Bayesian inference is a method of statistical inference in which some kind of evidence or observations are used to calculate the probability that a hypothesis may be true, or else to update its previously-calculated probability.
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Outline of benefits/costs of using Bayesian rather than Frequentist OLS and time-series?
I'm reading up on Bayesian techniques for Linear models and time series. While the texts are great at teaching the theory I would like to get a better handle on the pro's/con's of Bayesian analysis vs ...
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47 views
Regular conditional Bayesian experiment
In "Elements of Bayesian Statistics" (1990), Florens, Mouchart and Rolin describe two basic forms of reduction of a Bayesian experiment: Marginalization and Conditioning (Ch. 1). I don't understand ...
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19 views
Putting a prior on the concentration parameter in a Dirichlet process
Most of this is background, skip to the end if you already know enough about Dirichlet process mixtures. Suppose I am modeling some data as coming from a mixture of Dirichlet processes, i.e. let $F ...
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1answer
45 views
Help with Bayesian inference in OpenBugs
I have a task that involved Bayesian inference and could use some pointers and hints. I've already got some parts figured out but others remain blurred. Also, my OpenBUGS abilities are frankly limited ...
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45 views
Having a conjugate prior: Deep property or mathematical accident?
Some distributions have conjugate priors and some do not. Is this distinction just an accident? That is, you do the math, and it works out one way or the other, but it does not really tell you ...
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1answer
36 views
How to prove independentness of marginal/conditional (?) posterior distributions?
This is a question about exercises 4.2 and 4.3 of Jim Albert’s “Bayesian Comptutation With R” (p. 82). Note that while this might be homework, in my case it is not.
We are to prove that, given two ...
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1answer
83 views
Next steps after “Bayesian Reasoning and Machine Learning”
I'm currently going through "Bayesian Reasoning and Machine Learning" by David Barber and it is an extremely well written and engaging book for learning the fundamentals. So a question to someone who ...
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38 views
Causal models in pymc3
I'm trying to fit a causal model. Participants in a task are trained on the model then asked for their belief in all the joints over the variables (e.g., what are the chances of observing an item with ...
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30 views
Reductions of Bayesian experiments: regular conditional experiment
I'm reading Florens et al.'s 'Elements of Bayesian Statistics', currently working through chapter 1, 'Reduction of Bayesian Experiments'. I find most of it clear, except the definition of regular ...
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49 views
How does predictive model for the Eurovision Song Contest work?
I've encountered interesting prediction of Eurovision Song Contest http://mewo2.com/nerdery/2013/05/12/eurovision-2013-first-predictions/ it based on some kind of Bayesian model I assume but I don't ...
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25 views
Lognormal and Logit models in JAGS
I'm trying to run this two-part model in JAGS. I have two components, one logit and one lognormal regressions in there:
...
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63 views
What is the difference between a frequentist approach with meta-analysis and a Bayesian approach?
Say I am performing an analysis looking at a particular health measure. I am interested in the difference in that measure between patients and controls and wether or not the difference is different ...
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1answer
55 views
How to test if two samples are distributed from the same Gaussian process
Given a sequence $\mathbf{x} = (x_1,x_2,\dots,x_n)$ which is sampled from some Gaussian process $GP(\mu_1,\Sigma_1)$ and a "target" sequence $\mathbf{y} = (y_1,y_2,\dots,y_n)$ sampled from another ...
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16 views
Evidential reasoning in Gaussian Bayesian Networks
I am working on Gaussian Bayesian Networks (GBN) i.e. the Bayesian Networks where all the random variables are continuous in nature. I am seriously trapped in the problem of evidential reasoning in ...
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41 views
Bayesian inference and degrees of freedom
While learning frequentist linear regressions, one thing the professors always talked about was about the number of degrees of freedom, I never saw this expression in a bayesian book though. Perhaps ...
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0answers
48 views
Kolmogorov's paper defining Bayesian sufficiency
I'm looking for a translation to either English, French or German of Kolmogorov's Russian paper
Kolmogorov, A. (1942). Sur l’estimation statistique des paramètres de la loi de Gauss. Bull. Acad. Sci. ...
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1answer
56 views
Given known bivariate normal means and variances, update correlation estimate, $P(\rho)$, with new data?
I'm dealing with two correlated random variables which are modeled via a bivariate normal distribution. I have values for the means ($\mu_x, \mu_y$) and individual variances ($\sigma_x, \sigma_y$) of ...
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1answer
182 views
Should I expect it to be a chicken or a penguin?
An alien is trying to classify a group of only chickens and penguins into, well, chickens and penguins by analyzing 3 independent boolean features A, B, C.
If the animal (in reality) is a chicken, A ...
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1answer
59 views
Are the posteriors “different”? How does one discuss the result?
First, I realize this may be a basic question. However, when I search the web for references on this issue, I run into the problem of wondering if the description I'm reading is applicable to the ...
3
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1answer
63 views
Neg Binomial and the Jeffreys' Prior
I'm trying to obtain the Jeffreys' prior for a negative binomial distribution. I can't see where I go wrong, so if someone could help point that out that would be appreciated.
Okay, so the situation ...
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1answer
51 views
Integrating unknown parameter out of the likelihood function
Suppose we wish to model two variables x and y, as having an underlying linear relation with added errors. That is, with data $(x,y)_i: i = 1,...,n$, we model
$\begin{pmatrix} x_i \\ y_i \end{pmatrix} ...
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59 views
Bayesian analysis with histogram prior. Why draw simulations from the posterior?
This is a beginner’s question on an exercise in Jim Albert’s “Bayesian Computation with R”. Note that while this might be homework, in my case it is not, as I am learning Bayesian methods in R because ...
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26 views
Calculating HPD for marginal effects of interactions of lmer models
I am fitting a model with lmer, using the following code:
...
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21 views
How to calculate Hightest Posterior Density (HPD) of coeficients in a simple regression (lm) in R?
I am trying to calculate HPD for the coeficients of regression models fitted with lm or lmrob in R, pretty much in the same way that can be accomplished by the association of mcmcsamp and HPDinterval ...
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50 views
Derive Likehood of the data
Can somebody help me with this problem:
Suppose we wish to model two variables x and y, as having an underlying linear relation with added errors. That is, with data $(x,y)_i: i = 1,...,n$, we model
...
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1answer
77 views
Laplace approximation of the likelihood Bayesian
I need help with the following question:
Consider $m$ observations $(y_1; n_1); ... ; (y_m; n_m)$, where $y_i \sim Bin(n_i; θ_i)$ are binomial variables.
Assume that $θ_i \sim w_1Beta(α_1; β_1) + ...
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1answer
77 views
Introductory textbook into nonparametric Bayesian models?
I'd like to wrap my head around this topic but learning from white-papers and tutorials is hard because there are many gaps which are usually filled in textbooks.
If it is important I have ...
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25 views
Time spatial data analysis
Can anyone recommend some reading materials (books or papers) on the analysis
of time spatial data. I am particular interested in the bayesian model building
for this type of data. Thanks very much. ...
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33 views
Predicting with Relevance Vector Machines
I am trying out this Matlab toolbox for Relevance Vector Machines by Tipping: http://www.miketipping.com/sparsebayes.htm
This has an implementation of Relevance Vector Machines, and generates pretty ...
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23 views
How to quantify a sequential hypothesis testing problem to conclude a certain experiment is better over the other, in a bayesian framework?
I am a newbie.
I have the following setup of a hypothetical experiment.
I have N places in a big building (think a huge palace) where I have kept 'N' different types of bird-food for birds.
Birds ...
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1answer
83 views
Simple cloud computing to run R + JAGS simulations
I want to simulate the frequentist properties of a Bayesian model. So, for example, I might want to fit a Bayesian model 1,000 times to 50 different configurations each of which takes about 10 seconds ...
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43 views
Bayesian inference over an unknown variance
I am observing a random variable $X \in \mathbb{R}$ which can be assumed to be normally distributed with mean $\mu$ and variance $\sigma^2$. I am interested in fitting a posterior distribution over ...
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27 views
Learning parameters of non-parametric Bayesian models
I have a sample of Chinese restaurant process which I want to model as Pitman–Yor process. How do I determine parameters of Pitman-Yor model from given sample?
For Dirichlet process I would just use ...
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1answer
33 views
Need help calculating a Bayes estimation for a Poisson
My study group and I are stuck on this Bayes' estimator problem.
The question is:
Let X~Pois($\lambda$)
Find the Bayes estimator for $\lambda$ with respect to:
(i) The prior distribution: ...
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2answers
31 views
Naive Bayes feature probabilities (Do I double count words?)
I'm prototyping my own Naive Bayes bag o' words model, and I had a question about calculating the feature probabilities.
Let's say I've got two classes, I'll just use spam and not-spam since that's ...
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1answer
42 views
How to do a Bayesian survival analysis and determine which variables are useful?
I can measure two variables on each patient in a survival study (I have the measurements and the survival times; some patients outlive the study and are therefore censored). I know that it is possible ...
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13 views
Java, Weka: How to predict numeric attribute? [migrated]
I was trying to use NaiveBayesUpdateable classifier from Weka. My data contains both nominal and numeric attributes:
...
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1answer
63 views
Under what conditions do Bayesian and frequentist point estimators coincide?
With a flat prior, the ML (frequentist -- maximum likelihood) and the MAP (Bayesian -- maximum a posteriori) estimators coincide.
More generally, however, I'm talking about point estimators derived ...
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2answers
80 views
Why is the Likelihood function NOT a case of the inverse fallacy?
This may be a trivial question, but as a research psychologist I do not have a robust statistics background to answer it.
It appears to me that the likelihood function--$L(\theta | \text{data}) = ...
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4answers
387 views
Bayesian uninformative priors vs. frequentist null hypotheses: what's the relationship?
I came across this image in a blog post here.
I was disappointed that reading the statement did not illicit the same facial expression for me as it did for this guy.
So, what is meant by the ...
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1answer
26 views
Updating Time-To-Event distribution given quantity of time elapsed with no event occurence
I'm trying to find a method to update a time to event distribution given the passage of time without the event occurring.
For example, if I am waiting for a bus and the time to arrival can be ...
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1answer
56 views
Degrees of freedom for Gaussian Process
I am reading this paper on Generalised Wishart Process (GWP). It is about modelling covariance matrix of D - dimensional gaussian processes (GP) as GWP. I fail to understand interpretation of "degrees ...
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0answers
35 views
Kalman- Bucy filter: prior mean change
I have a question on Kalman-Bucy filter:
the prior distribution is $g \sim N(0,σ_g^2 )$, signal is $ds=(μ+g_t )dt+σdZ_t$, posterior distribution becomes $g_t \sim N((\hat{g_t},\hatσ_t^2)$. ...
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2answers
73 views
Do Bayes factors require multiple comparison correction?
As the title: Do Bayes factors require mutliple comparion correction?
For more context, I am calculating very many likelihood ratio tests and I am thinking about how to handle multiple comparison ...
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1answer
54 views
Bayesian hypothesis testing of two parameters
This question is about hypothesis testing in the Bayesian framework which I am new to.
Suppose I have two independent Poisson models with parameters $\lambda_1$ and $\lambda_2$ such that $X \sim ...
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2answers
88 views
Using the Bayes Theorem?
A certain town has two taxi companies, the Green Taxi Co (cars coloured green) and the Blue
Taxi Co (cars coloured blue). 10% of taxis are the Green and 90% are the Blue. There was an
accident ...
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2answers
48 views
How can I use Bayes rule for this question given additional data
I am required to use the Naive Bayes classifier to classify example 8, to see whether it is poisonous or not.
I gained the following results:
p(x|Poisonous=Y) = 0.0267857 and
p(x|Poisonous=N) = ...
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1answer
51 views
Normalization Factor Wrong? (Bug?)
I'm new to PyMC and Bayesian stuff in general, so I started off with what I thought was a very simple toy problem. I generated some normally-distributed noise with a given mean and standard ...
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3answers
79 views
Bayesian posterior: mean vs highest probability
I have calculated a posterior distribution where the highest probability (peak of posterior-curve) is at 99%. But the mean probability is lower, at about 98%. This is of course because "the curve" ...
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1answer
54 views
Find out the conditional probability
Consider I have the following probabilities:
$$P(A|B) = 0.86 $$
$$ P(A|B^C) = 0.35 $$
$$ P(B) = 0.80 $$
$$ P(A) = 0.758$$
Is there necessary information given to calculate $P(B^C|A^C)$? If so ...
