# Questions tagged [bayes-factors]

Given some data and two competing models, Bayes factor is the ratio of probabilities to observe these data under one and under another model.

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### strong evidence for H1 with Bayes factor but very weak with Bayesian regression estimation

I performed a Bayesian hierarchal regression with the brm package. Looking at the parameter estimation and confidence interval, I found no support for one of the parameters. However, when I computed ...
124 views

### 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 ...
1 vote
30 views

### Similarities between Bayes Factor and WAIC formulas?

It looks for me that WAIC and Bayes Factor are very similar in some circumstances. If we assume an equal prior for each parameter set Q (p(Q)), the Bayes Factor ...
41 views

### Compare two proportions with a Bayesian analysis

I'm conducting an experiment in which participants receive either an object A or an object B. Next, we ask participants if they want to trade their objects with the alternative object (i.e., object B ...
13 views

### Specifying Model of Alternative Hypothesis for Calculating Bayes Factors

I'm new to Bayesian statistics. I'm running a linear mixed effects model in R (using lmer), and I want to report Bayes Factors using these results, as demonstrated ...
89 views

### Using BayesFactor R Package Instead of P-Values in Mixed Modelling

I have been using lme4 in R to run a linear mixed effects model. ...
23 views

### Detection limit for a drop in speed, due to stopping between measurements

Assume that a device is traveling at a constant expected speed $\mu$, subject to random variation with standard deviation $\sigma$, for a measurement period of duration $t$. Then the expected travel ...
145 views

### ABC model selection from posterior samples

I would like to know if there is a general scheme to do model selection based on the posterior samples from a set of ABC (Approximate Bayesian Computation) runs for a given set of models. Particularly ...
45 views

### Bayes factor for testing fit of different spatial models in Stan

I have a question about testing of different spatial specifications of a polynomial regression. I am using Stan for Bayesian inference, but I did some initial exploration using the R packages ...
44 views

### Bayes factor for one-tailed correlation (differences between results from Bayesfactor package in R vs JASP)

I want to compute a Bayes factor for one-tailed correlation (n~600). Using NHS, Pearson's r = 0.01 and p-value =0.42 With JASP, I get a one-tailed BF of 0.059, so strongly in favour of the null ...
37 views

### 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 ...
122 views

### Multiple testing adjustments for Bayes Factors

I manage an platform that has succesfully gotten a Bayesian approach to experimentation in production. One new feature we want to implement is to do inference for multiple metrics (e.g. conversion ...
26 views

1 vote
214 views

### Relatively fast approximations to the marginal likelihood?

Let $\theta\in{\mathbb R}^d$ be a multidimensional parameters, where $d$ can be large (e.g. $d=100$ or more). What approximations can I use for the marginal likelihood: \int f(x\mid \theta)\pi(\...
1 vote
205 views

### 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 ...
623 views

### How to compute contrasts between levels of a parameter in bayesian mixed-effects models and produce bayes factors in R?

I would like to compute contrasts between different levels of a parameter from my Bayesian mixed-effects models in R, and produce bayes factors. My outcome (Jud) is binary (1=Yes/In synch, 0=No/Out ...
416 views

### Why does Bayes Factor go to infinity as $n$ goes to infinity?

Why does Bayes Factor go to infinity as $n$ goes to infinity when considering a bilateral alternative hypothesis? The Bayes factor is $BF=\frac{postodds}{prior odds}$, and since the prior odds are ...
163 views

### 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 ...
1 vote
170 views

### Can I exponentiate the log-Bayes factor to get the Bayes factor?

Simple question here. I'm using Bayesian Confirmatory Factor Analysis and I can get a log-Bayes Factor with the Laplace approximation. However, I'm wondering whether I can just exponentiate this value ...
1 vote
241 views

### Expressing one-sided p values of directional hypothesis tests as Bayes factors

Assume we want to test the directional hypothesis that $µ<0$. From a frequentist angle we use a one-tailed $t$-test and imagine we obtain a 1-sided $p$ value of say 0.07, which then would imply ...
862 views

### Bayes-Poincaré solution to the Behrens-Fisher problem 2: calculations for Jeffreys’ priors [closed]

In a previous post Bayes-Poincaré solution to k-sample tests for comparison and the Behrens-Fisher problem?, the classical Bayesian and likelihoodist solutions to 2-sample tests for comparison and the ... 1k views

### Bayes-Poincaré solution to k-sample tests for comparison and the Behrens-Fisher problem?

I’d like to share and submit for (dis)approval and discussion yet another, simple but original (to the best of my knowledge) Bayesian solution to the classical problem of comparing k samples or groups,... 131 views

### Bayes factors in R for correlated proportions (such as a "Bayesian McNemar's test")

Is there any way to get Bayes factors in R for correlated proportions (i.e., paired sample)? For example, the same group of 90 people is measured with one technique, then with another; once there are ...
38 views

### Likelihood ratio to quantify the similarity between one sample with two other matched samples

I conducted a study with 3 conditions and N subjects. All subjects performed all conditions once. I would like to know if the first condition is similar to the second or third condition. Formally, ...
1 vote
624 views

### Bayes factors and predictive accuracy in model comparison in rstan / brms

Despite reading up on the subject, I can't wrap my head round it, so the question remains on shaky grounds, and responses along the lines of "read chapter x" are very welcome. What I'm doing is I'm ...
3k views

### Why are the cut-offs used for Bayes factors and p-values so different?

I am trying to understand Bayes Factor (BF). I believe they are like likelihood ratio of 2 hypotheses. So if BF is 5, it means H1 is 5 times more likely than H0. And value of 3-10 indicates moderate ...
369 views

### Bayes Factor A/B Testing

I am just starting to look at Bayesian statistics and so far I am aware that Bayes factor summarizes some form of evidence of an alternative hypothesis against the null one. As far as I know we can ...
445 views

### Random effects in a linear model using BayesFactor package: why do bayes factors vary?

I'm using the BayesFactor package with the lmBF and generalTestBF functions to compare different linear models that include participant as a random effect. Below is an example of one of these model ...
I would like to perform model selection given a range of $k$ models $\mathcal{M}_1, \mathcal{M}_2, ..., \mathcal{M}_k$, each with some prior probability $f(\mathcal{M}_1), \dots, f(\mathcal{M}_k).$ ...