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 conditional probability of bernoulli data

Assume I have $i=1,\dots,N$ fathers, each with $j=1,\dots,n_i>0$ sons. Now there is a binary event $A_{i,j}$ with outcomes 1 and 0 and the respective probabilities $p$ and $1-p$. Now I want to ...
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10 views

Choosing which distribution is most accurate

Let's say we have two samples from different normal distributions and we want to determine which distribution is most accurate relative to an ideal value. How would we evaluate which one is more ...
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2answers
24 views

Observed and Observable

What is observed and what is observable? I found this two word frequently in the context of random variable and realization of ...
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13 views

Contaminated mark-recapture: estimating set size from sampled subsets

Someone poured marked balls in my urn! Simplistically, I think this is a capture-recapture problem where, after drawing and marking balls from the urn, somebody added an unknown number (approx 25% of ...
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2answers
127 views

A Question on Elementary Statistical Inference

A box contains $5$ white and $2$ black balls. A coin with unknown $P(Head)=p$ is tossed once. If it lands HEADS then a white ball is added, else a black ball is added to the box. Then a ball is ...
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41 views

Elastic/ridge/lasso analysis, what then?

I'm getting really interested in the elastic net procedure for predictor shrinkage/selection. It seems very powerful. But from the scientific point of view I don't know well what to do once I got the ...
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34 views

Is a coin fair? [duplicate]

Is a coin fair ? In other words, does a coin come up $50$% heads ? If a coin is unfair, then it would not come up $50$% heads. My thoughts : let's first identify the population and the parameter ...
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1answer
33 views

Estimating Size of a Set based on two Overlapping Subsets

I've searched everywhere for a similar question and many things come close but are not the same. I'm looking for a way to estimate the size of a set if two partially overlapping subsets are known ...
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2answers
32 views

Test if sampled data are randomly sampled

Is there a way to test if data are (or at least seem) randomly sampled? In other words, is there a way to measure if my data are randomly sampled -- instead of coming from a complex survey sampling ...
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1answer
20 views

How can I infer the joint distribution of an observed and a latent variable?

I have a dataset of school children with three features: Age $x$ of the student answering the survey Year group $a$ of the student answering the survey Year group $b$ of the best friend of the ...
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39 views

How to use MCMC samples for parameter estimation

My background is in optimization, and I am new in Bayesian inference. Very broadly speaking, I am trying to reproduce a latent feature model (see, Miller et al) for graphs. I want to uncover the ...
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1answer
51 views

$H_0=250g$ and $H_1\neq 250g$" [closed]

We have a sample of size $100$ with a standard deviation of $5g$ It was decided that if the sample mean is between $245g$ and $255g$ while the sample average is $250g$ if $\mu=250g$ or $\mu\neq250g$ ...
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A Hypothesis Testing Question and Verification

Suppose we have two p.d.f.'s: $f_0(x)=1,$ if $0\leq x\leq1$, and $f_0(x)=0$ otherwise $f_1 (x)=2x$ if $0\leq x\leq1$, and $f_1(x)=0$ otherwise We want to test the hypotheses ...
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0answers
22 views

Kalman filter with input control noise?

assume we have a standard Kalman filter with input controls, following wikipedia notation (http://en.wikipedia.org/wiki/Kalman_filter) where the latent state is $x_{t}$ and the observation is $z_{t}$, ...
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28 views

Observed versus hidden variables for Bayesian network in this particular context

I am a novice in Bayesian networks. I have a problem which is best described (at least I think so) in the following story. One wants to predict earthquakes. Let's say it has 5 variables, the last one ...
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2answers
24 views

Inferring on an unknown number of function approximation

I want to ask whether a procedure to do the following job exists (or whether it makes sense for it to exist). First, assume we have $k$ functions $f_1,...f_k$ that have the same domain and range. ...
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17 views

Topic Model inference for subselection

Question: Does the inference of a trained topic model (LDA) used on a subselection of a text corpus result in more accurate document-document-relations? I used the MALLET-LDA Java-library to estimate ...
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1answer
24 views

Iteratively solving for prior probabilites.

I'm using Bayes theorem to classify data into two groups, where the conditional probability is known but the prior is not. So I assume that the ratio of prior probabilities is 1 and calculate the ...
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11 views

Perturbation analysis for expectation propagation

Consider the clutter problem of Tom Minka where the goal is to get posterior of the mean of one Gaussian component. The likelihood is a mixture of two Gaussians, one of which is just noise. The other ...
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1answer
42 views

Mean separation when interaction is significant

I am analyzing a factorial experiment in RCBD (3 cultivars x 4 inoculation methods with 10 replicates). All main effects and interactions are significant for a particular response variable. But in ...
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1answer
29 views

Test equality of coefficients in separate regressions when populations are not independent

I have three regressions with the same IVs. Equation 1: Y1 = X Equation 2: Y1 = X Equation 3: Y2 = X X is a vector of IVs with B1-B8 coefficients. Equations 2 and 3 are tested on the same ...
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2answers
93 views

AR(q) model with F-test

I am wondering that if we have an AR($q$) model for time series: $$X_i=\beta_1X_{i-1}+..+\beta_{p}X_{i-p} + \beta_{p+1} X_{i-p-1} +...+\beta_{q} X_{i-q}+\epsilon_i,\epsilon_i \;\text{iid}\; ...
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26 views

Gibbs sampling version for estimating the Dynamic Topic Model (DTM)?

The paper of Blei et Lafferty published at ICML'06 implements a (quite complicated) variational inference (VI) technique for estimating the parameters of the Dynamic Topic Model, see: ...
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13 views

Estimate posterior distribution for a group given aggregate data

I have data describing over a 15 million individuals where each item includes variables like these: A. Amount spent on airfare last year B. Brand of shoes C. Number of times visited some website in ...
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2answers
46 views

Reasoning for comparing variance between and within for Anova?

I looking for some logic reasoning why ANOVA test uses $σ^2$ given by these to variables. a logical reasoning why the ratio of variance between these two would say that the each population has the ...
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16 views

ABC-based inference for a dynamic model of multiple time stages

I am working on a dynamic model of multiple time stages (e.g. 0-15h, 15-30h, 30-45h); the model has three time stages in total. Each stage has associated with it 4-8 different parameters and I am ...
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5answers
364 views

Inference vs. estimation?

What are the differences between "inference" and "estimation" under the context of machine learning? As a newbie, I feel that we infer random variables and estimate the model parameters. Is my this ...
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1answer
132 views

Sufficiency or Insufficiency

Consider a random sample $\{X_1,X_2,X_3\}$ where $X_i$ are i.i.d. $Bernoulli(p)$ random variables where $p\in(0,1)$. Check if $T(X)=X_1+2X_2+X_3$ is a sufficient statistic for $p$. Firstly, how can ...
10
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1answer
149 views

Hypothesis Testing and the Scientific Method

Reading the answers to this thread, I started wondering about how Hypothesis Testing relates to the Scientific Method. While I have a good understanding of both, I am having a hard time drawing the ...
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1answer
35 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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32 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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1answer
27 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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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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1answer
101 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 ...
1
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1answer
44 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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30 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
58 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 ...
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1answer
80 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
213 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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1answer
27 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
29 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 ...
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1answer
43 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
80 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
84 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
42 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
45 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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35 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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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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26 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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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 ...