# Tagged Questions

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### Jeffrey's Prior for Bivariate Lognormal

Exactly what the question says, I'm working on code for an MCMC simulation and need to set some uninformative or weakly informative priors. I haven't been able to find the prior for the sigma ...
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### Does the parameter change during data generation in Bayesian Inference?

Let's assume that we have the following graphical model: This graph encodes the joint distribution $P(p,x_1,x_2,x_3,x_4) = P(p)\prod_{i=1}^{4}P(x_i|p)$. In the Bayesian inference, if we know ...
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### Question about the Bayesian Inference of a parameter

In order to understand the difference between the Frequentist and Bayesian inference, I was reading the presentation at: http://www.stat.ufl.edu/archived/casella/Talks/BayesRefresher.pdf . In order to ...
62 views

### rationalwiki on “Extraordinary claims require extraordinary evidence”

I don't have a strong background in probability/statistics and I'm trying to understand the example at ...
33 views

### Bayesian linear regression cost function

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
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### Change of Variables for two level Guassian model

I have a multivariate Gaussian distribution from which two variables, u and v, are drawn. The next variables, U and V, are U = 1/(u^2+5) + N(0,sig_U) and V = v^3 + N(0,sig_V). U and V are known, ...
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### What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is $$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$ The standard way to estimate $\theta$ ...
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### How would I analyze the accuracy of a model that predicts World Cup matches?

Say, someone made a bunch of predictions for each game between Team A and Team B, such that there's a predicted probability for each of the three possible outcomes adding up to $1.0$ : Team A winning, ...
36 views

### Confusion in Posterior Probability Calculation

I know posterior probability as, $P(\theta|x)= [(P(x|\theta)*(P(\theta))/(P(x))]$, as given in http://en.wikipedia.org/wiki/Posterior_probability I am slightly confused with the term ...
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### determinant and trace of a huge positive definite matrix

I have a problem to compute the determinant and the trace of inverse matrix: $det(\Gamma^{-1}+I_n⊗\Phi^T\Phi)$ and $tr[(\Gamma^{-1}+I_n⊗\Phi^T\Phi)^{-1}]$ where $\Gamma$ is a huge positive definite ...
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### A house is guarded by two alarms

I am trying to wrap my head around the following problem A house is guarded by two alarms. If Alarm 1 fires, p(theft) = 80% If Alarm 2 fires, p(theft) = 70% If both alarms fire at the same time, ...
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### Bayesian statistics, bivariate prior distribution

I've got a simple question buy I'm not sure how to solve it. It's a bit long. Suppose you've got $n$ iid random variables $X_1$, $\dots$, $X_n$ from the normal distribution with unknown mean $M$ and ...
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### Bayesian estimate for unfair die

Suppose you have a six-sided die that you suspect is not fair and toss it N times. What would be a Bayesian approach to estimating the probability of the six outcomes given that you suspect the die ...
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### How do I prove and expand Bayesian Networks?

Attempting to understand Exercise 20 (pdf page 44) in the paper: (Warning: large paper; small exercise) Bayesian Reasoning and Machine Learning The party animal problem corresponds to the ...
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### conjugate prior

A class of sampling distribution is a conjugate family of a prior distribution, if the posterior distribution belongs to the same family for all priors and all samples. Why is this phrase incorrect?
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### Jeffery's prior - help

I'm studying Bayesian inference and looking at prior choices. Currently I have looked at Laplace's uniform prior choice and now I am trying to understand Jeffrey's prior. I am having trouble ...
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### When using Bayes Rule, what are the rules for flipping the conditions and the event of interest?

Here is Bayes Rule: $$P(A\mid B) = \frac{P(B\mid A) P(A)}{P(B)}$$ This paper (http://www.cogsci.northwestern.edu/Bayes/Sivia_1996.pdf) uses Bayes rule on page 21 in the context of model selection ...
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### Bayesian Probability Question - Parameter Estimation

I would like help on the following question and I will show my work. Here is the question in my notes and I will follow up with my work: Q: Suppose a forest is segmented into strips, referred to as ...
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### Hypotesis test: $X_i | \theta \sim Exp(\theta)$ (Likelihood Ratio Test)

Construct the Likelihood-Ratio Test to test $H_o: \theta = 0$ versus $H_1 :\theta \neq 0$ supposing that $X_1, X_2,...,X_n$ are c.i.i.d random variables such that $X_i | \theta \sim Exp(\theta)$ P.S: ...
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### Hypothesis testing with Baysian methods: How many animals must I test to be sure that a disease isn't present?

I colleague has come to me with a question which I have answered for him but the only statistics I have done was what I did at school and a one semester course on Bayesian methods at university, so I ...