Tagged Questions

2
votes
1answer
61 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 ...
1
vote
0answers
50 views

Pooling asymmetric confidence intervals for proportions?

I have several measurements of proportions (values in [0, 1]) $\theta_1,...,\theta_n$, each with an (asymmetric) 95% confidence interval. The $\theta$'s are repeated measurements of the same variable ...
2
votes
2answers
155 views

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 $x_i$ ...
3
votes
2answers
163 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: $$ ...
3
votes
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 ...
3
votes
2answers
152 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 ...
1
vote
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 ...
1
vote
1answer
54 views

Posterior probabilities of variables that aren't included in likelihood

Disclaimer: I'm not a statistician so I apologize if this is a trivial question or written in a way that convolutes ideas and abuses jargon. It seems like a problem that should be common but I ...
1
vote
1answer
55 views

Estimating conditional mean

Suppose I have a uniform random variable $X$ taking values $\{1,...,n\}$, and two functions $v(X)$ and $w(X)$. I know that $v(X)$ and $w(X)$ are jointly distributed with correlation $\rho$. (And can ...
3
votes
1answer
274 views

Posterior distribution for multinomial parameter

(topic moved from maths.stackexchange.com) I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of ...
2
votes
0answers
58 views

Inferring from a combination of uncertain and certain data

I am trying to estimate the surface (isochrone), zi(x) for which T(x,z)=0 from noisy measurements of T(x,z) everywhere and 3 almost noise free control points: Instead of using the T(x,z) data ...
2
votes
1answer
94 views

Pros/cons of estimating parameters for missing observations?

Some people are playing a game online. Every time a person plays, a new game board is generated randomly. On generation of a new board, the player can also choose a special weapon. (The choice of ...
6
votes
1answer
254 views

Is there a difference between the “maximum probability” and the “mode” of a parameter?

I am reading a manuscript that provides the "maximum posterior probability" in a Bayesian context as a statistical summary of a parameter. Is the term "maximum posterior probability" equivalent to ...
2
votes
0answers
43 views

Combining Deterministic and Random Unbiased Estimators

I am trying to compute an expectation $E[f(X;\theta,n)]$ where $\theta$ and $n$ are known parameters. I have an easy-to-compute deterministic function $\tilde{f}(\theta,n)$ that provides an ...
4
votes
1answer
251 views

Minimax estimator for the mean of a Poisson distribution

I recently took a course on Bayesian statistics based on The Bayesian Choice by C. Robert (aka Xi'an). I couldn't solve one of the exercises regarding minimax estimators and was hoping that someone ...
3
votes
2answers
179 views

Bayesian updating using $n$ noisy observations of Brownian motion

I am very new to Bayesian inference and can't figure out what may be an elementary problem. Also, please forgive me if I am screwing up the notation -- this is my first foray into Bayesian ...
4
votes
0answers
46 views

Estimation and functional space

In the first chapter of the book Algebraic Geometry and Statistical Learning Theory which talks about the convergence of estimations in different functional space, it mentions that the Bayesian ...
0
votes
1answer
134 views

Bayesian estimators

I have a model $f(x|\theta)$ ($\theta$ is a vector) for which I want to specify a prior $\pi(\theta)$. I only know that $\theta$ is in some interval. There are ways to specify an ignorance prior ...
3
votes
0answers
114 views

Estimating parameters in a model with a periodic design parameter

We recently studied a model with a likelihood function of the form $$\Pr(d_i|\omega,t_i)=(1-d_i)+(2d_i-1)\cos^2(\omega t_i),$$ where $d_i\in\{0,1\}$, $\omega$ is an estimation parameter, and $t_i$ ...
1
vote
1answer
186 views

Combining two pieces of evidence expressed as probabilities

I have a hidden binary random variable Z that can have a value of either 1 or 0. There is some true probability P(Z=1) = z that I do not know. I also have two separate pieces of "evidence" that give ...
4
votes
1answer
177 views

Bayesian analysis of data

I have a big dataset in the form: $X_1, X_2, X_3, X_4, Y$. All the $X_i, i \in {1,...,4}$ come from different unknown distributions and $Y$ follows a bernoulli distribution, so it can take only values ...
6
votes
2answers
540 views

Acceptance rates for Metropolis-Hastings with uniform candidate distribution

When running the Metropolis-Hastings algorithm with uniform candidate distributions, what is the rationale of having acceptance rates around 20%? My thinking is: once the true (or close to true) ...
1
vote
0answers
180 views

Confusion in MLE and EM [closed]

I was trying to read through Maximum Likelihood Estimation(MLE) and Expectation and Maximization(EM) algorithm. But while reading them, I got two interpretations. I am trying to post my questions, ...
7
votes
1answer
415 views

Bayesian vs Maximum entropy

Suppose that the quantity which we want to infer is a probability distribution. All we know is that the distribution comes from a set $E$ determined, say, by some of its moments and we have a prior ...
2
votes
2answers
415 views

Estimating distribution parameters from few data points

Say I'm doing stats on the height of adults from various countries. I assume the heights of adults from one country are normally distributed, and ignore sex differences (I also ignore the fact that ...
6
votes
2answers
237 views

Regularization and Mean Estimation

Suppose I have some i.i.d. data $x_1, \ldots, x_n \sim N(\mu, \sigma^2)$, where $\sigma^2$ is fixed and $\mu$ is unknown, and I want to estimate $\mu$. Instead of simply giving the MLE of $\mu = ...