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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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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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13 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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1answer
38 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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46 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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23 views

MCMC dont converge in two level hierarchical model

I'm doing simulation in following framework. I have some responses $\theta_{ik}$ and since K is very large, I try to have a bayesian factor model to reduce the dimension. Following is a factor part, ...
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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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Determining the total amount of evidence for covariates across multiple outcomes

I have a study comparing three different measures of disease severity ($M1$, $M2$, and $M3$) in a disease where there is no gold standard to measure severity. I have six outcomes that are ...
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1answer
110 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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21 views

Is this Bayes factor correct

I have 2 models, $M_1$, $M_2$. $M_1$ contains 3 reactions and $M_2$ contains 6 (two of each reaction in $M_1$). I assumed the priors for each rate constant to be independent and gamma and to be the ...
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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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118 views

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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27 views

Calculation of Bayes Factor for multinomial distributions

I'm trying to follow along with this document: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.11.293&rep=rep1&type=pdf As is also discussed as an answer here: https://stats....
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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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Using Bayes Factor to test geometric vs poissong 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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204 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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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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1answer
85 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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1answer
147 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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38 views

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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120 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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421 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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1answer
287 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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1answer
157 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....
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484 views

Reporting Bayes factors

I have calculated a Bayes Factor BF10 for the probability of the data under H1 vs. H0. I get very large numbers (the data are very clear, statistics are barely necessary here), in the order of 10^30. ...
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1answer
194 views

Bayes Factor and likelihood for two sample from different distributions?

I'd like to calculate Bayes Factor for two-sample t-test $H_0: \mu_1=\mu_2$ (model $M_0$) against $H_1: \mu_1\not=\mu_2$ (model $M_1$) My data are: $x_1,x_2,\ldots, x_{n_1}\sim N(\mu_1, \sigma)$ ...
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1answer
365 views

Discrepancy in the results of LMER and BayesFactor (R)

I have a within-subject dataset with 3 two-level factors and 1 numeric predictor. I was using LMER with a random-intercept model (a full random-effect model yield the same results though throws ...
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253 views

Different Bayes Factor values for correlation with the same JZS approach

Trying to get the Bayes Factor for a correlation between two variables in my data, I tried three different functions. All implement the Jeffreys–Zellner–Siow (JZS) prior, but I get quite different ...
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2answers
1k views

Mixed bayesian ANOVA using BayesFactor package in R

According to a recent paper (open pdf here), one can specify both within- and between-subjects effects in a Bayes factor ANOVA. In the example they give (p. 28), this is specified in the following way:...
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161 views

Directional vs Non-Directional Alternative Hypothesis in Bayesian Model Comparison?

I have recently completed a study where I hypothesised a significant difference between two groups. I hypothesised that Group B would be report a significantly lower score on the outcome variable on ...
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435 views

Bayesian Model Comparison - Neutral Prior Information

Let's say I estimate two models, $M_{0}$ and $M_{1}$. The posterior odds ratio for for model $M_{0}$ against $M_{1}$ given the data, $y$, is, $\frac{Pr\left(M_{0}\mid y\right)}{Pr\left(M_{1}\mid y\...
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80 views

Bayes factor and hypothesis test in Bayesian inference

Let $$\pi_0=P(\theta\in\Theta_0)=\int_{\Theta_0}\pi(\theta)d\theta$$ $$\pi_1=P(\theta\in\Theta_1)=\int_{\Theta_1}\pi(\theta)d\theta$$ $$a_0=P(\theta\in \Theta_0|x)$$ $$a_1=P(\theta\in \Theta_1|x)$$ ...
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1answer
109 views

Bayesian model comparison in high school

I teach physics to high-school students, and I would like my students to conduct a rudimentary Bayesian model comparison for data from their experiments. I figured out a way for them to do so (see ...
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297 views

Bayes Factor approximation

A brute force method to approximate the Bayes Factor (the ratio of the denominators (normalizing constants) in the Bayes formula) is to do the following for the two models of interest: repeat ...
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1answer
317 views

Can I make a decision using a Bayes factor?

Bayes factors denote how well a certain model is supported. Say that I am running a controlled experiment and I have two models: the null model and the alternative model. If I have a high Bayes ...
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82 views

Comparing the rates of Poisson distribution using Bayesian inference

In the 'Theory of Probability' book by Sir Harold Jeffreys, (5.15), the form of the Bayes Factors that he derives for the comparison of Poisson rates is the same as that of Binomial rates. But I did ...
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217 views

Bayes factor for effect size

I need to construct Bayes Factor for testing: $$ H_0: \quad 0 = \mu_t - \mu_c $$ $$ H_1: \quad 0 \neq \mu_t - \mu_c $$ and my prior knowledge is modeled by distribution of effect size: $ \delta = \...
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1answer
164 views

Bayes factor (B) vs p-values: sensitive (H0/H1) vs insensitive data

The question of a beginner in Bayesian stats. As far as I understand, it is claimed (e.g. Dienes 2014) that B-based inference allows us to either confidently reject/accept the null, OR declare the ...
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1answer
277 views

Bayes Factors for more than 2 hypotheses

Naïve question: I would like to use Bayesian framework for model selection. I have more than 10 models with the same number of parameters (just different assumptions on underlying parameters of the ...
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87 views

Anova with ordered alternative, which hypothesis to test?

I am interesting into the problem of testing a specific hypothesis of the form $H_1:\{ \mu_1<\ldots <\mu_N\}$. In the literature I found, such a hypothesis is compared to whether $H_2:\{\mu_1=\...
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1answer
138 views

Bayes factor from posterior odds

I tried to answer my own question Comparing two Bayesian models under disjoint prior supports using MCMC. Here is my intent. I am not confident in what I wrote so prefer to post it as a question : Is ...
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71 views

Are Bayes factors practically applicable?

According to Bishop's Pattern Recognition and Machine Learning on page 164, on average the Bayes factor will always favour the correct model. Given this, how can we use the Bayes factor in ...
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2answers
91 views

Comparing two Bayesian models under disjoint prior supports using MCMC

I have a Bayesian model involving three parameters $\theta_1$,$\theta_2$ and $\theta_3$. Experts think that $\theta_1 > \theta_2 > \theta_3$. So I would like to test the submodel $M_0$ ...
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1answer
640 views

Bayes factor using BayesFactor package in R

I only recently started using the BayesFactor package in R. I was trying to extract the Bayes factor from the S4 object to add the figure to a table and saw that ...
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2answers
1k views

Calculating Bayes Factor from a correlation coefficient

I'm wondering whether anyone knows whether it is possible to directly calculate a Bayes Factor (comparing null model of zero correlation to non-zero correlation) given just a correlation coefficient ...
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Bayesian association testing and simulation

I read some Bayesian references recently and came up with some basic or naive questions about Bayesian inference. My research question is to test the association between predictors and outcome, and it ...
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1answer
189 views

updating a Bayes factor

A Bayes factor is defined in Bayesian testing of hypothesis and Bayesian model selection by the ratio of two marginal likelihoods: given an iid sample $(x_1,\ldots,x_n)$ and respective sampling ...
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1answer
247 views

Can you calculate Bayes Factors for a Bayesian Random-effects meta-analysis?

I have the following problem and I wanted to see if somebody with more experience can help me. I'm doing a Bayesian random-effects meta-analysis in rJAGS with models like these: ...
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1answer
77 views

Familywise error with Bayes Factor

Recently a paper indicated a method to calculate Bayes Factor for correlations (http://link.springer.com/article/10.3758/s13423-012-0295-x/fulltext.html). This method doesn't use significance testing ...
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1answer
103 views

EM algorithm special case

I'm considering a collection of Bayes Factors, $\mbox{BF}(j)$, $j=1, ..., J$, so that the overall evidence against $H_0$ is represented by the overall Bayes Factor $$\frac{P(x|H_0 \mbox{ false})}{P(x ...