# All Questions

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### Given a marginal posterior distribution, when should I report an upper limit on the parameter?

I've been utilizing MCMC in the analysis of $\gamma$-ray spectra. For many of my model-parameters, the marginal posterior distributions, $p( \theta_i |X)$ where ($\theta_i\in(0,1]$), are normal ...
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### How does one determine which variables can be collapsed in Gibbs Sampling?

I am going through the derivation for Gibbs Sampling update equations for LDA. The claim is that $\theta_{d}$ (document specific topic distribution) and $\phi_k$ the topic-word distribution can be ...
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### Clustering in data

I have a set of data points (x,y) where y = f(x). My goal is to fit the function f using ols. The choice of function f is quadratic due to domain know-how.The independent variable i.e. x exhibits ...
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### Quantiles of big areas to calculate the associated quantiles of small areas

I have this question to solve and i don't understand it: How can i use quantiles of big areas to calculate the associated quantiles to small areas and construct a table that gives me the 0.05, 0.025 ...
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### K-means in R vs SPSS, update centroids after case assigned?

I am currently conducting k-means clustering in R using kmeans() in stats. When I previously did k-means clustering in SPSS, it was recommended to check 'running means', i.e. update centroids after ...
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### meaning of 'Monte Carlo' in this sentence

This is from a paper 'Algorithms for Inverse Reinforcement Learning' by Ng, Russell (2001) We assume that we have the ability to simulate trajectories in the MDP (from the initial state $s_0$) ...
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### Am I doing this right - choosing the order of p and q for an ARMA model (time series)?

I have a time series and have to come up with the ARMA(p,q) model that fits best to the data. (I have read ARIMA model identification, which was helpful, but doesn't completely resolve my question). ...
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### Poisson model and Multicollinearity

I have 2 questions to ask: fIRST, does Molticollinearity important in Poisson model?, as it is influential in OLS. And secondly how you can test it by using F-test since I can...
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### K-means in R, high nstart gives tiny clusters (n=1)

I am using kmeans() to cluster standardized scores from a factor analysis in R (20 variables, 919 cases). As R uses random cases for the initial centroids, I was hoping that choosing a high value for ...
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### How to verify that an implementation of a neural network works correctly?

I wonder what some useful techniques are to check whether an implementation of a neural network works correctly. Below are some checks I am aware of, I would be interested to know more of them: ...
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### Hamiltonian Monte Carlo with large parameter values fail to converge

I'm trying to learn about Hamiltonian Monte Carlo. Therefore I tried to infer the Parameters of a Multivariate Normal given some samples. My procedure is the following: Define $\mu$ and $\Sigma$ ...
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### Constraining the mean latent slope in lavaan

In lavaan, I can constrain the intercepts of the latent slope and latent intercept, like so: ...
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### Gaussian distribution samples' norm vs mean's norm

Consider a gaussian distribution with mean $\boldsymbol\mu$ and covariance matrix $\mathbf{Q}$, and suppose I take a sample from this distribution and compare its norm with the mean's norm. My goal is ...
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### Who invented INLA?

I am trying to do a literature review on integrated nested Laplace approximations (INLA). Most papers cite a popular paper by Rue and Chopin, however, this does not seem to be the seminal paper. Can ...
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### Define the quantity of ACF and PACF

a) Define the quantity of ACF and PACF? b) What are the major analogies and differences between the two? c) Explain the probabilistic meaning of the theoretical ACF?? a) unsure what quantity means ...
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### Bayesian models with categorical but non-binary observations

This is a very general question concerning Bayesian model design. I would like to construct a model that predicts a subject's performance in an experiment. The model will have a number of free ...
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### Ideas on Calculating cost matrix in cost-sensitive learning?

I went through lot of searches on Google, but couldn't find what I was looking for. In short: I need a way to calculate cost matrix for cost sensitive learning. Description of problem: I've number of ...
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### Estimate number of bidders above a price threshold

I am working on a project on an online auction system and we had an idea about estimate the number of bidders above a certain price threshold. The concept of the auction is: We have a number $p$ of ...
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### Why is the threshold in SVM estimated separately?

The optimal hyperplane in SVM is defined as: $$\mathbf w \cdot \mathbf x+b=0,$$ where $b$ represents threshold. If we have some mapping $\mathbf \phi$ which maps input space to some space $Z$, we ...
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### How to compare continuous variable and dichotomous variable and means differences

I have run an experiment on perceived size of discs in peripheral view. Participants had to adjust the peripheral disc in order to match it to a central one (fixed size). People performed the task ...
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### Finding the dimension of the reward matrix in an inverse reinforcement learning problem

In one of the easy cases of inverse reinforcement learning, we try to derive the unknown reward function assuming that an optimal policy is known and MDP is completely known. Let $P_{a_1}$ be the ...
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### Averaging Cumulative Distribution Function

I have several (x,y) datasets which form various CDF curves. These are generated by cross-validating models built with different parameters. For example: ...
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### Accounting for time series correlation in power calculations

we want to do power calculations for a clustered RCT design household survey. We have a good idea for cross-sectional ICC from a similar earlier survey in the same study area. However, this time we ...
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### Interpretation of Principal Component Analysis Results

I have a 13-item, 5-point Likert-type scale that I have put together from similar questions used in the literature (n = 96). What is the best way to analyse my scale data? Step-by-step, what I have ...
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### True signs of coefficient of variables in multiple regression [duplicate]

I do multiple regression (y ~ x1 + x2 + x3) where independent variables come up with positive and negative coefficients. However when i do the simple regression for each independent variable ...
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### Copula vs conditional distribution

Let $\xi_1,\xi_2$ be two real-valued random variables with joint distribution $P$. The latter gives us marginals $p_1,p_2$ conditional distribution $p_{12},p_{21}$ and the copula $C$. The latter ...
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### Number of values needed to distinguish two distributions

I have two normal distributions ($A$ and $B$). I know the standard deviation of both distributions ($σ_A$ and $σ_B$). I want to find out how many data points ($n$) I will need to be able to ...
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### Problems with probabilistic PCA implementation

I am trying to implement the probabilistic PCA, and I am having some troubles with the code. The fact is that the plots seem to select a sensible principal component, but the result is a bit different ...
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### Why is this basic LinearSVC (from sklearn) prediction example inaccurate?

Using the LinearSVC from sklearn, the following code predicts the class 3 where you might reasonably expect a 2 (as a vanilla SVC does), what's going on? X is the input vector, y the classes for ...
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### error when running JAGS

In an attempt to learn JAGS I am trying to fit a line to data points. The data points have errors in both directions i.e. along the xaxis and yaxis. Here is my model: ...
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### Generalized eta squared or Cohen's d with trimmed means

For my analysis I am currently running a 1-way within-subjects bootstrapped ANOVA with trimmed means (rmanovab from Rand Wilcox's ...
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### Regression: Scatterplot with low R squared and high p-values

Based on three datasets, I have produced the scatterplot below in Python: I am trying to fit a line on each dataset, but when I check the metrics this is what I get: Set 1 (red): R squared=0.002, ...
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### Truncated Dirichlet process vs Dirichlet distribution

As the topic suggests I was wondering what the main differences are in using one over the other. Suppose for sake of simplicity the Dirichlet distribution has all parameters set to $\alpha$. All I ...
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### Understanding Linear Discriminant Analysis in a bayesian setting

I present the current understand I have of linear discriminant analysis (LDA) in a bayesian setting, and then ask questions where I am stuck. I will discuss LDA for a two-class classification problem. ...
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### How can I asess performance of a semi-supervised learning method?

I'm working with a semi-supervised learning task, where I only have positive and unlabelled data (PU learning). I've tested a few algorithms and would like to assess their performance. For ...
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### Interpretation of results from Johansen's co-integration test

I am not able to interpret the following result output for gretl for co-integration: Rank $\$ Eigenvalue $\ \$ Trace test $\ \$ p-value $\ \$ Lmax test $\$ p-value 0 $\ \ \ \ \ \ \$ 0.032753 ...
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### Compare proportions between two groups on multi-categorical variable

I have a case-control study where I have a variable measures social deprivation into 5 categories 1, 2, 3, 4, 5. I want to compare if there is any significant different between the case and controls ...
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### Generalising correlation-based feature selection

One method to perform feature selection consists in calculating Pearson's correlation coefficient between each explanatory variable $X_i$ and the response variable $Y$. Then the absolute values of the ...
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### MCMC with dependent variables

I want to run Metropolis-Hastings on a problem which involves two parameters that are not independent. I.e. I want to estimate both of these parameters. At the moment I'm trying to understand if this ...
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### Does it make sense to exclude “good” predictions to understand the main drivers of difference between test and predictions?

With regards to the problem explained in this other question How to model the discrepancy between test result and prediction code, and find the main sources of discrepancy I've been asked to exclude ...
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### Non-parametric test that takes mean difference into account

I've the expression value for 20 genes of interest in 50 samples (10 treated, 40 untreated). I have to use a non-parametric test as my data are non-normal. So my first idea was to use Mann-Whitney U ...
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### Showing that chapman-kolmogorov ewuations are satisfied [on hold]

Let x(t) be a markov process woth the state space (0,1) and transition probabilities (T)=1/2{1+(-1)^x+y e^-2t}
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### Optimal matching with caliper in MatchIt package in R

I am using the package MatchIt in R to perform propensity score matching. The command is ...
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### What is the difference between Statistics and Data Science? [on hold]

I am not really a newbie in statistics, but I ain't an expert either. I have always been wondering what exactly is the difference between Statistics and Data Science and for that matter, how is a ...
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### Computing Seasonality Index and application to shorter time series

Background: I have an overall time series of close to 3 years of data. I need to forecast for different slices of data. When I slice the data, some slices results in a shorter time series. We go with ...
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### Sum of N Gamma distributed random variables being N another distribution random variable [duplicate]

Let $X$ a gamma-distributed random variable having scale $θ$ and shape $k$: $$X \sim \Gamma(k, \theta) \equiv \textrm{Gamma}(k, \theta)$$ with probability density function  f(x;k,\theta) = ...
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### Understand outer cross validation with caret in R

I have a question that I cannot solve. Sorry if it is too naive, I am a beginner. I have a data set from wich I would like to predict a continuous variable Y based on a set of features. By now I ...
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### Drawbacks of replacing a factor by average value of the target

I have to encode a lot of factors before feeding them to a gradient boosting algorithm. I noticed that the best method was to encode them replacing them with the average value of the target when this ...