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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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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19 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
20 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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16 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
21 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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10 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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13 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
17 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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32 views

What are sampling errors and why are they useful? [closed]

An example of where and how they are used, and how they fit in with the notion of the confidence interval will be useful.
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2answers
82 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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15 views

Reverse inference: getting $\mu$ from P(X)

Say I have a dataset where each sample is an observation of a random variable $X_i$, where each $X_i$ comes from the same family of distributions, but with different parameters. For each $X_i$, ...
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17 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
41 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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0answers
14 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
306 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
121 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
137 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
32 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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30 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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29 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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1answer
93 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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1answer
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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27 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
48 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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1answer
56 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
203 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
22 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 ...
3
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1answer
40 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
53 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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76 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
36 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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32 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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85 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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23 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
19 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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1answer
33 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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19 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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92 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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16 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
45 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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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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18 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 ...