
votes
0answers
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)?
0
votes
0answers
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 ...
0
votes
0answers
36 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 + ...
3
votes
1answer
43 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 ...
0
votes
0answers
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 ...
1
vote
1answer
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: ...
0
votes
0answers
20 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 ...
1
vote
2answers
76 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 ...
5
votes
2answers
197 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 ...
2
votes
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 ...
2
votes
2answers
104 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 ...
3
votes
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, ...
2
votes
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 ...
1
vote
0answers
61 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 ...
8
votes
2answers
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 ...
1
vote
1answer
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) ...
3
votes
1answer
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 ...
2
votes
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 ...
0
votes
0answers
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: ...
0
votes
1answer
83 views
0
votes
0answers
31 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 ...
1
vote
1answer
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 ...
1
vote
0answers
26 views

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 ...
6
votes
2answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
2
votes
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 ...
1
vote
1answer
268 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 ...
0
votes
0answers
56 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 ...
1
vote
0answers
118 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 ...
0
votes
0answers
38 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 ...
3
votes
3answers
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 ...
0
votes
1answer
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 ...
9
votes
2answers
277 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 ...
0
votes
0answers
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 ...
3
votes
1answer
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 ...
0
votes
1answer
138 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 ...
1
vote
0answers
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 ...
0
votes
1answer
37 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: ...
0
votes
1answer
97 views

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 ...
0
votes
1answer
344 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 ...
1
vote
2answers
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. ...
2
votes
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 ...