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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Bayes Factor Analysis

I am new to Bayesian statistics. I have one group (n=10) with two measurements per subject (before/after a treatment manipulation, i.e., Phase "2" and "3" below). I originally used ...
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Checking my understanding of Bayes factor hypothesis testing

I am new to Bayesian statistics. I am trying to understand my course notes on this topic. Here are the notes: I will try to explain what these notes are saying and hopefully someone can correct my ...
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The ratio of two Bayes factors for two opposite one-tailed hypotheses

I am trying to understand how Bayesian inference works, so this might be a very simple question. I have an experiment where I test two hypotheses predicting opposite results. Let’s say, hypothesis 1 (...
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Bayes Factor and Likelihood Function Estimate

I am so stumped on this too: Imagine that a researcher computes a Bayes Factor for a point-null hypothesis against an alternative with a weakly informative prior centered on zero. The resulting Bayes ...
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22 views

Significant p-value and anecdotical BF

I'm conducting frequentist as well as Bayesian analyses. However, I have difficulties to interpret data. Indeed, results showed significant p-value, but anecdotal BF10 (< 3). Likewise, there are ...
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32 views

Help for interpretation : significant p-value and anecdotical BF

I'm conducting frequentist as well as Bayesian analyses. However, I have difficulties to interpret data. Indeed, results showed significant p-value, but anecdotal BF10 (< 3). Likewise, there are ...
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151 views

Compare two models of binomial distributions via Bayes Factor

(This question is similar to How to compare two models of binomial distributions?, except that I would like to use a Bayes Factor for model selection) I have a bunch of binary (Bernoulli distributed) ...
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76 views

AIC model selection for group studies

In some areas, it is common to fit a model separately to multiple clusters in a data set, for instance fitting a cognitive model separately to data from each participant in an experiment. Model ...
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Asymptotics of Marginal Likelihood

I'm working with Bayes factors, and I want to develop some intuition for the result $$ \frac{m_1(\mathbf{X})}{p_n(\mathbf{X}|\hat\theta_n)}\xrightarrow{p}\frac{\pi_1(\theta_0)\sqrt{2\pi}}{\sqrt{\...
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42 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(\...
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63 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 ...
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87 views

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

I would like to compute contrats 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 of ...
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How to calculate a Bayes factor using a posterior sample? [duplicate]

I have two models that I want to compare. Both models have several parameters (more than 10). I want to compare them using the Bayes factor, but I only have an MCMC posterior sample for each model. ...
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112 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 ...
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70 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 ...
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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 ...
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104 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 ...
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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 ...
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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,...
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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 ...
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31 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, ...
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336 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 ...
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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 ...
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165 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 ...
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158 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 ...
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Model selection for this model with one observation

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 $f(\mathcal{M}_1), \dots, f(\mathcal{M}_k).$ ...
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403 views

Bayes factors from MCMC samples

I'm working to implement Bayesian model selection among models whose posteriors have already been sampled via MCMC. After reviewing some discussions of Bayes factors, I understand that they are ...
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166 views

How are Bayes factors actually Bayesian?

I have been doing some linear model analyses involving Bayes factors lately and I have two probably very basic questions: 1) As far as I understand, a Bayes factor is simply a likelihood ratio, i.e. ...
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41 views

How to interpret a statistically signficant finding that becomes unsignificant after bonferroni correlation

I hypothesised I would find a main effect of X which I did (p=0.028), however, upon using the bonferroni correction my alpha dropped to 0.0125, making this result no longer significant. I found a ...
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Bayes Factor Poisson-Hidden Markov Model

I am following the Hidden Markov Models guide text for Time Series An Introduction Using R (Walter Zucchini). Chapter 7. Bayesian inference for Poisson-hidden Markov models. Specifically in section 7....
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1answer
153 views

ABC, compute Bayes factor from posteriors

I am pretty new to ABC stuff so I may be saying dumb things. My question is: I ran an ABC with two models $M_1$ and $M_2$ and now I have an approximation of the posterior distribution for both model. ...
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192 views

Calculating Bayes Factor from Z score, n, and No

I'm completely stuck on how to get this answer from a course below. I guessed the answer, but I'm lost on how they get to it. I did the following in R ...
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139 views

Computation within log space

What is the conversion of the following equation into log space? $bf2 = 1 + (p * (bf1 - 1))$ Given log.bf1 (log Bayes factor), how do I get to log.bf2 without having to compute bf1, but instead ...
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178 views

Diffuse priors Bayes Factor

In textbooks I always read that it is necessary to have a proper prior on the parameter that we want to test with Bayes factor, otherwise we would always posteriori favor the model with less ...
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Uniqueness on bayesian factor model's loading matrix

I'm doing uniqueness on factor loading matrix in a factor model. $ y = \Lambda f + \epsilon$ where $ f \sim N(0,\Sigma)$ , $\epsilon \sim N(0,\Omega) $ and $\epsilon \perp f$. It's well known that ...
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How does Lindley compare a Bayes factor and a p-value?

I was reading this paper by Dennis Lindley ("Analysis of a Wine Tasting", J. Wine Econ. 2006). Statistically, the paper is a straightforward analysis of a $10\times 11$ two-way table. To test whether ...
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155 views

Bayesian models: Bayesian t-test on effect posterior against 0 as index of effect existence

I am fitting Bayesian models (using R and rstanarm). Beyond estimating the effect of each predictor (and extracting pointwise indices such as median, MAD and 90% CI), I am also interested in having a ...
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How do I prepare data for Rouder & Morey (2012) default prior?

I am going to run an analysis using the default prior outlined by Rouder and Morey (2012); however, I am unclear how exactly to prepare the data. As a quick overview, I have a continuous DV and a ...
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How would I use the largest expected effect size to determine a prior?

I have a simple experiment in which ~30 people responded to 100 words, half of which were of Type A and half of which were of Type B. I am using a mixed effects linear regression to predict reaction ...
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112 views

Calculating Bayes' factor for 2 Gamma distributions

I have 2 model $M_1$ and $M_2$ which both have a gamma distribution and the same priors $H_0 : \quad x_i \sim M_1 \\ H_a: \quad x_i \sim M_2$ Both $M_1$ and $M_2$ have prior $\sim Ga(7,3000)$ but my ...
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75 views

Using Bayes Factor to test Geometric vs Poisson distribution

I have a sample of 200 observations and need to test $H_0: X \sim Geom(p)$ vs. $H_1: X \sim Pois(\lambda)$. Prior distributions are $U[0, 1]$ and $U[0, 20]$. I need to construct a bayes test to ...
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449 views

Why is the calculation of Bayes Factors for regression coefficients based on model comparison while delta-R^2 tests are discouraged?

The vast majority of the statistical inference I do is on the basis of multiple regression models (not always OLS, not always single level). Usually the focus is not on the model, but on particular ...
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82 views

Bayes Factor for model and variable selection and type I & II error rate

I am trying to implement Bayes Factor for model and variable selection in Bayesian Linear Regression and finding out corresponding type I and type II error. I need your help regarding this. I will be ...
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176 views

Choosing a Model Selection Criterion [closed]

I am trying to decide which among for model selection criteria to use for a Bayesian nonparametric model. The candidates are: The L-criterion, as defined by Laud & Ibrahim (1995); Bayes factors; ...
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272 views

How to account for temporal autocorrelation when computing a Bayes factor between two linear regression models?

I have data of some physiological measure, represented as a vector of 185 measurements taken every 2 seconds. I can model this response in two different ways, and I wish to compare the fit of my two ...
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Bayes Factor for two exponential samples

I'm trying to solve myself such a problem: calculation of Bayes Factor for two groups from exponential distributions. $$x_1, x_2, \ldots, x_n\sim \exp(\lambda_1)$$ $$y_1, y_2, \ldots, y_m\sim \exp(\...
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171 views

Marginal likelihood (or Bayes factor) when true model *not* in the set

The marginal likelihood (or Bayes factor) method to perform model comparison, based on $\Pr(\text{data}|\text{model})$, assumes that the true model is the model set (closed world assumption). What ...
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637 views

Computing DIC and Bayes factor in R

How can I compute the DIC value and Bayesfactor value for a bayesian glm model? (for both models or even just 1 of the models) I have 2 models I would like to compare. 1. ...
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555 views

What is the difference between the posterior density, and the posterior “ordinate” in the context of Bayesian modelling

This is the first time I've come across the term posterior "ordinate" and I'm not sure what it means. I understand what the posterior density of some model parameters given some data refers to, but ...
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179 views

Replication study and Bayes factor

I ran an experiment and got a statistically significant result with an effect size of cohen's d=0.36 (N=20). I decided to run a replication study, this time with 60 participants, and got nothing (d=0....