In Bayesian statistics a prior distribution formalizes information or knowledge (often subjective), available before a sample is seen, in the form of a probability distribution. A distribution with large spread is used when little is known about the parameter(s), while a more narrow prior ...

learn more… | top users | synonyms

1
vote
0answers
42 views

Relationship between low identifiability and prior weight in Bayesian model

I'm trying to get intuition into the relationship between low identifiability and prior weight in Bayesian model. Is it true to say that in lowly identifiable model + data the prior will have a higher ...
0
votes
0answers
6 views

Alpha Parameter Specification Dirichlet Prior

I have a straightforward Dirichlet-Multinomial model with code that is running in RJAGS. The data are a collection of 200 2 x 2 contingency tables. The multinomial counts are those of a 2 x 2 ...
0
votes
0answers
40 views

How to exploit relationships between independent variables?

Data: Each instance (representing a document) is a bag-of-entities (like BOW, except they're Wikipedia entities instead of words), so each feature is a binary or tfidf-like score based upon the ...
0
votes
0answers
22 views

Meaning of the prior and loss parameters in rpart in R

Could someone please explain to me what specifying priors and/or loss parameters in R's rpart actually do? I found R's documentation completely unhelpful. For example, let's suppose I have a highly ...
1
vote
1answer
82 views

Interpreting prior and posterior

I am bit puzzled on how we can interpret the posterior. Assume a coin which is 0.1 probable to be unfair. So our prior probability on the coin being unfair is 0.1, and being fair is 0.9. Also by ...
1
vote
0answers
28 views

Stochastic Block Model Priors

In the generic stochastic block model (binary edge data, no degree correction, etc.), if an uninformed prior is used for the Bernoulli coefficients i.e. Beta with $(a,b) = (1,1)$, will the model ...
-2
votes
2answers
1k views

Priors in Bayesian MCMC

I am trying to understand how the choice of priors affects a Bayesian model estimated using MCMC. At a basic level I understand that the product of the prior and the likelihood are proportional to the ...
0
votes
0answers
16 views

Jeffrey's Prior for normal distribution with mean = 0

How would I go about calculating Jeffrey's Prior for a normal distribution with mean = 0, So far I get: But then don't know where to go next. Any help much appreciated
7
votes
2answers
188 views

How does one use Bayes theorem with a continuous prior?

If my prior is modelled as a continuous probability distribution, say, a beta distribution skewed to reflect my bias towards certain models, how can I calculate the posterior probability? The ...
0
votes
0answers
21 views

Likelihood of hypothesis in live data

Bayes rule is $P(H|E)=\frac{P(H)P(E|H)}{P(E)}$ I have a prior distribution from categorical data prior={'a':0.2,'b':0.6,'c':0.1,'d':0.1} Which forms my ...
2
votes
2answers
42 views

Marginal likelihood vs. prior predictive probability

In the Bayesian framework, to me, it seems that the marginal likelihood and the prior predictive distribution/probability are equal. Is that the case? Or maybe this just holds for single data points? ...
0
votes
1answer
57 views

Why do we use Gamma($\epsilon, \epsilon$) as non-informative prior for precision and Normal prior for betas in Linear Regression

Suppose my regression model is $$Y_i = \beta_0 + \beta_1X_{i1} + \epsilon_i $$ In most books I am seeing that the prior used for precision $\tau = 1/\sigma^2 $ is $Gamma(\epsilon, \epsilon)$. However ...
0
votes
2answers
38 views

Return value of uniform distributions for MCMC simulations

I am confused about how what value should be returned from a uniform distribution when using MCMC simulations. The proper normal distribution is define as $$ p(\theta) = \left\{ \begin{array}{cc} ...
1
vote
1answer
30 views

Estimating von Mises Parameters for Angular Data

I want to model some angular data. Any input on how to incorporate the von Mises distribution and suggestions on appropriate priors in RJAGS for von Mises mean and concentration would be greatly ...
1
vote
2answers
36 views

Augmenting Kalman filter with parameter — what does the initial value mean?

It is a fairly standard trick to augment a Kalman Filter with unknown parameters and to propagate them forth with zero error to estimate them. I was wondering if anyone could tell me what the ...
3
votes
0answers
63 views

How to use information about likelihood of classes in a classifier?

General question: How can information about the likelihood of classes be used to improve a classifier? Suppose that the probability of each class is known quite precisely (from a very large sample), ...
4
votes
1answer
147 views

Is a spike-and-slab prior a proper prior?

Is a spike and slab prior a proper prior? (I am talking about a (product of Bernoulli) spike and Normal slab) If not, does it still lead to a proper posterior?
0
votes
0answers
20 views

Posterior predicted distribution, practical question

I'm new here to this place but I have already learned so much here. Yet I still remain with a large question involving my thesis in econometrics and medical scoence. For a starter, I have read ...
0
votes
1answer
31 views

Why using vague (or noninformative) priors? [duplicate]

In my Bayesian class, we are always required to specify vague (or noninformative) priors for bayesian modeling. I am quite confused about that. If I understand correctly, the main advantage of ...
0
votes
0answers
29 views

Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
2
votes
2answers
100 views

Can my Bayesian prior reflect what the data should say rather than what it could say?

Can my Bayesian prior reflect what the data should say rather than what it could say? For example, assume I collect data where $Y_i$ is whether or not student $i$ passed the test and $X_i$ is whether ...
1
vote
1answer
19 views

Prior for gamma distribution in “mean form”

I need to specify priors for the parameters of a gamma distribution. Normally the gamma distribution is parametrized in either the "rate-form'': ...
2
votes
0answers
20 views

Do mildly informative prior distributions tend to mitigate false positives (i.e. Type I error rates)?

I am curious if others have sources that speak to the matter that providing informative and/or mildly informative prior distributions on a parameter tend to mitigate false alarm rates? I know from the ...
2
votes
0answers
31 views

Incorporating population priors into MLE fits with few/limited samples

I am fitting Beta distributions to data resulting from each of many experiments using maximum likelihood. My goal is for each experiment, given iid data $y_{1:k}$, fit a Beta distribution, and then ...
0
votes
1answer
111 views

How to select hyperprior distribution for Beta distribution parameter?

I have a parameter $\theta$ whose value should lie between $(0,1)$. Therefore, I am assuming the prior distribution of $\theta$ to be a beta distribution with hyper-priors $\alpha$ and $\beta$ ie. ...
2
votes
0answers
22 views

prior for integer-valued random variable taking values 1 or greater

In my model I have an integer-valued random variable which should only take values one or greater. I would like to specify an appropriate prior for this which has most of the mass say around 1 to 5 ...
3
votes
1answer
43 views

Is it possible to define the mean of a varying distribution?

Suppose $(p_1,\ldots,p_k)$ be the vector of multinomial parameters and $$(p_1,\ldots,p_k)\sim \mbox{Dirichlet}(\alpha_1,\ldots,\alpha_k).$$ Let's define a function $f(p_1,\ldots,p_k) \in \mathbb{R}$. ...
1
vote
1answer
47 views

How is data generated in the Bayesian framework and what is the nature on the parameter that generates the data?

I was trying to re-learn Bayesian statistics (every time I thought I finally got it, something else pops out that I didn't consider earlier....) but it wasn't clear (to me) what the data generation ...
0
votes
0answers
24 views

Why does Empirical Bayes work in my simple case?

I have a problem where I am trying to classify data into two groups using a single parameter. The distribution of this parameter is Gaussian for two groups, so what I'm dealing with is two overlapping ...
1
vote
0answers
13 views

Creating a model for a webshop

I'm going to create a Multi-armed bandit algorithm to handle recommendations for a large scale webshop. I'm going to use Thompson sampling (http://en.wikipedia.org/wiki/Thompson_sampling) and would ...
3
votes
0answers
57 views

Prior for the coefficients of a linear regression model

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
2
votes
1answer
27 views

Iteratively solving for prior probabilites.

I'm using Bayes theorem to classify data into two groups, where the conditional probability is known but the prior is not. So I assume that the ratio of prior probabilities is 1 and calculate the ...
0
votes
0answers
13 views

How can i get prior information using my few data set from the whole data? [duplicate]

I have a data set (x1...x500, y1....y500 ) I want to know about bayesian regression I want to know the prior information , few data set(400) from the whole data (500) using MCMCregress( packages in ...
3
votes
1answer
20 views

Is this notation for the improper uniform prior correct?

Can I write: $\mu \sim U(0,\infty)$ ? Or do I have to use the notation $p(\mu) \propto 1$? Thank you.
1
vote
0answers
23 views

Can improper priors be implemented in some way?

I'm new to bayesian inference. I've just discovered that improper priors can't be specified in WinBUGS/OpenBUGS. I was wondering if this is common or not in bayesian inference. Are there same cases in ...
0
votes
1answer
24 views

Definition of weakly informative prior [duplicate]

According to Gelman, a weakly informative prior is defined in the following way: We characterize a prior distribution as weakly informative if it is proper but is set up so that the information ...
1
vote
0answers
42 views

Doubt about conditional conjugate priors

I've just read the definition of conditional conjugate prior in this discussion but I have still some doubts. According to the definition given, it seems that the prior distribution of $\theta$, ...
1
vote
0answers
84 views

Bayes Linear regression- logarithmic transformation of prior distribution of the variance

I have a Bayesian version of a linear regression with 3 covariates. The model is given by \begin{align*} Y\sim N(\mu,\tau)\end{align*} \begin{align*} \mu=\alpha + \sum\beta_{i}x_{i}\end{align*} where ...
0
votes
0answers
36 views

Explanation that the prior predictive (marginal) distribution follows from prior and sampling distributions

While I have a vague intuition that this makes sense, I am interested in the formal demonstration that the prior predictive distribution in Bayesian inference is equal to the integral over $\theta$ of ...
0
votes
1answer
90 views

How to elicit prior distribution parameters?

A random sample of 300 women aged 60–69 years whose immediate families have had histories of cancer are to be screened for breast cancer. Let $y_i$ be 1 if woman i has a positive test, and 0 if not, ...
0
votes
0answers
26 views

Incorporating Risk Aversion in Bayesian Expected Loss functions

In Berger's Statistical Decision Theory and Bayesian Analysis, he presents the following expected loss function for decision theory: $\rho(\pi^*,a)=\int_\Theta L(\theta,a)d\pi^*(\theta)$ Where ...
0
votes
1answer
77 views

define prior probabilities in naive bayes with unbalanced classes and asymetric cost

I'm trying to apply Naive bayes to the following supervised problem: It's a binary classification problem The classes are unbalanced. The target class represents the 0.004266432 of the total and the ...
3
votes
1answer
47 views

What are examples of “flat priors”?

For example, for p as the parameter to a binomial or bernoulli, or a Poisson, what would a flat prior p be? What does it mean to be "flat" - does this refer to diffuse?
5
votes
1answer
92 views

Truncated Von Mises-Fisher distribution

I am putting a von Mises-Fisher prior on my data. The data does lie on a unit sphere, but the only problem is that my data is always positive. So I feel like I am wasting my prior on unnecessary ...
1
vote
0answers
33 views

p-values, prior probabilities

I've got a set of N normal independent normal distributions, each representing a signal. I also got a new data sample, a vector $v$ of size Nx1. Now let's say I compute the p-value using the ...
1
vote
1answer
36 views

Constructing gamma prior from Poisson

So if we have a Poisson distribution with a rate lambda we know that the prior is a gamma with alpha,beta. But suppose we didn't know that the prior was a gamma. How would we do the derivation please? ...
0
votes
0answers
15 views

The validity of using truncated PDFs as prior distributions?

I am trying to implement an ABC (Approximate Bayesian Computation) rejection-sampling algorithm in R. I am currently working with a six-parameter model and for each of the parameters I have specified ...
0
votes
0answers
80 views

Interpretation of priors in example

Suppose you have 3 variances $W_{1},W_{2},W_{3}$ that can be expressed as $W_{j}=q_{j}V$ with $j = 1,2,3$. According to one model, $W_{3}$ should be pronounced and $W_{1}$, $W_{2}$ should be small to ...
4
votes
1answer
130 views

Bootstrapping the data to set up a prior

I am using a Gaussian model with a conjugate Normal-Inverse-Wishart (NIW) prior, as described here. The advantage of this approach is that the marginal likelihood $p(y)$, which is what I am interested ...
0
votes
1answer
239 views

Undefined real result error at WinBUGS

I am currently working on my thesis and interested in estimating a multilevel differential item functioning model and I using at WinBUGS. Until I had done model check-up, there are no errors. However, ...