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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Estimating total number of people from an observed sample

The well known "German tank problem" shows how to answer the question: "If I have tanks which have an increasing serial number, and I see a sample of tanks and record their serial numbers, what is the ...
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9 views

Do I need to care about constants in Expectation Propagation

I am trying to approximate a certain factor in my graph. Following Tom Minka's tutorial what I have to do is as follows: $$ \prod_{i=1}^3 q_{w_i}(\pi_2)\approx \int ...
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20 views

inference Single sample [on hold]

Can someone Answer this question. Thanks in advance. 6.17 the one with black circle. Right now i have no idea how to approach and solve it.Any help would be highly appreciated. Thanks.
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60 views

Basic problem in Bayesian inference

I have questions with the following Bayesian inference problem I found in the book by Bertsekas & Tsitsiklis (Introduction to Probability 2nd ed.). Problem is as follows (P.445, Problem 2): ...
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1answer
33 views

Getting all zero correlations,$\rho_{ij}=\frac{\mathbb cov(e_i,e_j)}{(V(e_i)V(e_j))^{1/2}}$

Consider the general regression model $$Y=X\beta+\epsilon$$ where, $Y$ is an $(n\times 1)$ vector of observations, $X$ is an $(n\times p)$ matrix of known form, $\beta$ is a $(p\times 1)$ vector ...
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83 views

Estimating abundance using non-normal count data

I have sample counts of $n=20$ or $n=7$ taken from right-skewed and zero-inflated populations. The challenge in each case is to use the sample to estimate the total count in that population. Each of ...
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24 views
+100

What is max-sum / max-product variant of loopy BP computing?

In (Nowazin and Lampert, Structured Learning and Prediction in Computer Vision, p. 29.), they say that in the max-sum variant of loopy belief propagation, the "variable max-beliefs are no longer ...
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3answers
411 views

Do the pdf and the pmf and the cdf contain the same information?

Do the pdf and the pmf and the cdf contain the same information? For me the pdf gives the whole probability to a certain point(basically the area under the probability). The pmf give the probability ...
2
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4answers
142 views

Can a trend stationary series be modeled with ARIMA?

I have a question / confusion about stationary series required for modeling with ARIMA(X). I am thinking of this more in terms of inference (effect of an intervention), but would like to know if ...
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31 views

Maximum likelihood estimator for variance in two linear models

I am learning MLE's at my inference class and this is a problem I came accross. Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha ...
2
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1answer
95 views

Asymptotically unbiased estimator using MLE

I am learning Maximum likelihood estimators for a inference class. And this is a problem I came across. Let $X_1,X_2,X_3,\ldots, X_n$ be a random sample with p.m.f $$p(X)=\theta(1-\theta)^x; ...
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27 views

UMVUE for normal distribution $\sigma$

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
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0answers
16 views

Maximum Likelihood estimators in reation to linear models

Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha _2+\beta_{2}x_{2j}+\epsilon_{2j}$ , $ j=1,2,...,n>2$ where $ ...
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2answers
21 views

Pivotal to estimate lambda of a exponential

I am studying interval estimation by the method of pivotal quantities. Let $X_1,X_2,...,X_n$ be a random sample from a p.d.f $f(x;\lambda)=\lambda e^{-\lambda x}, x>0,\lambda >0$. I have to ...
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0answers
22 views

Constructing Counterfactuals and Estimating Prevalence

I'm a social scientist working on a research project where I try to estimate the prevalence of lying in responding to a certain sensitive question. The way I estimate it is to rely on a ...
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26 views

Updating a Dirichlet distribution with partial data

I've got some categorical data where each observation has multiple attributes, and I want to make a probabilistic model of this using Dirichlet distributions. For example, in the two dimensional case ...
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0answers
28 views

Expectation maximization with variant length at observing data

Imagine one loaded dice. Based on EM algorithm, how could we compute how much it loaded if we introduced: Variant length on each rolling attempt (look at first and second attempt below 1st one has 6 ...
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1answer
47 views

Testing significance of a random effect glmmADMB model

Below is the output from a model of novel object test scores fit with the nbinom1 (quasi-Poisson) option in glmmADMB. I used ...
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0answers
22 views

Superiority test versus non-inferiority test

What is your best (or the best quote that you have) plain language explanation of the difference between tests for superiority and tests for non-inferiority? I think a test of superiority a simply a ...
4
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2answers
88 views

How to statistically test upper bound

Suppose a theory claims that a random variable $R$ (of unknown distribution $F$) must satisfy a certian upper bound $R < c$ (where $c$ is known constant). Suppose I perform a set of measurements ...
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0answers
23 views

Model averaging effect sizes of Gamma family GLMs

I'm trying to get some model averaged effect sizes from a set of candidate models, all of them assuming a Gamma error distribution, according to the theory given by the book from Burnham and Anderson ...
2
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1answer
62 views

What the dimension of an exponential family tell us about that family?

In Wikipedia it is stated that: A vector exponential family is said to be curved if the dimension of $$ {\boldsymbol \theta} = \left (\theta_1, \theta_2, \ldots, \theta_d \right )^T$$ is ...
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13 views

statistical inference [duplicate]

I guess this issue must be somehow cliched, yet I wasn't able to find the answer that would satisfy me. The key role of statistics and econometrics is to make inference about population using some ...
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27 views

Which statistics to use?

I have a medical research in which I have two sets of data Control group: People who have no ailment. Study group: People who have some particular ailment. Within each category there are ...
14
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1answer
535 views

How to interpret a QQ plot

I am working with a small dataset (21 observations) and have the following normal QQ plot in R: Seeing that the plot does not support normality, what could I infer about the underlying ...
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1answer
61 views

Find the UMVUE for $\Phi(\mu)$

Question: Suppose $X_1, \cdots, X_n$ are $iid$ normal random variables with unknown mean $\mu$ and known variance $\sigma^2$. Find the UMVUE for $\Phi(\mu)$, where $\Phi(\cdot)$ is the cdf of a ...
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1answer
43 views

Can Someone Explain How Factor Multiplication Works with Factor Graphs?

I'm taking the Probablistic Graphical Model course here: https://class.coursera.org/pgm-003/ This class uses the concept of Factors extensively with regards to graphical models: ...
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115 views

How to find this integral [duplicate]

Let $X_1, \cdots, X_n$ be $iid$ normal random variables with unknown mean $\mu$ and known variance $\sigma^2$. How to find $E[\Phi(\bar X)]$, where $\bar X:=\frac{\sum_{i=1}^nX_i}{n}$, please? I guess ...
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14 views

SPM for spatial analysis

Do you know of any study where researchers have used Statistical Parametric Mapping for spatial data only? I found a lot of studies that used it for time-series analysis, but does this analysis work ...
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0answers
50 views

Inference from simulated quantile function

I generated a quantile function $\hat X$ using Monte Carlo simulation. The random variable I simulate is the mean value of 5 draws from an i.i.d. range statistic $Y$. I.e., I have $Y(\sigma) \sim ...
0
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1answer
42 views

When is the IID Assumption too strict for the bootstrap?

The Bootstrap (Efron 1979) assumes that the data are IID. Obviously, if we have time series data then we probably cannot make that assumption unless we have a special case that we a time series of ...
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32 views

Gibbs sampling with Log-Normal observations

I am writing a Gibbs sampler for data that is Log-Normal (LN) distributed, with unknown mean and variance. There is a wealth of information on inference for LN models when either the mean or variance ...
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2answers
43 views

explanatory variables may bias predictions

I' m asking this question out of sheer curiosity, my teacher was not able to explain it. If I'm using logistic regression with categorical variables they are coded like {1,2,3}. I guess it wouldn't ...
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21 views

Forward Sampling for HMM

Is it reasonable to use forward sampling to compute the probability of P(X_1=x_1, ..., X_N=x_n) in an HMM where is the observation variable? Is the forward sampling algorithm related to the ...
0
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0answers
37 views

Quantifying variable importance for GLMM using hierarchical partitioning (in R)

I am interested in quantifying variable importance for a binomial logistic mixed-model regression. My model has 5 fixed effects, and 3 random effects (2 nested). I am doing model selection and ...
0
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1answer
19 views

Efficiently finding approximate factors in expectation propagation

I've been trying to wrap my head around expectation propagation for a while now, but I'm struggling a bit with finding approximate factors in an efficient way and 'fully-factorized' approximations. ...
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29 views

I need an insight on result of my analysis

I need some help/insights on result of my data analysis. My object is to classify 3 types of different numbers. ie) 1 or 2 or 3 I built C5.0 tree + leave group out cross validation (hold out) ...
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1answer
95 views

ML vs MAP estimation, when to use which?

ML = Maximum Liklihood MAP = Maximum a-posteriori ML is intuitive/naive in that it starts only with the probability of observation given the parameter (i.e. the likelihood function) and tries to ...
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27 views

Bayesian inference with the change of variables

I have a following question which I haven't been able to solve on my own. Imagine that I have measured some property X from data and for simplicity the posterior is Gaussian: $P(X|D) \sim ...
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1answer
23 views

How to statistically analyse the survey data of the same sample taken at two points in time

I am conducting a study on a sample of 100 people in order to test whether or not education has an effect on employment status. Basically i'm running a logistic regression where education is the ...
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40 views

Finding optimal parameter values using a Bayesian model

I have a problem with the following setup. I've been reading "Doing Bayesian Data Analysis: A Tutorial with R and BUGS" and it seems like the Bayesian approach is a good one, but I'm not entirely ...
2
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2answers
68 views

Why we shouldn't be obsessed with unbiasedness

In my Bayesian statistics class, my professor makes the remark that we should not be obsessed with unbiased estimator. First: I understand this statement in the sense of trading biasedness for ...
2
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0answers
38 views

Importance of multivariate normality assumption for BIC-like sparse model selection inference with PCA

I am reading a paper for robust, sparse PCA in which they propose a BIC-like criterion for selecting the appropriate value of the sparsity parameter $\lambda$. They define this as: ...
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261 views

Testing equality of coefficients from two different regressions

This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this? More formally, ...
1
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1answer
57 views

Consistency of an order statistic in exponential distribution

I have two questions. 1) If $X_1,X_2,X_3,...,X_n$ constitute a random sample of size $n$ from an exponential distribution, show that $\bar X$ is a consistent estimator of the parameter $\lambda$. ...
2
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0answers
22 views

How do I check for variation of a distribution over spatial scales?

I have about 30000 particles distributed (not randomly) in space; I have their vector positions and velocities. I'm trying to characterize if and how the (underlying) velocity (magnitude) distribution ...
1
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1answer
31 views

Inferring testlet structure in item response theory

Is it possible to infer the testlet structure in a set of items using item response theory? Specifically, I've created a lot of variations on the story recall task, each variation being scored on 25 ...
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18 views

Standard Deviation Grows Quadratically with Input Variable

I take an input x, based on which I do an experiment that gives me several data points. I compute the standard deviation of these data points. Then, I change ...
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32 views

How to model to improve the room usage efficiency based on motion sensor history

To reduce the confusion, I changed my application from traffic to meeting room, so this application is about modeling a meeting room efficiency , the data collection is built by placing a kind of ...
1
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0answers
25 views

Any fancy application of convergence (in probability, law, CLT, etc)?

As part of the inference course in an applied stats masters degree, we've to prepare a talk about convergence (see, for example, Lehmann 1999 Chapter 2). We'll be explaining to other students some ...