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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Bayesian parameter estimation of a Poisson process with change/no-change observations at irregular intervals
Consider a Poisson process with unknown parameter $\lambda$.
We perform a sequence of $n$ observations at intervals $\overline{t}=t_1,\,t_2,\,\dots,\,t_n$. Each observation is a binary variable $x_i$ ...
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1answer
106 views
Bernoulli variable on pymc
Im not fully sure that this is the right place to ask, but I have a problem with pymc that I'm not able to grasp.
I'm trying to simulate a simple counting under two different scenario: Under the ...
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65 views
Can someone point me to a good example of using bayesian models for making marketing decisions?
I am tasked to build a bayesian model to support decision making for paid search marketing. I've researched online and found several scholarly articles on using Hierarchical Bayesian model or MCMC in ...
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1answer
39 views
Multiplying a matrix by a scalar which has a prior distribution in OpenBUGS
So I am having a problem specifying my model in OpenBUGS. A set of vectors in a linear regression model is given a multivariate normal prior with a constant mean vector and a constant precision matrix ...
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1answer
63 views
Is there any reason to prefer a bayesian model with few variables?
I have two alternative hierachical bayesian models that were designed to the describe the same process (from a high-level point-of-view). Both model provides
comparable (but not identical) inferences ...
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2answers
164 views
Estimating the covariance posterior distribution of a multivariate gaussian
I need to "learn" the distribution of a bivariate gaussian with few samples, but a good hypothesis on the prior distribution, so I would like to use the bayesian approach.
I defined my prior:
$$ ...
7
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1answer
161 views
From standard HMM to Bayesian HMM
I'm trying to understand what the difference between a standard HMM and a Bayesian HMM is. Wikipedia just briefly mentions how the model looks like but I need a more detailed tutorial. Does someone ...
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51 views
How to use an initial posterior for recursive / sequential updating in WinBUGS
I am using WinBUGS to estimate / update the parameters of a model. The model is:
$$
\begin{aligned}
D(T,B,a)&= B*(a_0+a_1T+a_2T^2+a_3T^3)+error(B,T,a) \\
error &= \mathcal N(0, ...
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147 views
Calculating conditional probabilities given a bivariate gaussian
This is a continuation of my previous question.
I have two classes, $C_1$ and $C_2$.
$C_1$ is a bivariate Gaussian with mean $\mu = (0,0)$ and covariance $\Sigma = I$
$C_2$ is a bivariate ...
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2answers
70 views
Bayesian Inference Notation Confusion
In Bayesian Inference the following notation is quite common:
$P(H|D) = \frac{P(D|H)P(H)}{P(D)}$
where $D$ is data and $H$ is hypothesis. Moreover $P(D)$ is represented as total probability.
$P(D) ...
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1answer
115 views
What is the name of the estimator that takes the mean of likelihood?
Let $X,Y$ be input and output (observed) continuous variables in $\mathbb{R}$. Let $\{y_1,...,y_n\}$ be the set of $n$ observations. Is there a name for the estimator $\hat x = \int_{x \in X} x ...
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163 views
Bayesian estimation of Dirichlet distribution parameters
I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that:
Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
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103 views
How to derive the conditional posterior density in hierarchical bayesian models?
I was reading on Gelman's Bayesian Data Analysis - Chapter 5 - Hierarchical model
Suppose:
data : $y_j$ s
parameter: $\theta$
hyperparameter: $\phi$
On page 126, he mentions the analytical ...
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0answers
99 views
How to set up a posterior predictive test quantities (Bayesian context) to check for independent Poisson distributions?
Suppose we are given data $y_j \sim \text{Poi}(\lambda)$ and assume $y_j$ are iid.
We can assume the prior distribution for $\theta$ follows $\text{Gamma}(\alpha, \beta)$,
The posterior ...
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1answer
153 views
Bayesian approach and least-squares approach to multivariate regression with structural design
Assume for example a trivariate Gaussian model:
$$
{\boldsymbol Y}_1, \ldots, {\boldsymbol Y}_n \sim_{\text{iid}} {\cal N}_3\left({\boldsymbol \mu}, \Sigma\right) \quad (*)
$$
with ${\boldsymbol \mu} ...
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230 views
Exponential Distribution - Rate - Bayesian Prior?
I have gone through WinBugs documentation (for example, http://www.mrc-bsu.cam.ac.uk/bugs/thebugsbook/examples/html/Chapter-11-Specialised/Example-11_7_2-leukaemia.html). And also through this book ...
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39 views
How would you approach this problem on the Bayes theorem [closed]
I've been reading a book on Statistics and I could COMPLETELY understand all of its text. It basically explained the bayes theorem and what priors were, what posteriors were etc. But then in the ...
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62 views
Help with determining the optimal AR-model order when using BIC?
I'm trying to build an AR-model for my temperature data and I'm using the Bayesian information criterion to determine the model order, but it seems my BIC-values keep decreasing the more I add ...
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73 views
How do you perform a bayesian ordered logistic regression in R?
Trying to perform a Bayesian ordered logistic regression in R where age is my outcome variable. I have installed the ARM package but I am unsure how to go about generating my model in R. I also need ...
2
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1answer
189 views
Logistic Regression - Bayesian Approach - Assessing Classification Precision
I have recently begun to read about bayesian statistics and I am playing around with the R2WinBUGS package. I'm trying to fit a logistic regression to the spam data (that can be found on the webpage ...
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How do BART (Bayesian Additive Regression Trees) work?
I am confused about two concepts about the BART model:
How is each tree created?
i.e. is a random sample taken from the training data and the tree built from that sample (as in random forests), or ...
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2answers
86 views
what distributions could help describe my uncertainty about a probabilistic forecast?
I'm dealing with binary events and I've got people guestimating the chance that they occur. I'd like to translate someone else's guestimate into a probability distribution representing my belief ...
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57 views
Credibility Intervals
I'm trying to understand when credibility intervals are useful?
Are there examples of real world situations where credibility intervals are the better thing to use compared to confidence intervals? ...
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1answer
72 views
Marginal posterior and prior are similar (and flat!)
I designed a Bayesian model and sampled the posterior using a MCMC algorithm.
My problem is that the posterior marginal distribution of a given latent intermediate variable appears to be uniform just ...
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2answers
151 views
Recommendations for learning probability and Bayesian statistics? [duplicate]
I have been very interested lately in learning Bayesian Statistics, but I have only a little bit of background in the frequentist statistics, only one term at University.
Some of the books that I ...
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1answer
90 views
Thinning chains in BUGS/JAGS
Hi I have a quick question about the details of running a model in JAGS and BUGS.
Say I run a model with n.burnin=5000, n.iter=5000 and thin=2. Does this mean that the program will
run 5,000 ...
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88 views
How do I identify this trap error in WinBUGS?
I am currently working on my thesis and interested in estimating a Weibull conditional Hazard Frailty Model for recurrent event data using WinBUGS. I wrote the model but when am trying to use it with ...
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1answer
54 views
Why is the posterior proportional to $P(X=x|C=c_i)P(C=c_i)$?
When we are trying to maximum a posterior, we apply Bayesian rule to convert them into posterior probabilities!
$P(C=c_i|X=x) = P(X=x|C=c_i)P(C=c_i) / P(X=x)$
proportional to ...
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2answers
81 views
What is the name of (and alternatives to) this Bayesian point-estimate?
Assume that we have a Markovian environment that generates at every time step an event $A$ with probability $p^*$ and an event $B$ otherwise. Now suppose you are a Bayesian agent that wants to learn ...
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112 views
How to calculate the probability of absence for a certain category of artefacts from a sample, given prior knowledge about its abundance?
In archaeology, artefacts are commonly classified in categories according to certain criteria (those may include manufacturing technique, decoration, function, chronology, etc).
I am trying to ...
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1answer
139 views
Reasonable assumption in Bayesian linear regression
I'm learning bayesian linear regression from the book Bayesian Data Analysis. Here is my questions.
Notation (follow the book): $X$ stands for explanatory variables, with parameter $\psi$; $\bf{y}$ ...
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58 views
Conjugate prior for a Gaussian model with shifted variance
Consider a set of observations $ \{ y_i \}$ and assume a Gaussian model for these data: $y_i \sim \mathcal{N}(\mu, \sigma^2)$. Suppose the mean parameter $\mu$ is known, but the variance parameter ...
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1answer
73 views
Predicting continuous variables from text features
I want to predict a continuous variable from text features. Lets say I have some student essays and I want to predict their quality, as measured by a human grader, using text features (mostly words ...
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2answers
56 views
Regarding the convergence assessment on Markov chain monte carlo (MCMC)
During studying the convergence assessment on Markov Chain Monte Carlo, I once read the following statement:
A slowly converging sampler may be indistinguishable from one that will never ...
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75 views
Multilevel calibration curve in jags
The problem
I am trying to fit a calibration curve from known x and y with jags. I would then like to predict new xes, based on the measurement of new ys. For this, I am following Hamada et al. ...
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31 views
Anomaly prediction confidence for frequentist vs bayesian parameter inference
I am comparing the behavior of some implementations of Bayesian and frequentist approaches to parametric anomaly detection and currently trying to figure out the differences when the sample set is ...
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1answer
158 views
Bayesian and frequentist approaches: What are some success stories for the former? [duplicate]
Possible Duplicate:
Examples of Bayesian and frequentist approach giving different answers
What are some practical examples where a Bayesian approach has an edge over frequentist ...
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126 views
Unscented Kalman Filter-Negative Covariance Matirx
I have recently started working on the Unscented Kalman Filter. I coded the numerically stable version (i.e Square root Kalman filter) and use matlab for implementing.
In the final update step , ...
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2answers
159 views
Results Difference: Frequentist vs. Bayesian
I fit a lognormal model on some data points using both frequentist and Bayesian (using a non-informative prior) approaches. However, I got different results. Here are my codes and outputs:
...
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1answer
100 views
Bayesian Batting Average Prior
I wanted to ask a question inspired by an excellent answer to the query about the intuition for the beta distribution. I wanted to get a better understanding of the derivation for the prior ...
3
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1answer
100 views
Calculating the likelihood of time series data when there are missing data
I am trying to calculate the log-likelihood of some time series data given parameter sets estimated in BUGS. I can not figure out how to handle some missing values at random points in time.
For the ...
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1answer
83 views
How concerned should I be about the appropriateness of my prior?
As I understand it, selecting a prior provides something of a starting point for your analysis. From there, the distribution is shaped by the observed data. Obviously, the more data you observe, the ...
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155 views
Fitting Lognormal Distribution in WinBugs
Let's suppose that some data points follow $Lognormal(\mu,\sigma^2)$ and both parameters are unknown . My goal is to obtain the posterior distribution by assigning conjugate prior distributions on ...
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0answers
118 views
How to compare a frequentist model with a Bayesian one
I analyzed my data by using maximum likelihood estimation and a Bayesian approach. Now, I want to see which model has a better fit. How could I do this using either plots or numbers? Please be ...
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2answers
107 views
How can I use KL-divergence to weight features?
I have a naive Bayes classifier with two classes (target and non-target) and distributions for a number of features (the same for both classes).
I know that some features contribute more, or less to ...
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73 views
How to present the Bayesian approach
I am writing a dissertation in which I use maximum likelihood estimation and an alternative Bayesian approach. I have written up the maximum likelihood estimation approach. However, I need some advice ...
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123 views
Free PDF for Bayes
Is there an good book/pdf similar to Elements of Statistical Learning that's available for free, online that deals with Bayesian statistics, ideally with code for ...
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1answer
194 views
Basic Bayesian MCMC to estimate two parameters from binomial distributions given unknown number of trials
This is a very basic question about Bayesian inference. I'm not grasping one or more fundamental concepts.
Let's say I have two observed outcomes, X and Y. I want to infer the probabilities (px and ...
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1answer
71 views
Luck or skill in 3-person game
Two friends and I have been playing a game that is a combination of skill and luck. (as most games are). We assume that if the game was all luck and/or we all had the same skill level eventually the ...
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170 views
“forgetfulness” of the prior in the Bayesian setting?
It is well-known that as you have more evidence (say in the form of larger $n$ for $n$ i.i.d. examples), the Bayesian prior gets "forgotten", and most of the inference is impacted by the evidence (or ...
