All Questions
Tagged with prior likelihood
47
questions
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26
views
How to obtain likelihood ($P(B/R)$ given the prior $P(R)$ and the posterior $P(R/B)$
I am working on a topic related to multiple-choice response. I would like to measure the efficiency of the information source (or a student’s information search) and I believe Bayesian statistics is ...
- 21
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13
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Turning a list of cost into categorical probability mass distribution
Background
Given a noisy dataset $D$, I have to solve a classification problem where the possible anserwer is $i\in\{1,\dots,N\}$. So far I can get pretty decent result with an algorithm that, based ...
- 373
1
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27
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Understanding the Binomial likelihood notation
Let $X \sim Bin(n,\pi)$.
I don't understand why the binomial likelihood is then given by $f(x|\theta)=\binom{n}{x} \theta^x (1-\theta)^{n-x}$. Shouldn't it be $B(x|\pi,n)=P(X=k)=\binom{n}{k} \pi^k (1-\...
- 137
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139
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Computing log-posterior for large variance priors
Let's say that some quantity is modelled by a time-dependent Poisson distribution,
$$
y(t) \sim \text{Pois}(\mu(t))
$$
where
$$
\mu(t) = \alpha_0 \exp(-\alpha_1 e^{-\alpha_2 t})
$$
and $\alpha_k > ...
- 111
1
vote
1
answer
83
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How to compute Bayesian estimate of a mean using data?
I'm trying to learn Bayesian statistics, but I'm having a lot of trouble actually applying theoretical concepts to data. I'd appreciate any feedback on my line of reasoning.
Say I have historical data ...
- 13
1
vote
2
answers
87
views
Is it practical to derive the prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"?
Is it practical to derive the optimal prior distribution by dividing the posterior by the likelihood and multiplying by the "evidence"?
Suppose you assume a probability distribution.
You ...
user318514
0
votes
1
answer
73
views
Posterior distribution when the domain of the likelihood depends on the parameter
I am trying to calculate a posterior density given distribution and a prior. And I am a bit confused about how I should act as the domain of the distribution depends on the parameter.
I am talking ...
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43
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How to update a prior probability distribution of hurricane occurrence based on absence of hurricanes to date?
For a forecasting tournament, I am trying to forecast the number of Atlantic basin hurricanes in the 2022 hurricane season. I have reason to believe that my prior distribution looks as follows:
At ...
0
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0
answers
69
views
Reparametrizing a Uniform Prior Distribution to Multivariate Standard Normal
Problem Description
I have a posterior distribution
$$
p(\theta\mid y) \propto p(y \mid \theta) p(\theta)
$$
with a uniform prior $p(\theta)= \mathcal{U}([a, b]^n)$, which is bounded. However, for my ...
- 2,236
2
votes
2
answers
160
views
Find a likelihood to calculate a posterior probability
I am having trouble understanding a basic Bayesian inference exercise:
Suppose we are interested in inferring the proportion $\theta$ of
individuals in a given population suffering from a certain ...
- 121
1
vote
1
answer
145
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Mixtures vs Multi-level models?
I'm confused on how mixture models and multi-level models are different (if at all.) Are there general rules for when to use one and not the other, pros/cons, etc?
- 3,382
0
votes
1
answer
199
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Nested sampling: What does "uniform sampling over the prior" mean?
I'm reading up on Nested Sampling in the book "Data Analysis - A Bayesian Tutorial" (Sivia and Skilling, 2006), and I do not understand the following:
What I understand:
Given a prior $\pi(\...
- 245
0
votes
2
answers
394
views
If the prior and likelihood not be conjugate, how to get conditional distribution to sample from using Gibbs sampling?
I know that when prior is conjugate with the posterior, by writing the loglikelihood and log prior and eliminate the non-independent terms for each parameter one can get the conditional distribution ...
- 135
2
votes
1
answer
379
views
What if the prior not be conjugate with posterior in Bayesian learning?
I know that when the prior is conjugate with posterior then one can get an analytical representation for the posterior distribution, but what if these two are not to be conjugate? For example, I would ...
- 135
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0
answers
36
views
Converting posteriors to likelihoods by removing prior
I have a set of MCMC chains (i.e., unnormalized posteriors) for a parameter I modeled for a sample of objects. I have a model that requires that I condition on the likelihoods of this parameter. My ...
- 101