Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [bayes-theorem]

For questions related to Bayes' theorem, a result about conditional probabilities.

0
votes
0answers
5 views

Decomposition of posterior porbability

So, I'm currently working through "Data Analysis: A Bayesian Tutorial 2nd Ed." by D.S. Sivia and I am stuck an equation, which I am not able to reproduce (p.40 - 42 for those who might have a copy). ...
2
votes
1answer
24 views

Probability of a false negative

A population includes a fraction m of individuals carrying a disease exists and has the following characteristics: P(positive test | individual with the disease) = p P(positive test | individual ...
0
votes
1answer
29 views

Bayes Formula for more than 2 events

I have the following result used in one of the paper that I'm reading. I can't seem to get around how it is derived. Please help. $$ P(M\mid D,R) = \dfrac{P(M\mid R)\,P(D\mid M)}{P(M\mid R)\,P(D\mid ...
0
votes
0answers
5 views

can you help me understand the inputs for this bayes theorem calculator for my scenario?

I'm trying to calculate the probability of delivering a website based on the conditional delivery of an underlying database. I entered some inputs into this online Bayes Theorem calculator: https://...
7
votes
7answers
921 views

Monty Hall Problem-Probability Paradox

I just learned about the Monty Hall Problem and it seemed pretty much amazing to me.I am just a bit confused with it. So,according to the problem we are on a game show, and we are given the choice of ...
2
votes
2answers
42 views

Die roll and coin flip - Bayes' theorem

I am thinking to the question posed here: Die roll and coin flip. "Suppose I roll a 4-sided die, then flip a fair coin a number of times corresponding to the die roll. Given that i got three heads on ...
0
votes
0answers
9 views

Bayes Theorem with multiple conditions.

I have a problem involving Bayes theorem with multiple explanatory variables and I'm not sure how to calculate a Bayes theorem prediction. I have the equation for Bayes theorem but I don't know how to ...
5
votes
1answer
40 views

Bayes' Theorem with Multiple Tests

I'm having difficulties with this problem: Suppose you have an entire city afflicted with four distinct and exclusive diseases and a laboratory is assigned to test which disease each citizen has. ...
0
votes
0answers
6 views

Bayes' theorem and likelihood that an observation belongs to one of x clusters

I am trying to write a script is inspired by the following website. Here they examine mixture models, where they treat the distribution of batting averages as a mixture of two beta-binomial ...
0
votes
0answers
10 views

Bayes rule for joint distribution

How does one correctly apply Bayes rule to the full SLAM posterior $p(x_{0:t},m \mid z)$ over robot poses $x_0, x_1, ..., x_t$ and map $m$ with measurements $z_1, z_2, ..., z_t$? In his paper (sec. 5....
1
vote
0answers
25 views

Identify which normal distribution generated a given sample

I have $d$ Normal Distributions, $N_1(\mu_1, \sigma_1^2) \cdots N_d(\mu_d, \sigma_d^2)$. We pick one of the $d$ distributions with each distribution having a probability of $\frac{1}{d}$ of being ...
1
vote
0answers
48 views

A variant of the boy/girl paradox

Some friends and I were arguing about the two following word problems, which are variants of the classic boy/girl paradox. (i) "Mrs.Smith lives in a world where the eldest child is always male. She ...
0
votes
1answer
30 views

Conditional probability/Bayes

An IT worker works from home 1 day a week. When she works from home she answers 80% of the emails within an hour, 15% of the emails within 2 hours and 5% of the emails within the day. When she is at ...
1
vote
1answer
23 views

Finding an unconditional joint probability in a Bayesian Belief Network

I have a Bayesian network as drawn in the picture: We can see that $B$ and $C$ are conditionally independent given $A$. My goal is to find $P(B\cap C)$. My first thought was to use the Law of Total ...
0
votes
0answers
50 views

Bayes thereom without test accuracy

In a population presenting for testing at a certain clinic, 10% of patients will later develop Alzheimer’s disease. The clinic applies two tests: Test 1 identifies 14% of participants as likely to ...
1
vote
1answer
39 views

Clarification regarding Parameter Estimation (Andriy Burkov's book)

So I recently decided to read Andriy Burkov's "The 100-Page Machine Learning Book" and got confused in Chapter Two (Page 11) where he discusses Parameter Estimation techniques. A picture of the ...
0
votes
1answer
31 views

Does this elementary probability theory problem make sense?

The problem forumaltes as: Student takes test of 12 questions, each question is single-choice with 4 options. For each question he answers correctly if he knows the question, otherwise he guesses ...
0
votes
1answer
21 views

Determine the number of samples needed with Bayes theorem

I have a simple sample statistic problem, but I am not sure that I solve it properly. I have to enter many student marks to a test in an Excel table. After entering all $N$ marks, I want to know the ...
1
vote
3answers
31 views

Coin flips with two fair coins and one biased coin

I encountered this problem: We have three coins, two fair coins and one coin with heads on each face. One coin is picked randomly among those three coins and is flipped two times. We see the ...
1
vote
1answer
11 views

Computing posterior density

If I have two observations $X=n,X=m$, how do I then compute the posterior density? I can think of 2 ways but I don't know which one is the right one: 1) First compute posterior given $X=n$ $$p(\theta|...
2
votes
1answer
35 views

Proof of an Abstract Bayes' Theorem

In Björk (2009) a Bayes' theorem is given by Assume that $X$ is a random variable on $(\Omega, \mathcal F, P)$ and let $Q$ be another probability measure on $(\Omega, \mathcal F)$ with Radon-...
0
votes
1answer
10 views

Linear Bayes Optimal Classifer for Bernoulli distributed features

Consider the following two-class problem: We have two classes $c_1, c_2$ and binary data $x \in \{0,1\}^d$. Each dimension of $x$ is drawn independently from a Bernoulli distribution, according to ...
0
votes
2answers
38 views

Is Bayes' theorem, is the denominator always assumed to be non-zero?

Is Bayes' theorem, is the denominator always assumed to be non-zero or, in certain circumstances, you can prove that it is actually never zero?
0
votes
1answer
18 views

Conditional Bayes' theorem with 3 conditions

How would Bayes' theorem work for $P(s \mid o, a, b)$? I have looked at the following questions Bayes rule with multiple conditions and Bayes rule for two conditioned events, but I couldn't come up ...
0
votes
0answers
46 views

Why do we refer to the term $p(x \mid \theta)$ in Bayes' theorem as “likelihood”?

In the similar question (1339666) we have Bayes theorem: Bayes' Theorem Given some observed data $x$, the posterior probability that the paramater $\Theta$ has the value $\theta$ is $p(\theta ...
0
votes
1answer
41 views

Bayesian network network problem

I want to find: $P(C=0,A=1,D=1)$. I know the following: $P(C=0,A=1,D=1) = P(C=0|A=1, D=1)*P(A=1|D=1)*P(D=1)$ From the image, we can see $P(D=1)$ is $P(D=1) = P(D=1|A=0)*P(A=0) + P(D=1|A=1)*P(A=1) =...
0
votes
0answers
10 views

Bayesian inference considering known correlation

Let's suppose there are many states that we want to observe: $x_i, i\in \{1...N\}$, and suppose that for each state $x_i$ observation equation $p(y|x_i)$ is given. In this case, given an observation $...
0
votes
2answers
69 views

Marbles Probability question using Bayes Rule

Marbles Probability question using Bayes Rule I have this question from my revision booklet that I cant understand. A bag initially contained 4 white marbles and 9 black marbles. A marble was drawn ...
1
vote
0answers
57 views

How to use absolute discounting when the denominator and the numerator are both zero

Absolute Discounting Method for Smoothing Sometimes when we are using Bayes Classifier for classifying text (e.g. a sequence of words), we face a probability which is equal to zero and this makes the ...
0
votes
1answer
29 views

What's the probability that the ball (taken from the first box and dropped in the second box) was white?

I have one pretty tricky question: There are two boxes. Each one has 7 balls: 3 white and 4 black. One ball was taken from the first box and dropped in the second one. After that, ball was ...
1
vote
1answer
26 views

One coin chosen between a biased coin and a fair coin, and is tossed n times. Find probability of having gotten the biased coin.

In a different question, I had asked for clarification on the following problem where I wanted to just understand the problem. Now, I have attempted it and wish to know if my solution is right. ...
1
vote
0answers
40 views

One of two coins chosen, tossed n times

I am looking at the following problem about a coin toss experiment. I cannot understand the statements in the problem. Problem statement is given below. A drawer contains two coins. One is an ...
4
votes
3answers
58 views

Intersection of Probabilities and Bayes Theorem

It is known that 70% of women and 60% of men have voted in a poll, in a village where 500 women and 400 men live. If only 80% of the inhabitants tells the truth, what is the probability that a person ...
2
votes
1answer
44 views

Interpretation of Bayes Theorem Example

A protein that has the objective of assisting pig growth is given to pigs in their lunch. A researcher observes that few pigs may have developed tumours as a result of their eating which comprises the ...
0
votes
2answers
41 views

Coin flipping and Bayes' theorem… but where does binomial theorem come in?

Consider the following question: You are face with two identical coins. One is fair, and the other comes up Heads 90% of the time. You flip coins, which results in THHHTHHHTH (seven heads, ...
0
votes
1answer
24 views

Conditional problem with Bernoulli variables

Let $S_{n}=\sum_{k=1}^{n}X_{k}$ and $T_{n}=\sum_{k=1}^{n}Y_{k}X_{k}$ with all $X_{k}$ and $ Y_{k}$ are mutually independent and of law Bernoulli respectively of parameters p and q. Let $N=inf\{n>0 ...
0
votes
2answers
42 views

conditional probability and Bayes' rule

What's the between $P(x|y)P(y|z)$ and $P(x|y,z)P(y|z)$, it seems to me they both equal to $P(x,y|z)$. Does any condition should be satisfied if they both equal to $P(x,y|z)$.
1
vote
0answers
24 views

How to interpret the proof that information cascades will form?

I am reading the 1992 paper of Bikchandani, Hirshleifer and Welch on information cascades. They claim and prove that, given an environment of sequential decision making, an information cascade will ...
0
votes
0answers
17 views

Product of two conditional distributions in Bayesian modelling

I am currently reading an introduction to Bayesian Modelling. Im trying to understand why the following is true: $$p(w|x,t,\alpha,\beta)\propto p(t|x,w,\beta)p(w|\alpha)$$ where: $w$ is are the ...
3
votes
1answer
37 views

Is this an application case of Bayes theorem? Is my book wrong?

A sickness has a heterozygote frequency of $\frac{1}{20}$ ie. 1 in 20 people of a population will have the allele combination $Aa$ where a denotes the recessive and A the dominant allele. To become ...
0
votes
1answer
19 views

Bayesian probability question and conditional probability based on falsehoods

I'm having trouble understanding how to compute (a), if it's not a Bayes theorem problem. Why bother telling me about $A$ and $A^C$ compliment in that case? How does this help me compute parts (b) ...
0
votes
0answers
13 views

Crash rate after patch, Bayes' theorem

I have the following problem: Computers with a certain OS have a crash rate per month that is distributed as Poisson with $\lambda = 5$. After a patch is installed, the crash rate is distributed as ...
1
vote
1answer
28 views

Comprobation for mutually exclusive dependent events using Bayes Theorem

I know that for mutually exclusive events: $P(A\cup B) = P(A) + P(B) $ However, I'm having some trouble deriving this from the Bayes Theorem for practical cases. Let's say that we have a toy, and ...
3
votes
0answers
41 views

Maximum bound using Bayes Theorem

A protein that has the objective of assisting pig growth is given to pigs in their lunch. A researcher observes that few pigs may have developed tumours as a result of their eating which comprises the ...
0
votes
1answer
54 views

Bayes theorem algebra question

A protein that has the objective of assisting pig growth is given to pigs in their lunch. A researcher observes that few pigs may have developed tumours as a result of their eating which comprises the ...
1
vote
2answers
37 views

strange Bayessian probability calculation in book

let us consider following problem taken from book An appliance store purchases electric ranges from two companies. From company A, 500 ranges are purchased and 2% are defective. From company B, ...
0
votes
0answers
52 views

Bayes Rule - Expanding the conditional probabilties

Suppose I am generating a sample for $P(A=0|B=0,C=0,AvB=0,CvA=2,BvC=0)$ The pseudo probability for this would be given as: $P'(A=0|B=0,C=0,AvB=0,CvA=2,BvC=0) = P(A=0)P(B=0,C=0,AvB=0,CvA=2,BvC=0|A=0)$ ...
0
votes
0answers
46 views

Multiple Choice Test, conditional expectation, Bayes - Theorem

There are a multiple choice task given with four statemants for each task, which we describe by the set $ \{1,2,3,4\} $. Each of these four statements must be assigned one of the attributes "false"$(=...
0
votes
1answer
20 views

Am I Calculating The Results Of This Bayes Theorem Correctly?

The problem in question Hello. I have been trying to calculate what the probability is that p(A|not Favor) from this problem. This is specifically referring to part b. The results that I got were: ...
0
votes
0answers
14 views

compare Bayesian linear regression vs standard linear regression

1st question, I recently learnt bayesian linear regression, but I'm confused that in what situation we should use bayesian linear regression, and when to use standard linear regression? What is the ...