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How do you derive the equation (1.69) from (1.68) in "Bishop Pattern Recognition and Machine Learning" page 31

I've been told that I needed to do completing square but I have no idea on how to do it.
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0 answers
2 views

Spatial Statistics (for mathematicians) lecture notes request

I'm currently doing a master's in mathematics, and I'm interested in spatial statistics, mainly for a project. Unfortunately, it seems impossible to find lecture notes on this topic. I have seen some ...
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0 answers
8 views

How to control for gender when looking at group differences with a 4-level factor (ANCOVA)?

So I have a dataset with 4 distinct groups, and I am trying to see if there is a difference between these groups on a dependent variable Y which is cardiorespiratory fitness. I did an ANCOVA and added ...
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10 views

The bayes estimator of Bernoulli model with constant prior

I'm currently reading "All of statistics" by Larry A. Wasserman. In the chapter on statistical decision theory, we are given the following example: Consider the Bernoulli model with loss ...
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Is it better to drop rows with Missing at Random if it's more than 10% of the population?

My goal is to understand when I need to: Mean imputation. Median imputation. Drop the rows. The problem is, I did not have proper statistical knowledge. I just jumped to this industry 8 weeks ago. ...
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Test if two dependent, unequal size samples are from the same distribution

I read Non-parametric test if two samples are drawn from the same distribution and have tried permutation test, KS test The issue is I have data of different sample size that are collected from the ...
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0 answers
11 views

exercise autocovariance function

I don't know how to obtain the autocovariance function of the following process, having a multiplication makes it difficult for me. $X_t = Z_t + \theta Z_tZ_{t-1}$ with $Z_i \sim N(0, \sigma^2)$ (...
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0 answers
14 views

How can I discover similar or resembling sets by a statistical method?

Let say, I have such m datasets: ...
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1 answer
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Why is the pooled variance calculated using the variation of the two tested groups?

When comparing between two populations, or two groups from the same population, a t-test assumes that both those groups have the same variance. However, a t-test works by using the pooled variance ...
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1 answer
24 views

Generalized linear models (GLMs)

Let's say, I want to establish a relation between the distribution of $Y$ and $p$ covariates. I denote the covariates with $x_1,x_2,...,x_p$. Then, I denote the linear predictor with $\eta$ , where $\...
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What is a good dissimilarity on rooted ordered labeled trees with probabilities on the leaves?

Consider a rooted ordered labeled tree that is "binary" in that there are at most two children of any vertex and whose leaves are decorated with probabilities (the sum of the leaf ...
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7 views

Comparing multiple regression models vs. using covariate

I have found from previous data that men and women differ significantly in the way that they interact with my variables. I now want to make a regression model trying to ascertain the interactions ...
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0 answers
8 views

Freezing parts of neural net depending on classification label

I have a classification model that is trained to predict the probability of approve/reject on an object, and we use the output of the final sigmoid as our final score to rank these object. These ...
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7 views

How to compute the decrease in impurity in tree regression?

I fitted a regression tree using rpart function. The summary of this model is provided below. I need to know how to calculate the decrease in impurity in each node. For example, in the node number 1, ...
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Paired data machine learning classifier

I have a training dataset of 153 observations (3 times repeated measures in 51 individuals) and 84 variables. The dataset is processed for a classification issue. By the 84 variables, there is 53 ...
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How to solve a multi-class and multi-label classification?

im trying to classify a picture of columns with 4 squares that need to be marked and 26 question that represent a Multi Choice Question exam each question labeled like this: [],[],[],[X] -> 1, [X],[...
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Finding uncertainties of a measured quantity when the distribution of the measured data points is not symmetric

If I have a set of data points and they do not take up the form of a symmetric distribution when i plot them as a histogram. Then, can I calculate the mean and standard deviation from their usual ...
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29 views

What does "true mean is not equal to 0" mean in R?

I'm doing test for set a data and a statement appears true mean is not equal to 0 What does it mean? ...
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0 answers
13 views

(R e1071) Why attr() of predict(svm, probabilties=TRUE) returns NULL [closed]

svm1=svm(Species~., data=iris, probability=T) svm1.pred=predict(svm1, data=iris, probability=T) str(svm1.pred) attr(svm1.pred,"probabilities") I tried ...
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Optimization of Box-Cox and Yeo-Johnson Log-Likelihood function

This question is a continuation of this question: Derivation of Box-Cox and Yeo-Johnson Log-Likelihood Functions. In order to derive the maximum lambda value in log-likelihood objective function for ...
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Choosing the right statistical method - predictors for Knee function

I am new to statistics and I am struggling to choose the right statistical method for my work. I am trying to determine predictors for knee function after a specific type of knee surgery. I have a ...
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0 answers
6 views

Imputing entirely missing rows omics data

I have a dataset of 153 observations and 84 variables. The dataset is processed for a classification issue. Observation are three time repeated measures of radiomics in 3 different regions of a soft ...
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Mediation analysis: How to interpret indirect significant effect + direct insignificant effect?

I have a Question regarding Mediation analysis. The thing is, my results surprise me. X- Time pressure Y- Proactive work behavior M- Stress Results are: The effect of X (independent variable) on Y (...
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How to test if $x_1$ has a positive partial effect on $y$ taking into account the linear and quadratic components of $x_1$?

I have a quadratic population model of the form: $y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_1^2+\mu$ I want to test if $x_1$ has a positive partial effect on $y$. How can I run such a hypothesis test ...
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0 answers
20 views

Manual calculation of ARIMA(2,1,1) forecast

I'm trying to calculate manual forecast of dataset using python generated ARIMA(2,1,1) coefficients for small testing dataset that contain 10 points. Python gives me ...
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-2 votes
0 answers
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How to solve this problem? [closed]

Problem 1. The stress-life data for one material is given in the following table for fully reversed loading. Stress range (MPa) Life (cycles) 397.536 212454.2243 359.7439 312653.943 ...
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Does measurement non-invariance between groups matter in difference-in-difference designs?

Claim: If a measure has a difference in measurement invariance (i.e. the measures are non-invariant) between two groups (say treatment and control), which is constant across time, then a difference-...
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10 views

How do I reduce the rmse while performing multiple linear regression?

So I have a dataset which has 84 rows and 18 predictors. I need to predict Annual_salary based on the data provided. I did create a model after changing all the categorical variables to factors. Then ...
3 votes
1 answer
56 views

A reasonable number of covariates after variable selection in a regression model

I read an unpublished paper. There is a regression model with about 20 covariates. The authors use a stepwise variable selection method and come to a model with two covariates with small p-values. The ...
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14 views

Why did my arima model predict like average?

I tried to predict this data with arima; And my prediction of last samples appeared like below; My code is; ...
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0 answers
7 views

Why do GAMMs provide random effect significance tests while GLMMs do not?

Motivating Question I was fitting some models in R and recalled that significance terms are shown for random effects in the mgcv package for Generalized Additive ...
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1 answer
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Get label names from loaded model in sklearn

Is it possible to get the label names from an sklearn SGDClassifier model that is loaded from a pickle file? ...
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0 answers
10 views

Using Gibbs sampling to verify the analytical solution of 2D Ising Model

Suppose a 2-D Ising model on a period lattice $L\times L.$ I want to apply Gibbs sampling to verify the analytic solution of spontaneous magnetization in 2D Ising model given the Hamiltonian $H=-J\...
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How do I create a table showing my diminishing regression and analyze such a table?

I am currently working on a project for my graduate course on international conflict and peace, and in my project I ran a lagged, diminishing return regression regarding security assistance. My main ...
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17 views

Non-numeric argument to binary operator

I'm trying to find out a model that adequately describes effects of gender and length on food choice. For gender; 0=Male and 1=Female, length; 0=Subadult 1=Adult, Choice; F=Fish I=Invertebrates and O=...
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1 vote
1 answer
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How to prove that this statistic is not sufficient? [duplicate]

Problem. Given $X_1,X_2,X_3$ a random sample from the Bernoulli distribution with success $\theta$, show that the statistic $T= X_1+2X_2+3X_3$ is not sufficient. My attempt When I try to apply the ...
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1 vote
0 answers
14 views

Nested random effect, and converting from R formula syntax to math

I have an experiment where I am looking at species-specific responses to a treatment application. Within each species, I have 3 genotypes, arbitrarily chosen to ensure we aren't detecting genotype-...
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0 answers
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R wilcox test result conflict

I have gotten R Wilcox test results I do not understand. Comparing two non-Normal independent sets of ~500 ages. The p-value ~.17 but results is "alternative hypothesis: true location shift is ...
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0 answers
10 views

Testing for significant difference in mortality rate between 3 groups across 3 stages

I am looking for a way to check if there is a significant difference between mortality of egg embryos across three groups (DYF1- double yolk with one embryo; DYF2 - double yolk with two embryos; ...
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0 votes
0 answers
12 views

Have Average Stat of Category; Want Likelihood of Category Based on Stat

This is technically a baseball question, but no baseball knowledge is needed. I have a list here of the average OPS (an offensive stat, the range) by position in baseball (the "variable", in ...
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2 votes
1 answer
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bias-variance decomposition for OLS

Section 7.3 of Elements of Statistical Learning (2nd edition) gives the bias-variance decomposition for OLS prediction first for a single input $x_0$, and then averaged over a set of inputs $x_1, \...
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8 votes
1 answer
92 views

Minimax estimator for geometric distribution

I'm trying to solve this problem: Let $X$ be a single sample from Geo($p$) where $p ∈ (0, 1)$. Find a minimax estimator for $p$ under the loss $L(p, δ(x)) = (p−δ(x))^2/ p(1−p)$ . I'm trying to put ...
2 votes
1 answer
20 views

What is the benefit of using Newey-West when there is no impact on the coefficient estimates in OLS?

Since my residuals failed the test for heteroscedasticity and autocorrelation, what is the benefit of using Newey-West when there is no impact on the coefficient estimates in OLS? Does the Newey-West ...
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1 vote
0 answers
14 views

Is reaching perfect performance on the training set feasible for large neural networks in regression?

Suppose I have a large training sample, say a million observations, and want to perform regression with a large ReLU-activated neural network (both deep and wide, with many times more parameters than ...
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0 answers
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Can I use Information Value in a ML algorithm like random forest?

I have a logistic regression model used in credit scoring and I am studying the metrics used in the credit scoring field to evaluate the quality of the model. My ultimate objective is to understand if ...
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0 answers
7 views

Summarizing effect of a predictor in logistic regression

Prediction equation for proabibiltiy $\pi$ of a win in a game for a player with predictors $X_1,X_2,X_3$ of which $X_1,X_2$ are continuous and $X_3$ is binary with values $0$ or $1$ is given as $$\...
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2 votes
1 answer
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How to interpret a small regression coefficient with a p-value of 0.01 in an OLS model?

I have built a multiple regression and estimated it using OLS. All the variables are significant. One of the coefficients is close to zero (around 0.0003) with a significant p-value of 0.01. How to ...
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0 votes
0 answers
12 views

What is the difference between Linear Regression and Support Vector Regression?

My goal is to understand the advantages of Support Vector Machine. What I have in mind is that Support Vector Machine can have kernel Radial Basis Function ie ...
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0 votes
0 answers
11 views

How to conduct an orthogonal transformation? [closed]

Our professor advised us to use OLS even if ardl is fine in estimating the long-run and short-run estimates and identifying if ekc exists in our country. So the problem of multicollinearity exists ...
-1 votes
0 answers
11 views

I don't know how to find a numerical solution using deSolve in this code [closed]

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