# Tagged Questions

Inference, in a statistical context, refers to drawing conclusions about a population from information about a sample from that population.

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### Iterated Conditional Mode approximation in E step of EM

I wanted to know what is the mathematical justification for using ICM as an approximation for the E step in an EM algorithm. As I understand in the E step the idea is to find a distribution that is ...
1answer
62 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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26 views

### Measuring some of the patients more than once

I'm conducting a clinical study where I determine an anthropometrical measure of the patients. I know how to handle the situation where I have one measure per patient: I make a model, where I have a ...
1answer
35 views

### how to calculate E[vech(x x')vech(x x')']?

Supposing a vector x follows normal distribution. I want to calculate the expectation of the "fourth moment" in a vector form, meaning $\text{E}[\text{vech}(x x')\text{vech}(x x')']$, given that we ...
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### Hypothesis Testing

A Lab has been asked to evaluate the claim that drinking water in a local restaurant has a lead concentration of 6 parts per billion (ppb). Repeated measurements follow a normal distribution ...
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### Calculating confidence intervals for a proportion when there are no 'successes' in the sample

Newbie here! Apologies in advance if I'm asking something that is based on flawed understanding of statistical analysis. I'm looking to analyse 400k replies to a Facebook-equivalent post, to ...
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### Naive Bayes without model

I have the following scenario: I have two "states". I measure variables $n$ that are affected by the state. A state of 0 is the background state and in this case I expect each variable $n_i$ to be ...
1answer
82 views

### Prior for Bayesian Inference on Failure Rate in Poisson Distribution

I'm trying to derive the posterior distribution for the failure rate (lambda) of a process with poisson distribution. I have tried the use of an improper uniform distribution on lambda by letting the ...
2answers
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### Bayesian inference with Gaussian distributions

This is Problem 4(c), Chapter 2 from Thrun's Probabilistic Robotics . Note that this is self-study and not homework. Suppose I know my position $x$ to be a normal distribution with density ...
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### Statistical inference about degree of a node in a genetic network

I am working on Gene-Gene interaction networks. I build a graph by adding edges between genes (nodes) representing statistical interaction in prediction of a quantitative parameter value (say, brain ...
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### Heterogeneous Treatment Effects - How to test differences in the ATE?

I have the following problem: I want to conduct a simple Propensity Score Estimation where the treatment D is a binary variable (D=1 individual i participates in the labor market program, zero ...
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### 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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### Inference from linear regression slope and Pearson

Sorry if this has been asked before but I've already done quite a bit of work here and I feel like I'm quite close to an answer. I am interested in testing whether the PHP function array_key_exists ...
2answers
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### Why is the Fisher Information matrix positive semidefinite?

Let $\theta \in R^{n}$. The Fisher Information Matrix is defined as: $$I(\theta)_{i,j} = -E\left[\frac{\partial^{2} \log(f(X|\theta))}{\partial \theta_{i} \partial \theta_{j}}\bigg|\theta\right]$$ ...
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### 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 ...
1answer
235 views

### If a tennis match was a single large set, how many games would give the same accuracy?

Tennis has a peculiar three tier scoring system, and I wonder if this has any statistical benefit, from the point of view of a match as an experiment to determine the better player. For those ...
2answers
32 views

### How to determine influence of two time series with feedback?

Say you have two time series, A & B. Each have a mutual effect on the other. To give a real-world example, say that time series A measures an artist's CD sales per month, and time series B is some ...
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### 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 ...
2answers
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### How to show the significance of the difference in means in a paired test

Suppose I perform a paired test. The null hypothesis is that mean of difference is zero: $\mathrm{E[X-Y]} = 0$. The actual difference is positive but distributed non normally. Which statistical ...
1answer
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### Statistical test for computer-systems performance analysis?

Suppose we do the following study. We have 2 web-servers (server A and server B) which are processing user requests. Both run on the same hardware, but one of them (server B) uses a slightly different ...
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### Multiple categorical Variables and Multiple Hierarchical Counts- how to infer the effects?

I have the following categorical/count data : ...
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### Matrix completion: How to assign names to the completed columns?

I am wondering if this the right place to ask this question. Normally it should be :). I am recently reading some papers about matrix completion such as in here, and here. I didn't go through some ...
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436 views

### How would you do Bayesian ANOVA and regression in R?

I have a fairly simple dataset consisting of one independent variable, one dependent variable, and a categorical variable. I have plenty of experience running frequentist tests like ...
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### Can we apply inferential statistics on the entire population? [duplicate]

Possible Duplicate: Statistical inference when the sample “is” the population Greeting, My question is:Can we apply inferential statistics on the entire population in case of the possibilty ...
1answer
158 views

### Latent Dirichlet Allocation (LDA): What exactly is inferred?

I am working my way through LDA and I think I got they main idea of it. Please correct me if I am wrong. Given the Plate notation: The variables $\alpha$ and $\beta$ are Dirichlet distribution ...
2answers
143 views

### Restricted Boltzmann Machines and Markov Networks: relationship in inference?

I am wondering if there is some equivalence between retricted Boltzmann machines and pairwise Markov networks in terms of MAP inference. More specifically, let $y \in \{0,1\}^m$ be the ...
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### Are these statistics sufficient?

Question (Casella and Berger 6.5): Let $X_1 \ldots X_n$ be independent random variables with pdfs: \$f(x_i|\theta)= \begin{cases} \frac{1}{2i\theta}, & -i(\theta - 1)<x_i<i(\theta+1) \\ ...
2answers
171 views

### Non-fair die - College Probability

How many times must you roll a non-fair die to be at least 84% sure that the sample probability will be within 3% from the actual probability. Since the die is not-fair, we do not know p. My question ...
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191 views

### Computing marginals on a graphical model in Python

I am looking for libraries available from Python to compute marginals on an undirected graphical model (i.e. a random field) with loops. Some algorithms for this could be LBP (loopy belief ...
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158 views

### Sufficient, Complete Sufficient, UMVUE, Rao-Blackwell, Admissible. What are ties between these?

I am taking stat inference course. I have some trouble understanding some these terms: Sufficient Statistics: a stat that does not depend on the parameter, say $\Sigma X$ for normal distribution ...
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### If the likelihood principle clashes with frequentist probability then do we discard one of them?

In a comment recently posted here one commenter pointed to a blog by Larry Wasserman who points out (without any sources) that frequentist inference clashes with the likelihood principle. The ...
2answers
674 views

### How to find an unbiased estimator?

Suppose $X_1, X_2, ...,X_n$ are samples from a uniform discrete distribution with probability 1/3 on each of the points $\theta-1, \theta, \theta+1$, where $\theta\in\mathbb{Z}.$ From "Theory of ...
1answer
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### What to look for in a pocket calculator for a Graduate level statistics course midterm / final [closed]

Soon I'll be sitting for a midterm (and then the dreaded final) for a graduate class in Statistics. It's open book / notes but I'll be needing a calculator -- something I've not used for years. Any ...
1answer
327 views

### How to show order statistic is sufficient

I have some trouble showing sufficiency for largest order statistic ${x}_{n}$. This is from Casella's text, problem 1.6.3. Let ${p}_{\theta}$ be a density function. ${p}_{\theta}{x}=c({\theta})f(x)$ ...
1answer
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### Inference from conditional observations

Let $(x_1, \ldots, x_n)$ be an i.i.d. random sampling from a conditional normal distribution ${\cal N}(\mu,\sigma^2)$ distribution given some event $A$ possibly parameter-dependent: for instance when ...
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### Marginal parameter estimation in copula with copula (dependence) parameter known

Suppose we have data $x_i, i=1,2,3,...n$ that are dependent and identically distributed with marginal $f(\cdot|\alpha)$. If we model this with the likelihood \$ L = ...
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120 views

### Understanding the Behrens–Fisher problem

This section of this article says: Ronald Fisher in 1935 introduced fiducial inference in order to apply it to this problem. He referred to an earlier paper by W. V. Behrens from 1929. Behrens and ...
4answers
777 views

### What hypothesis test to use for categorical variables?  Possibly in R?

Edit: I think this is a better question, Say, I have categorical characteristics such as gender, race. How should I use Fisher's test and chi-square test? I was looking at this: ...
4answers
223 views

### What if your randomly formed groups are clearly not similar?

What if, before you begin the data collection for an experiment, you randomly divide your subject pool into two (or more) groups. Before implementing the experimental manipulation you notice the ...
1answer
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### Inferring multiple ratios and binomial proportions with missing data

I have a number of studies describing families tested for a genetic condition. For each study the following data are described: $n_p$, number of probands (the proband is the first person in a family ...
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### Optimal software package for bayesian analysis

I was wondering which software statistical package do you guys recommend for performing Bayesian Inference. For example, I know that you can run openBUGS or winBUGS as standalones or you can also ...
1answer
551 views

### How to write a poker player using Bayes networks

This is my first question on stackexchange and also my first time implementing a Bayesian network so I will apologize ahead of time for any novice mistakes I make. The goal of my project is to ...
2answers
257 views

### Behrens–Fisher problem

Is there a good published expository account, with mathematical details, of the various approaches that have been taken to the Behrens–Fisher problem?
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### What if your random sample is clearly not representative?

What if you take a random sample and you can see it is clearly not representative, as in a recent question. For example, what if the population distribution is supposed to be symmetric around 0 and ...
3answers
291 views

### Good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)?

Are there any good summaries (reviews, books) on various applications of Markov chain Monte Carlo (MCMC)? I've seen Markov Chain Monte Carlo in Practice, but this books seems a bit old. Are there ...
2answers
100 views

### How to go about selecting an algorithm for approximate Bayesian inference

I am wondering if there are any good rules of thumb for how to go about selecting an approximate inference algorithm for a problem/model (specifically when exact inference is intractable)? When you ...
1answer
135 views

### Does Loopy BP give the same solutions as a Gibbs sampler?

The literature in MCMC and LBP never refer to the fact that the two methods look (on expectation) exactly the same. To illustrate, first consider a simple Ising model, that is, a graphical model ...
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159 views

### Inductive vs deductive Inference

I am curious to know exactly, what are the (possible) differences between inductive and deductive statistical inferences in applied statistics. Suggestions for some good resources to learn their ...
3answers
465 views

### Mixture Models and Dirichlet Process Mixtures (beginner lectures or papers)

In the context of online clustering, I often find many papers talking about: "dirichlet process" and "finite/infinite mixture models". Given that I've never used or read about dirichlet process or ...
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### Querying a junction tree for joint probability

How do I query a junction tree for a joint probability? Let's say I have a factor graph of the form: \$P(x_1, x_2, x_3, x_4, x_5) = \frac{1}{Z} F(x_1) F(x_2) F(x_3) F(x_4) F(x_5) *\\ \qquad \qquad ...
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