All Questions
Tagged with likelihood-ratio bayesian
22
questions
0
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39
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Likelihood ratios not distributed as a chi2 distribution with the correct dof (Wilks' theorem)
I perform Bayesian inference on a mixture model such that $\mu$ is the mixture weight for a feature in the mixture
$p(x | \mu, \theta) = \mu p_{f}(x|\theta) + (1-\mu)p_{nf}(x|\theta)$
I have prior $p(\...
0
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0
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33
views
How to perform likelihood ratio test for bayesian neural network?
I am building a Bayesian neural network with Poisson likelihood and 50 features for time series prediction. Parameters of the model are learned using variational inference. I am trying to see whether ...
- 225
3
votes
3
answers
158
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Why can a likelihood ratio not give evidence for the null since it is a model comparison?
I am curious as to why a likelihood ratio cannot give positive evidence for the null, since it is a model comparison.
Indeed, this is more confusing given the fact that Bayes Factors are similar ...
- 121
0
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52
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Asymptotical convergence of the Likelihood ratio test in general hypotheses testing
I'm aware that the 2-loglikelihood ratio is asymptotically distributed as a Chi-squared distribution under the Null hypotheses for nested hypotheses. My question is, there is any generalized formula ...
- 101
1
vote
1
answer
890
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Comparison between Nested and Non-nested Model: BIC and LRT
I would like to select the best model for predicting breast cancer risk, specifically, it is the comparisons between weight/BMI/height, as other covariates remain the same in all the models. But I got ...
- 143
6
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1
answer
92
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Does ( P(B|A) - P(B|~A) ) / P(B|A) have a name?
Without going into the details, which are unnecessary here, this morning I found uses for the quantity
$$ S = \dfrac{P(B|A) - P(B|\overline A)}{P(B|A)} , $$
something like the amount of "...
- 163
1
vote
1
answer
117
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Manually calculating `false negative risk` (using Likelihood ratio and Bayesian analysis)
The question is with reference to this paper: https://arxiv.org/pdf/1802.04888.pdf and https://royalsocietypublishing.org/doi/full/10.1098/rsos.171085
It give clearly how to calculate ...
- 10.1k
1
vote
1
answer
59
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Manually calculating `false positive risk` (using Likelihood ratio and Bayes analysis)
The question is with reference to this paper: https://arxiv.org/pdf/1802.04888.pdf
In the real life example on page 17-18, it is advised that the ...
- 10.1k
1
vote
0
answers
244
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Bayes Factor, Likelihood Ratio, and p-values
I am interested in "simple" changepoint detection algorithms.
I originally was using very simples approaches that consist of making t-test calculations and calculate a p-value (similar to what is ...
- 49
0
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0
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167
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How to calculate Bayes factor for conditional probability?
I have a data set of 1000 drug-effect pairs. I am trying to identify which drug is most likely given the observed effect.
My original approach was to calculate $P\left(d_j | e_i\right)$ for each ...
- 181
2
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0
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365
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Can the r-scale value (for Bayes Factor) be directly based on Cohen's d?
I want to set an r-scale value for a Bayesian t-test (i.e. to calculate Bayes Factor likelihood ratio) based on previous results (i.e., from a posterior). But I simply cannot find a straightforward ...
- 234
4
votes
1
answer
121
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Philosophy behind "hypothesis" in Bayes factor
The posterior odds is the ratio of the Bayes factor $\times$ prior odds of the hypotheses.
$\frac{p(H_0 | D)}{p(H_1 | D)}$ = $\frac{p(D | H_0)}{p(D | H_1)} \frac{p(H_0)}{p(H_1)}$
It is considered a ...
- 423
3
votes
0
answers
67
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Bayesian Decision Making (for particular problem)
I've read several papers why p-values should be replaced by Bayes factors and trying to use them.
What I have: say, I have matrix of 2000 rows and 1000 columns. In each column I need to make a ...
- 1,741
1
vote
1
answer
145
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Does weighting the Likelihood Ratios by a prior give the Likelihood ratios any Bayesian property?
I have a question regarding Bayesian Hypothesis testing using "Bayes Factors".
Does weighting the Likelihood Ratios by a prior give the Likelihood ratios any property (e.g., removing conditionality ...
- 4,076
4
votes
1
answer
2k
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How to compare two models of binomial distributions?
Assume we have two series of indepedent success-failure observations, e.g. coin tosses
$$
\boldsymbol x_1 \in \{H,T\}^{n_1} \\
\boldsymbol x_2 \in \{H,T\}^{n_2}
$$
Also, let $k_i$ be the number of ...
- 143