The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.
Questions tagged [bayesian]
2030 questions
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Standardize in bayesian analysis
I am doing a bayesian spatial analysis of crime in new york city.
I collected the crime statistics from the NYPD departmen; in particular I am focusing on the robberies. I collected geostatistical information (so the latitude and longitude); then, I…
lgndrzzz
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Unexpectedly small likelihood function
My question is premised on this one, which I'm trying to do in a Bayesian style. I'm a Bayes noob.
In a recent poll of 755 randomly selected adults, 587 said X. Test the claim that 75% of adults think X.
I'm starting out just by working out a…
Patrick Stevens
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Defining prior as combination of two distribution
I'll trying to understand an exercise where it defines the prior as "$\theta$ is $N(\mu, 1)$ or $N(-\mu, 1)$ with equal probability".
I try to add up normal distributions but it will result in a zero mean distribution which is not the expected. Does…
zeferino
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Did I draw this tree diagram correctly?
On the way home from work Chris goes through a traffic light then passes over a level crossing, the probability that Chris stops at a traffic light is $\frac{2}{3}$ while the probability that he is stopped at the level crossing further up the road…
Modrisco
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Bayesian Predictive distribution with two marginal posteriors
If we have a random variable $Y$ with pdf $P(Y|a,b)$, where $a$ and $b$ are parameters (with range $0$ to $\infty$).
As well as marginal posterior distributions for $a$ and $b$, these are $P(a\vert x)$ and $P(b\vert x)$, where $x$ is observed…
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Bayesian analysis problem
The problem in hand is that the prior distribution which I have received from experts (loan recovery data) ranges from 0 to 100%. Thus a beta distribution was assumed. Where as the actual data shows that loan recovery can be more than 100% due to…
Bik
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Bayesian statistics - explanation of evidence
Despite trying to read multiple resources about Bayesian statistics, I cannot find a (free) resource which explains what is exactly $P(D)$. Most of the resources explain it somehow conceptually instead of numerically. Some call it "evidence", some…
J. Doe
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Bayesian networks problem - Find the probability of rain gives grass wet given conditional probability values
Problem statement
Rain influences sprinkler usage. Rain and sprinkler influences whether grass is wet or not. What is the probability that rain gives grass wet?
Edit: The problem statement is verbatim from my question paper. I understand "rain gives…
Absee
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Confused with Bayesian parameter estimation and Maximum Likelihood Estimation
I'm confused with an example in MLE and Bayesian estimation.
It's about 'coin tossing', where we toss a coin n times, and the probability of observing head is theta. 'theta' is an unknown parameter in this case.
The textbook says, we denote x as :
1…
Cork
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Bayesian updating
"An object hides in one of 3 boxes. If the object is in box i, i = 1;
2; 3, and if box i is searched once, then the object is found with
probability 0.7. Suppose that it is initially believed that the object
is in box i with probability 0.2, 0.3…
dewewdew
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Understanding the explanation of a Bayesian prior for the weight of a linear regression model in Ian GoodFellow's Deep Learning
In Ian GoodFellow's Deep Learning textbook, there is a description of using a Gaussian prior for the weight $w$ of a linear regression model.
$$p(w) = N(w; u_0, \Lambda_0) \propto exp(\frac{-1}{2}(w-u_0)^T \Lambda_0^{-1}(w-u_0))$$
Where $\mu_0$ and…
IntegrateThis
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how to find a posterior with min of observation and constant
There is a variable Y with exponential distribution with parameter theta. The prior distribution is gamma distribution with parameters alpha and beta. If we don't have an actual observation of Y, but only observations that are equal to the minimum…
crab13
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Poisson Gamma Bayesian Statistics
I have a Bayesian stat question where I am a little confused.
Let $N_{1}$ and $N_{2}$ independent having $\mbox{Poisson}(\Lambda)$ distribution and $\Lambda \sim \mbox{Gamma}(\alpha,\theta)$. Then how we prove that $N_{1} + N_{2} \sim…
Matt
- 153
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Negative Binomial likelihood and Beta prior
I'm trying to settle what the posterior is (or more specifically, the parameters for the posterior) when we have a likelihood function that is coming from a Negative Binomial distribution and that we are assuming that the prior is beta [since it's a…
Aerdennis
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bayes probability for consecutive tests
Looking for some guidance for using Baysian probability for consecutive independent tests.
Using the traditional example of disease testing efficacy (say the 1% of the population are infected and the test is 95% accurate), I would like to understand…
Bryon
- 227