All Questions
Tagged with prior estimation
20
questions
1
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0
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81
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The Elephant in The Room: How is Real-World Domain Knowledge Converted into Bayesian Priors?
I have been trying to look into the daunting problem within Bayesian Models: How is Real-World Domain Knowledge Converted into Bayesian Priors?
Logically speaking, it seems that Bayesian Priors can be ...
4
votes
4
answers
688
views
Is it really worth doing Bayesian Analysis if you have no idea about Priors? [duplicate]
I have heard that if you use uniform priors in Bayesian Analysis, it is the same as doing Frequentist Analysis. If you are creating statistical models and you really have no idea about the prior ...
0
votes
0
answers
46
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The Role of Summary Statistics
I am reading about this algorithm called "ABC" (Approximate Bayesian Computation).
https://cran.r-project.org/web/packages/abc/vignettes/abcvignette.pdf (page 3)
Over here, it makes mention ...
2
votes
1
answer
216
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Confusion about prior used in Recursive Bayes Filter
I'm currently using this thesis to understand key concepts about probabilistic inference in computer vision which is being a great source.
The frame of the question is the following:
Let us assume we ...
- 1,220
-1
votes
1
answer
37
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Bayesian estimation Prior adaptation [closed]
I have a dataset of 1 dimensional 20points as prior information, so assuming prior distribution to be Gaussian distribution we can easily find its variance and mean. Now we will use this prior finding ...
- 21
6
votes
3
answers
974
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Putting prior on a function of parameters
Suppose that we have a likelihood for a conditional distribution $p(y|X,\theta)$. For clarity purposes we can consider linear regression with homescadastic errors. It is clear to me how one will put a ...
- 4,634
1
vote
0
answers
128
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Multiple priors in Bayesian estimation
Typical Bayesian estimation equation is:
Estimate = ( SampleSize * SampleEstimate + PrioriEstimateWeight * PrioriEstimate) / ( SampleSize + PrioriEstimateWeight )
Typically, the PrioriEstimate is ...
- 1,249
41
votes
6
answers
7k
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If a credible interval has a flat prior, is a 95% confidence interval equal to a 95% credible interval?
I'm very new to Bayesian statistics, and this may be a silly question. Nevertheless:
Consider a credible interval with a prior that specifies a uniform distribution. For example, from 0 to 1, where 0 ...
- 813
5
votes
1
answer
985
views
Bayesian estimation by sampling the prior?
Given a quadratic loss function, the Bayes estimator is given by \begin{equation}\hat{\theta} = E[\theta|y] = \frac{\int_\Theta\theta p(y|\theta) p(\theta) d\theta}{\int_\Theta p(y|\theta) p(\theta) ...
- 309
2
votes
1
answer
2k
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Bayesian prior choice for multivariate Gaussian distribution
Consider spatially distributed data $\boldsymbol x = \{x(t_1),x(t_2),\dots,x(t_n)\}$ which is described by a multivariate Gaussian distribution with mean $\mu$, standard deviation $\sigma$ and ...
- 1,215
1
vote
0
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370
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KL divergence between discrete data and model (choosing hyperprior over Dirichlet concentration parameter $\alpha$)
I have some categorical data that follow an unknown true multinomial distribution $p$ and a model with known multinomial distribution $q$.
I want to estimate the KL divergence between $p$ and $q$ ...
- 5,226
5
votes
1
answer
77
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Posterior probability when data consists of $k$ largest of $N$ samples
Given an underlying unknown distribution, I sample $N$ numbers. From those $N$ numbers I take the highest $k$ numbers. How do I model the posterior probability from those $k$ numbers.
I know I can ...
- 203
2
votes
0
answers
67
views
Prioritizing A/B tests by using the prior data
Let's say that I am an active user of the Tinder app and in addition to the standard features, I've got access to the A/B testing of my primary picture (the one that appears first when users stumble ...
- 121
12
votes
2
answers
4k
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When does the maximum likelihood correspond to a reference prior?
I have been reading James V. Stone's very nice books "Bayes' Rule" and "Information Theory". I want to know which sections of the books I did not understand and thus need to re-...
- 6,369
14
votes
1
answer
2k
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Jeffreys prior for multiple parameters
In certain cases, the Jeffreys prior for a full multidimensional model is generaly considered as inadequate, this is for example the case in:
$$
y_i=\mu + \varepsilon_i \, ,
$$
(where $\varepsilon \...
- 5,063