Inference, in a statistical context, refers to drawing conclusions from data containing an element of randomness introduced by e.g. measurement error, sampling variation, or assignment of experimental treatments. A common inferential paradigm is drawing conclusions about population parameters from ...

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23 views

Reparameterization of probability distribution (spike and slab)

I try to understand a statement in this paper: http://papers.nips.cc/paper/4305-spike-and-slab-variational-inference-for-multi-task-and-multiple-kernel-learning.pdf In particular, I am talking about ...
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28 views

$3^3$ factorial design

Suppose in a $3^3$ factorial design, factor A has three levels. We want to test the significance of A and after setting hypothesis $$H_0:\alpha_i=0 \quad\text{for}\quad i=1,2,3 \quad\text{Vs.}\quad ...
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21 views

Assumption about Systematic Errors

In Maronna, Martin and Yohai's Robust Statistics (2006, p.17), they describe a location model as follows. $$x_i = \mu + u_i,$$ where $x_i$ is the $i$th observation; $\mu$ is the hypothetical mean ...
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25 views

How to Get this Confidence Interval

One example in Maronna, Martin and Yohai's Robust Statistics (2006, p.2) is as follows. Given 24 measurements of certain quantity (see below) and their sample mean 4.28 and sample standard variation ...
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28 views

How can I write the t-statistic in cases where I have three populations and linear relationship between the three?

I sample height measurements from people from three populations, which I call P1, P2, and P3. My null hypothesis that the average height in group P1 equals 2/3 times the group P2 average plus 1/3 ...
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78 views

Sufficient statistics for $\mu_1 - \mu_2$

If $ X_1, ..., X_n$ is a random sample from $ X \sim N(\mu_1, \sigma^2)$ and $Y_1,..., Y_n$ is a random sample from $Y \sim N(\mu_2, \sigma^2),$ if the samples are independent and $ \sigma^2$ is ...
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37 views

nonparametric method to calculate the probability how alike two samples are

I have two samples with each couple of hunderd observations. I want to calculate a probabilty how much they look alike. I'm aware of tests like kolmogorov smirnov but I don't think I need this. I ...
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26 views

Greedy subtree selection in Nested Hierarchical Dirichlet Processes

I'm implementing the Nested Hierarchical Dirichlet Process as described in this paper by Paisly et. al, 2014: http://arxiv.org/abs/1210.6738 My question is about the variational objective in Equation ...
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1answer
38 views

Is there any method to quantify parameter estimation uncertainty of method of moments fitting technique?

If I want to fit a distribution (let's say we can be certain about the type) to observations using maximum-likelihood method, I have many options to express the parameter estimation uncertainty due to ...
3
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48 views

Copulas with Regression

Copulas are joint distribution of uniform marginal distributions. Traditionally I have seen examples of fitting a Copula to the data and then simulating from the data. I haven't seen much on Copula ...
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1answer
192 views

Why doesn't the standard deviation represent a normal distribution?

Why doesn't the standard deviation of a sufficiently large sample represent a normal distribution that we can make inferences from? Let me list my thought process, so hopefully someone can highlight ...
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21 views

How to find three probabilities with two different values or ratings?

I would like to know how to find three probabilities of two values.... Specifically...I want to know the three soccer venues (HOME DRAW AWAY) proabilities with two ratings... Example: I have two ...
2
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1answer
28 views

How to infer correlations from correlations

I have a question regarding correlation inference. Consider, I have two sets of variables X and Y. For an x element of X I know the correlation to an unknown variable z. I also have the covariance ...
3
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1answer
39 views

Inference about the true intercept of the model and the OLS being BLUE

Consider the following population regression model: $$y_{i} = \beta _{1} + \beta_{2}x_{i} + \epsilon _{i},$$ where $i=1,...,n$. Assume $\epsilon \sim iid$, with the pdf in equation: $f(\epsilon ) = ...
2
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1answer
47 views

Poisson confidence interval using the pivotal method

I am trying to build a confidence interval for the Poisson distribution using the pivotal method. I have the theory down but I am struggling to come up with $h(Y, \lambda)$, the probability ...
2
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0answers
71 views

Expectation-Maximization with dependent latent variables

Deriving the equations for a Expectation Maximization over my model, I end up with a posterior for the latent variables (E-step) that prevents me from going on. Generative model I assume my data is ...
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1answer
33 views

Backward message passing in variational Bayesian inference

I have come across in a research paper that, I do understand the logic. But the paper has't mentioned about the way of updating $\eta_{t}$. When I asked from the authors they said when we equate ...
2
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1answer
42 views

Bayesian inference

Assume two demographics $[F,M]$ and each person has a choice of attending only one of four different lectures $[A,B,C,D]$ all occurring at the same time so they can only attend one. The following ...
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27 views

Conjugate prior equivalent prior sample size with respect to the mean

In Cowles's book ([Applied Bayesian Statistics - With R and OpenBUGS Examples–(http://www.springer.com/statistics/statistical+theory+and+methods/book/978-1-4614-5695-7)), page 108, there is a ...
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80 views

Optimal Stopping for Bernoulli One-Armed Bandit with a Fixed, Known Payout

I'm very new to bandit problems (apologies if I've formatted my question incorrectly), but I have to solve the optimal stopping of what I think is a very simple case. Suppose I have two arms $k = {1, ...
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20 views

How Can I Build A Regression Model With Collinear Data?

Hello there my fellow Cross Validated members; I’m here today to brainstorm a little bit with all of you out there, to flesh out our collectively acquired data analytic skills, and to try and find new ...
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5 views

Multiplying distributions with different conditioning

I saw this expression in a UBC machine learning class lecture, and I'd like to understand how the math works. Suppose we're trying to predict a class label $y$ given some data $x$. There are prior ...
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1answer
17 views

Variance of precision in conjugate prior

How can I calculate the variance of the precision in a normal distribution, knowing I used a conjugate prior?
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3answers
112 views

What is the distribution of the conditional mean E(Y|X) in a multiple regression?

Suppose the model is $$ Y = b_0 + b_1X_1 + b_2X_2 + b_3D + b_4X_1D + e \\ e \sim\mathcal N(0, \sigma^2) $$ Where $D$ is a categorical variable. $$ E(Y|X_1, X_2, D=1) \sim\mathcal ?? \\ E(Y|X_1, ...
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31 views

asymptotic distribution of joint random variables

I am trying to understand the asymptotic distribution of the following expression under normality $$ {\hat \sigma \hat S - \sigma S} $$ Where $\sigma$ and $S$ are the population standard deviation ...
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16 views

Compare two diagnostic Likelihood Ratios

I want to compare the LR+ and LR- in substratas according to age, gender, duration of symtoms. LR+ is the proportion of true positives/proportion of false positives so what I need is to compare ratios ...
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79 views

What is relationship between Fisher Information and Variance in natural exponential Family?

I know that $Var(\hat\theta)\geq 1/I(\theta)$ where $I(\theta)$ is Fisher information. Let take an example of natural exponential family with density $f(x)=\lambda\exp(-\lambda x)$. In this case we ...
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23 views

Score Confidence Interval for Difference of Proportions

In Agresti et al. (2008) "Simultaneous confidence intervals for comparing binomial parameter", it is suggested to use a studentized range distribution with a score statistic. However, exactly how you ...
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15 views

Is data fusion suitable for this application?

I have a situation where the delay vehicles experience at an intersection can be obtained through 3 or 4 types of sensors. Each sensor provides its own type of data with their own unique ...
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1answer
44 views

What criterion are used to accept/reject hypotheses in ridge regression?

On what basis might one accept/reject a hypothesis when running ridge regression? For example, if I have five predictor variables as part of a ridge regression... what criterion would I use to accept ...
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0answers
14 views

Why are chordal graphs special for inference in the context of Probabilistic graphical model?

I was trying to make a list of the reasons of why chordal graphs are important or interesting in the context of inference and probabilistic graphical models. Some of the reasons I have so far are: ...
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16 views

adaptive surveying for a maximal income that depends on a parameter

I have a product that I would like to price for the highest income. The income $I$ from this product will depend on the asking price $c$: $$ I(c) = N \cdot E(c)$$ where $E(c)$ is the expected ...
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1answer
22 views

Sampling: the % of homeowners who own at least 2 TVs

It is planned to conduct a study on the percentage of homeowners who have at least two TVs. What should be the sample size if we want to ensure that $95\%$ of estimation error is less than ...
8
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1answer
107 views

Observed Fisher information under a transformation

From "In All Likelihood: Statistical Modeling and Inference Using Likelihood" by Y. Pawitan, the likelihood of a re-parameterization $\theta\mapsto g(\theta)=\psi$ is defined as $$ ...
1
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1answer
47 views

Finding the unbiased variance estimator in high dimensional spaces

The problem comes from linear regression. Assume the regression function is linear, i.e. $$ f(X) = \beta_0+\sum_{j=1}^pX_j\beta_j $$ .Given a set of training data $(x_1, y_1),\ldots,(x_N,y_N)$,we try ...
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200 views

Invalid inference when observations are not independent

I learned in elementary statistics that, with a general linear model, for inferences to be valid, observations must be independent. When clustering occurs, independence may no longer hold leading to ...
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2answers
130 views

Example of an inconsistent Maximum likelihood estimator

I'm reading a comment to a paper, and the author states that sometimes, even though the estimators (found by ML or maximum quasilikelihood) may not be consistent, the power of a likelihood ratio or ...
2
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1answer
52 views

Sufficient and complete statistic

Let $ X_1, ... , X_n $ be i.i.d random variables with pdf given by $$f(x;\theta) = \exp(-(x-\theta))I_{(\theta, \infty)}(x)$$ It is asked to find a sufficient statistics for $ \theta $ and to verify ...
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0answers
31 views

Robust multivariate Wald test for significance in proportional odds model

I am using the rms package (Harrell) to estimate a proportional odds model to determine the association between an ordinal outcome (frequency of pain) and the ...
0
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1answer
72 views

LR test on marginal effect

Say I have the following regression model: $$\text{Wage}_i = constant + α·\text{YearsOfEduc}_i + β·\text{Age}_i + γ·\text{CompletedHighSchool}_i + \mbox{δ·$\text{NumOfSiblings}_i$} + ...
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1answer
46 views

Wald test on marginal effect

Say I have the following regression equation: $$Wage_i = YearsOfEduc_i + Age_i + NumOfSiblings_i + u_i$$ How would I go about peforming a wald test of the hypothesis that for an individual with ...
9
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121 views

Should we address multiple comparisons adjustments when using confidence intervals?

Suppose we have a multiple comparisons scenario like such as post hoc inference on pairwise statistics, or a multiple regression, where we are making a total of $m$ comparisons. Suppose also, that we ...
3
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73 views

Unbiased estimator with minimum variance for $1/\theta$

Let$ X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e, $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$ Find the unbiased estimator ...
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17 views

Detecting parameter influence

I have a data set consisting of a system's responses to various test configurations. Every test configuration corresponds to a different parameter set. These parameters can have either continuous ...
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0answers
10 views

Combining weighted evidence based probabilities?

I'm trying to identify people by determining if a data sample matches a set of existing samples (assume DNA if it helps). In addition to the samples I have a function which gives a probability that ...
3
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0answers
69 views

Inference of Pearson's rho from distribution perturbation

I would like to infer the correlation between random variables $Q$ and $R$, however, I have access only to the distribution of $Q$ and the distribution of $P=Q+R$. We can see how Pearson's $\rho$ ...
5
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2answers
109 views

Maximum likelihood estimator for $\theta$ and $E[X]$

Let $X_1,..., X_n $ be a random sample of a variable with PDF: $$f(x|\theta)=\frac{\theta}{x^2} I_{(\theta, \infty)}(x), \theta >0$$ Find the maximum likelihood estimator for $\theta$ and $ E[X]$ ...
2
votes
2answers
203 views

How can I calculate t-score without knowing true population mean?

I am studying now t-scores. As far as I understand, t-scores are used when we don't know true population parameters (such as: standard deviation and population mean) and cant use z-scores. Here is ...
1
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1answer
80 views

Bayesian inference of a clinical trial for clinicians

I am a clinician who is more adept than average at interpreting clinical trials in a frequentist manner. At this point, interpreting a trial as a frequentist has kind of become a procedure: check ...
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2answers
88 views

Inferring prior distribution

Suppose that we take a sample ($X_1, X_2, ... X_n$) from a distribution where we assume that $X_i $~$ Bin(n_i, p_i)$ and $n_i$ is known for every $i$. We also assume that $p_i$'s are independent and ...