Tagged Questions
2
votes
1answer
187 views
Should I expect it to be a chicken or a penguin?
An alien is trying to classify a group of only chickens and penguins into, well, chickens and penguins by analyzing 3 independent boolean features A, B, C.
If the animal (in reality) is a chicken, A ...
3
votes
1answer
63 views
Neg Binomial and the Jeffreys' Prior
I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated.
Okay, so the situation ...
2
votes
2answers
89 views
Using the Bayes Theorem?
A certain town has two taxi companies, the Green Taxi Co (cars coloured green) and the Blue
Taxi Co (cars coloured blue). 10% of taxis are the Green and 90% are the Blue. There was an
accident ...
1
vote
1answer
54 views
Find out the conditional probability
Consider I have the following probabilities:
$$P(A|B) = 0.86 $$
$$ P(A|B^C) = 0.35 $$
$$ P(B) = 0.80 $$
$$ P(A) = 0.758$$
Is there necessary information given to calculate $P(B^C|A^C)$? If so ...
2
votes
0answers
46 views
Using probability scores from a random forest
I've the following problem. I've a data set that tries to predict whether a given buy event will happen or not (0/1) when a customer sees a certain product, and I've features created for both the ...
0
votes
2answers
75 views
Estimating probabilities using Bayes rule?
I am working on a past exam paper. I am given a data set as follows:
Hair {brown, red} = {B,R}, Height {tall, short} = {T,S} and Country {UK, Italy} = {U,I}
(B,T,U) (B,T,U) (B,T,I)
(R,T,U) (R,T,U) ...
1
vote
0answers
55 views
How to model a network analysis problem
I have a weighted graph in which the nodes represent users and weighted undirected edges represent the tie between a pairs of users. For a piece of content $c$, and a node $A$ in the graph, given that ...
0
votes
1answer
56 views
How would we get the conditional distribution?
Having the marginal distributions, say $f(x)$ and $f(y)$, how would we get the conditional distribution $f(x|y)$? The relation is given by:
$$f(x)=\int f(x|y)f(y)dy$$
Do we need to find the ...
0
votes
2answers
122 views
Bayesian inference with Gaussian distributions
This is Problem 4(c), Chapter 2 from Thrun's Probabilistic Robotics . Note that this is self-study and not homework.
Suppose I know my position $x$ to be a normal distribution with density ...
0
votes
0answers
104 views
How to derive the conditional posterior density in hierarchical bayesian models?
I was reading on Gelman's Bayesian Data Analysis - Chapter 5 - Hierarchical model
Suppose:
data : $y_j$ s
parameter: $\theta$
hyperparameter: $\phi$
On page 126, he mentions the analytical ...
1
vote
0answers
100 views
How to set up a posterior predictive test quantities (Bayesian context) to check for independent Poisson distributions?
Suppose we are given data $y_j \sim \text{Poi}(\lambda)$ and assume $y_j$ are iid.
We can assume the prior distribution for $\theta$ follows $\text{Gamma}(\alpha, \beta)$,
The posterior ...
0
votes
0answers
39 views
How would you approach this problem on the Bayes theorem [closed]
I've been reading a book on Statistics and I could COMPLETELY understand all of its text. It basically explained the bayes theorem and what priors were, what posteriors were etc. But then in the ...
0
votes
2answers
151 views
Recommendations for learning probability and Bayesian statistics? [duplicate]
I have been very interested lately in learning Bayesian Statistics, but I have only a little bit of background in the frequentist statistics, only one term at University.
Some of the books that I ...
5
votes
0answers
113 views
How to calculate the probability of absence for a certain category of artefacts from a sample, given prior knowledge about its abundance?
In archaeology, artefacts are commonly classified in categories according to certain criteria (those may include manufacturing technique, decoration, function, chronology, etc).
I am trying to ...
7
votes
1answer
120 views
Is this a correct way to continually update a probability using Bayes Theorem?
Let's say I'm trying to find out the probability that someone's favorite ice cream flavor is vanilla.
I know that the person also enjoys horror movies.
I want to find out the probability that the ...
0
votes
1answer
86 views
Moralization and triangulization on belief networks
Assume that I have a belief network with a set of nodes.
In order to create a valid junction tree I have to moralize the graph. Assume now that I have nodes with more than 2 parents (e.g 3 parents) ...
2
votes
1answer
81 views
Determining conserved features using a Bayesian approach
I would like to perform some sort of binary classification, and my data set consists of 100 examples (for each class), which are vectors with 2500 elements. Ideally, I would like to determine which ...
0
votes
0answers
70 views
Bayesian Network parameter Estimation
I am doing a project in which I need to estimate the parameters(Conditional Probabilities) for a bayesian network. I am estimating the parameters from the given sample and using the dirichlet prior. ...
6
votes
1answer
337 views
Help me understand Bayesian updating
Suppose I have 5 possible events which either happened or did not happen in the preceding 10 time periods. How do I figure out how probable any event is in the 11th period?
...
0
votes
0answers
100 views
Building a probability distribution function from observation
There are N players and M objects, each of the objects has a value. Each player has a strategy in choosing an object. Each round a player will choose an object, many players can choose the same ...
0
votes
1answer
144 views
Bayesian network fundementals
What is the formula of P(W) at this Bayesian network?
PS 1: Is that formula gives me P(W) or not:
P(Cloudy) × P(Sprinkler|Cloudy) × P(Rain|Cloudy) × P(Wet Grass | Sprinkler, Rain)
PS 2: How we ...
3
votes
2answers
141 views
Are there any other interpretations besides bayesian and frequentist?
I am aware of the frequentist and bayesian interpretations of statistics. I prefer Bayesian because I think it's closer to how people think, and because we in practice often can't rerun a trial a ...
0
votes
0answers
62 views
Random sample of population sub sample size
I am generating models and each model is a random sample of the total model population. It is recommended that I generate 30,000 models and cluster taking the top 5 to 10 clusters to reach the native ...
1
vote
1answer
89 views
Distribution of $R^2$ for pairs of random variables
if I have two uniform random variables $X$ and $Y$, and I sample $N$ values for each, what's the probability of getting an $r$ Pearson's correlation coefficient (or Spearman correlation) between them ...
4
votes
1answer
93 views
Generalizing Add-one/Laplacian Smoothing
Let us assume we are estimating a proportion or rate of "hits". If we have $h$ hits and $m$ misses, the obvious estimator is
$\dfrac{h}{h + m}$
In order to avoid unreasonable estimations of $0$ or ...
2
votes
0answers
106 views
Is there any problem with a Bayesian setting that gives positive prior probability on malformed events?
I have a model class $M$. Each $\theta \in M$ defines a probability distribution $p(x,y | \theta)$ such that $x \in A$ and $y \in B$.
I am interested only in probability distributions of $\theta$ ...
1
vote
0answers
88 views
How do I calculate the Bayes error of a multivariate normal Bayesian classifier?
I have a 4 dimensional feature and each of them are independent normal distributions. I want to calculate the bayesian error associated with this classifier. The covariance matrix and the mean have ...
1
vote
1answer
117 views
How is this equation read?
I want to understand this paper on brain tumour segmentation.
How is this equation read?
I'm guessing $q_i(t_i)$ represents the likelihood of tumour on voxel i.Is q usually used to represent ...
1
vote
2answers
275 views
need help understanding Dirichlet (coursera's PGM class week 7 - Bayesian prediction)
I'm trying to work through Coursera's probabilistic graphical models class (week 7: Baeysian prediction) and a have several questions.
In the Dirichlet distribution, I'm having difficulty trying to ...
3
votes
1answer
133 views
Conjugate prior for a binomial-like distribution
Every week, my $m-1$ friends and I enter a pub quiz which has $n$ points available. In any given week only some of us are there. Record the presence/absence of member $i$ in week $t$ in the matrix ...
17
votes
3answers
404 views
Elementary statistics for jurors
I have been summoned for jury duty. I am conscious of the relevance of statistics to some jury trials. For example, the concept of "base rate" and its application to probability calculations is ...
9
votes
2answers
396 views
Optimal software package for bayesian analysis
I was wondering which software statistical package do you guys recommend for performing Bayesian Inference.
For example, I know that you can run openBUGS or winBUGS as standalones or you can also ...
3
votes
1answer
276 views
Posterior distribution for multinomial parameter
(topic moved from maths.stackexchange.com)
I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of ...
7
votes
4answers
795 views
Bayesian vs frequentist Interpretations of Probability
Can someone give a good rundown of the differences between the Bayesian and the frequentist approach to probability?
From what I understand:
The frequentists view is that the data is a repeatable ...
2
votes
1answer
84 views
Absolute error loss minimization
From Robert (The Bayesian Choice, 2001), it is proposed that the Bayes Estimator associated with the prior distribution $\pi$ and the multilinear loss is a $(k_2/(k_1+k_2))$ fractile of ...
4
votes
2answers
157 views
How to move from some arbitrary “distance” to a probability distribution?
I'm doing some object recognition, and when I compare two images, I get some unbounded "distance" between the two images, representing how similar they are. This is somewhat useful, but it seems like ...
0
votes
1answer
95 views
Bayesian Theorem Update Inference
According to Bayes theorem $P(A|B) = \frac{P(B|A)*P(A)}{P(B)}$
I've found somewhere that: $P(x_t|z_{1:t}) = \frac{P(z_t|x_t)*P(x_t|z_{1:t-1})}{P(z_t|z_{1:t-1})}$ but I don't really understand it, is ...
1
vote
1answer
108 views
Posterior distribution and computation of probability of a future event
I am a beginner in statistics, and am self-studying from "Information Theory, Inference, and Learning Algorithms" by David MacKay. I've hit a wall with one of the questions, and was wondering if any ...
2
votes
1answer
131 views
How can the F distribution be used, other than for hypothesis testing and confidence interval estimation?
I am trying to fit informed prior distributions to data using MLE, and F occasionally provides a best fit (lowest AIC value).
I am starting with only very basic knowledge of probability theory, so I ...
4
votes
3answers
304 views
What does Jaynes' continous pdf notation “g(x)dx” actually mean?
Something has been bugging me about E.T. Jaynes' treatment of continuous parameters.
In his book Probability Theory: The Logic of Science, uses notation that I am unfamiliar with when getting ...
7
votes
1answer
252 views
Why do people use the term “weight of evidence” and how does it differ from “pointwise mutual information”?
Here, "weight of evidence" (WOE) is a common term in the published scientific and policy-making literature, most often seen in the context of risk assessment, defined by:
$$w(e : h) = ...
6
votes
4answers
563 views
Derive P(C | A+B) from Cox's two rules
I am working my way (self-study) through E.T. Jaynes' book Probability Theory - The Logic of Science
Original Problem
Exercise 2.1 says: "Is it possible to find a general formula for $p(C|A+B)$ ...
1
vote
1answer
186 views
Combining two pieces of evidence expressed as probabilities
I have a hidden binary random variable Z that can have a value of either 1 or 0. There is some true probability P(Z=1) = z that I do not know.
I also have two separate pieces of "evidence" that give ...
4
votes
3answers
110 views
How to visualize iterative parameter constraint?
I have conducted an analysis in which I start with a set of informed prior parameter distributions, and then conduct sequential analyses that constrain the distributions with data.
I am currently ...
0
votes
0answers
76 views
calculating conditional probability-bayes rule
I'd like to calculate the conditional probability in the following case:
I was told that a box contains a BLUE ball. this is my evidence, my prior probability of a BLUE being drawn is 0.3. and this ...
1
vote
2answers
286 views
probability question
I would like to calculate the following conditional probability:
I know that the probability of a BLUE ball being drawn is 0.3.
I receive a message from A or B who saw the ball that has been drawn.
...
9
votes
2answers
148 views
Can I test the validity of a prior given data?
Problem
I am writing an R function that performs a Bayesian analysis to estimate a posterior density given an informed prior and data. I would like the function to send a warning if the user needs to ...
2
votes
2answers
968 views
Normalizing constant in Bayes theorem
Folks, pardon my noobness but I have not touch maths for some time and need a refresher into statistics:
I read that in Bayes rule, the denominator of ...
12
votes
5answers
424 views
Is there more to probability than Bayesianism?
As a student in physics, I have experienced the "Why I am a Bayesian" lecture perhaps half a dozen times. It is always the same -- the presenter smugly explains how the Bayesian interpretation is ...
-1
votes
2answers
682 views
How to calculate Bayesian probability between two variables?
I have 1000 data for two continuous variables (pressure and temperature). I'd like to calculate Bayesian probability between two variables.
In other words, I would like to determine probability that ...
