0
votes
1answer
35 views

determining maximum a posteriori (MAP) hypothesis

I have this problem: You are given a coin that may or may not be biased. Specifically, you have three hypotheses about the coin: ...
1
vote
1answer
40 views

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 ...
0
votes
1answer
27 views

Finding a posterior distribution of an exponential distribution parameter theta

Suppose that $X_1, ... , X_n$ each have an exponential distribution with parameter $\theta$, and suppose that the prior for $\theta$ is an exponential distribution with parameter $\lambda$. Find the ...
2
votes
0answers
17 views

Is this problem suited for Bayesian inference?

Suppose that the quality of a widget is distributed according to a score, given by a normal distribution with mean 1 and variance σ^2. A fraction, π of all widgets are defective. The cost of having an ...
1
vote
1answer
44 views

Questions about Auctions

I am having a hard time figuring out a problem. In a first price auction with a reserve price R and values of the bidders are U[0,1], how do we find expected revenue given the strategy of both of them ...
0
votes
1answer
70 views

Bayesian Network - unclear homework example

I am not sure if it is me or the example: A doctor gives a patient a drug dependent on their age and gender. The patient has a probability to recover depending on whether s/he receives the drug, ...
0
votes
2answers
53 views

Conditional Independence - Bayesian Network

May the probability distribution $ P(A,B,C,D) $ given as: $ P(A,B,C,D) = P(A)P(B)P(C|A,B)P(D|C) $ The task is to show that this holds $ A \bot B | \emptyset $ and $A\bot D|C$. First thing I'd like ...
0
votes
0answers
23 views

Deriving posterior pdf in classical linear normal regression model under noninformative prior

Question: Assume the following classical linear normal regression model: \begin{gather*} y_{i} = \beta_1 x_{1i} + \beta_2 x_{2i} + \cdots + \beta_K x_{Ki} + e_i \\ \underbrace{\boldsymbol{y}}_{n ...
2
votes
2answers
110 views

Comparing uniform priors

The background of the problem is this: Assume that we have a parameter vector $\Theta$ which satisfies $\Theta^\prime\Theta=1$. If we let this vector have the uniform prior, the density of the prior ...
0
votes
0answers
235 views

Bayesian computational problem with R

I can't understand the iter (this is me) to solve this kind of exercise involving the approximation of the posterior density. Consider this exercise taken from Bayesian computation with R: We ...
1
vote
1answer
68 views

Bayes theorem for calculation with personal probabilities

I'm completely stuck on some homework I have and can't figure it out. The task is to calculate the probability of a bus being late conditional on the weather being snowy and bus driver being ...
1
vote
1answer
212 views

Using Bayes Theorem intuitively without equation (tree-diagrams)

I am working on the following question and I am having some difficulty. The thing is I understand that I must apply Bayes Theorem but to be honest, I like to do problems using Bayes Theorem ...
0
votes
1answer
121 views

question related to Bayes' rule and Bays' risk.

Let $X_1, X_2, X_3, \ldots, X_n$ be a random sample for $N(e,1)$. Let the prior p.d.f. of $e$ be $N(0,\sigma^2)$ under the square error loss function $L(e,d)={(d-e)}^2$. Find the Bayes' decision rule ...
0
votes
0answers
186 views

bayesian estimation on the poisson distribution

Suppose X~Poisson($\lambda$) and $\lambda$~Gamma($\alpha,\beta$). Find the posterior distribution and the Bayesian estimator of $\lambda$. Thus the prior distribution is: ...
1
vote
1answer
757 views

Bayes' Rules: The probability of at least one event occurring?

There is a 60 percent chance that the event $A$ will occur. If $A$ does not occur, then there is a 10 percent chance that $B$ will occur. (a) What is the probability that at least one of the ...
0
votes
1answer
193 views

Exercise 2.8 in Mackay's Information Theory, Inference and Learning Algorithms

[Editing question per Leon's suggestions - thanks for these!] Could someone walk me through a solution to Ex 2.8? 2.7: Bill tosses a bent coin $N$ times, obtaining a sequence of heads and tails. ...
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0answers
111 views

Probability Question.

Every morning, I roll a die to decide how to travel to work. If I roll a $1$ or $2$, I take the train, if I roll a $3$, I catch a bus and otherwise I cycle. The probability that I am late for work is ...
1
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3answers
171 views

What is the probability of a product being defective, given subsequent observations?

Let's say I have a factory producing 28% defective bottles. A defective bottle has a 66.5% chance of breaking when dropped on the ground and a non-defective bottle only has a 9.5% chance to break. ...