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Bayesian inference out of partial information - Dirichlet example

Suppose we have two coins $X_1$ and $X_2$. They are possibly biased and correlated coins. The heads probability of each coins is denoted by $p_1$ and $p_2$ which we don't know at the beginning. The ...
0
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1answer
40 views

Bayes formula alternate expression using alpha

I know that Bayes theorem is: Posterior = Likelihood * Prior / Evidence However, I am confused about the above notation in the picture. How do we get to the above three notation? How does ...
3
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1answer
104 views

How is MAP 'not invariant to reparametrization'? [duplicate]

I was watching a lecture on coursera on 'Bayesian Methods on Machine Learning' and I came across a statement that: MAP(Maximum a posteriori) is not invariant to reparametrization. I didn't quite ...
0
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2answers
38 views

Understanding Product of individual PDF for Joint PDF

Let's say that we make multiple noisy observation from a sensor node where $h$ is the parameter we want to deduce and $v$ is the noise. $$y[k] = h + v , k=[0,1,..n] $$ Question: The PDF for each ...
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0answers
30 views

Recommended textbooks for student majoring in applied statistics [duplicate]

I am currently a second year science student double majoring in biochemistry and applied statistics. The stats course im doing this semester (Statistical Theory) is focused on joint probability ...
0
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1answer
27 views

I was doing this course ' Bayesian Methods for machine learning' on coursera and I got stuck on few conditional statements expansion and manipulation

I have doubt in three conditional expansions : How is P(w,y|x) = P(y|w,x).P(w) ? How is P(w|y,x) = P(y,w|x)/P(y|x) ? How is <...
0
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2answers
57 views

Relationship between mean and variance of samples

I am thinking about the relationship between sample mean and variance in an example. If we want to look at the average goals per month for a soccer team. And we have mean and variance of goals for ...
4
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1answer
43 views

Motivations for experiment design in statistical learning?

My interests in statistics centre around statistical learning, including Bayesian inference, inference in combinatorial spaces, Monte Carlo methods, Markov decision processes, modeling stochastic ...
0
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0answers
16 views

Robust Expectation-Maximization?

The Expectation-Maximization (EM) algorithm is useful for applying the Maximum Likelihood Estimation (MLE) when there exist latent (hidden) variables in the model. However, when dealing with outliers, ...
3
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0answers
35 views

Who invented train/validation/Test method and when?

I can't seem to find here or in other places the earliest source for this method. it seems the holdout method was separately proposed by Highleyman in 1962, and cross validation was separately ...
0
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1answer
20 views

Causal Inference in Mortality Rates

I was wondering how does one study the average treatment affect in scenarios suchs as mortality rates. For example: suppose we want to study the effect that a certain medicine has on the mortality ...
1
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1answer
51 views

How to generate more samples from a dataset

My question is simple: I have a dataset with multiple numerical features (let's say 1500 data points with 7 features). The question is the following: ...
0
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0answers
10 views

What is the suitable distance function for zero-inflated matrix?

I have a feature matrix, where the columns correspond to the features and the rows are the data points. My matrix is zero-inflated, meaning there are many false-negative zero entries in my matrix. I ...
1
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1answer
21 views

Extracting useful metrics from price info

First, an admission: my stats knowledge is minimal - purely practical applications in a fairly narrow range. I'm mostly a mechanic with a good bit of experience building and wrenching on ML/DS systems ...
0
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0answers
15 views

A measure of confidence given data with known variation coefficient

I need to create a classification model to diagnose a certain illness, for that i have been given a dataset of 7 analytes (medical features) with known variation coefficients due to biological ...
0
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1answer
33 views

How can I normalize Bayesian Network query result?

While taking a Bayesian network tutorial on YouTube, I was watching a video explaining the Bayesian Network probability inference. Somehow, at the end of the tutorial, the lecturer did not explain how ...
0
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1answer
292 views

If the VIF is 2 then what is the value of correlation coefficient $R^2$

If variance inflation factor is 2 what is the value of correlation coefficient $R^2$? $$VIF = \frac{1}{1-R^2}$$ Given $VIF =2$, then is this calculation correct? $$\begin{align} 2 &= \frac{1}{1-...
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0answers
14 views

In the fully supervised case, provided we have contingency matrices, is Bayesian inference the optimal method?

BACKGROUND Imagine that we have contingency matrices, i.e., counts or frequencies, linking the features (say, columns) and targets (rows). One could then compute the posterior probabilities, i.e., ...
0
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0answers
14 views

Machine learning: is the effect of one predictor adjusted for the others?

In machine learning - notably ensemble methods such as random forest, gradient boosting, extreme gradient boosting etc - can we say that the effect obtained for one predictor is ADJUSTED for all other ...
0
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0answers
40 views

relation among loss function / MLE / Bayesian estimation

I have read a lot of stuff on the relation between minimizing a loss function / maximizing the likelihood / choose a centrality measure of the posterior (Bayesian estimation); but I cannot see a clear ...
0
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0answers
22 views

Extracting likelihoods from generative model

I am looking for papers dealing with the extraction of explicit descriptions of probability distributions from a generative model. My use case is the following: I trained a GAN to generate samples ...
0
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1answer
28 views

What is a factor in the context of Bayesian networks and inference?

I have come across the term "factor" in the context of Bayesian networks and inference (which I am not very familiar with). I've also heard of the expression "factor graph", which is an undirected ...
0
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0answers
57 views

Advantages of Wasserstein barycenters

Which are the advantages of using Wasserstein distance when averaging many probability distribution estimates? How does uncertainty of each affects the computation of the barycenter? Does the ...
0
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1answer
106 views

Chi Square Analysis Throws Error - The internally computed table of expected frequencies has a zero element at (0,)

I am trying to see the association between two variables. I used Chi-Square analysis in Scipy package in Python. Here is the crosstab result of the two variables: ...
2
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1answer
67 views

Best Course of Study for Data-Science/Statistician Interviews [closed]

This is my first question here, so please pardon my gaffes. I am currently working as a Data-Scientist, a position which I worked up from Junior Analyst position.My bachelors is in Computer Science ...
0
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1answer
19 views

Optimizing multiple objectives with different scales

I have multiple objectives, such as $f(\mathbf{x})$, $g(\mathbf{x})$, and $h(\mathbf{x})$. I would like to find a set of $x$ that can $\underset{\mathbf{x}}{argmin} [ f(\mathbf{x}) + g(\mathbf{x}) + ...
0
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0answers
23 views

How to statistically infer common pattern in text

Am trying to solve a problem where I need to infer common patterns in text for example, the data below, with bare eyes it can be noticed there is a pattern and that is ...
5
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2answers
612 views

Differences between prior distribution and prior predictive distribution?

While studying Bayesian statistics, somehow I am facing a problem to understand the differences between prior distribution and prior predictive distribution. Prior distribution is sort of fine to ...
2
votes
1answer
105 views

K - means, expected shape of the curve [closed]

I want to understand what happens as we increase the number of clusters using k- means, what is the expected shape of the curve showing the average distance between points and their assigned clusters? ...
1
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0answers
35 views

Understanding probabilistic inference graphs

I am having trouble understanding inference graphs. In the diagram below I understand the graph on the left (forward graph) where the arrows describe the direction that data flows when training for ...
0
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0answers
14 views

Getting parameters of new distribution after moment matching using expectation propagation

In this paper, the authors apply Expectation Propagation for feature selection. However, I don't understand how to get the analytical expression from equation 25. They say: The right-hand side of (...
2
votes
1answer
223 views

Using logistic regression scores for inference

I'm training the logistic regression for binary classification on a labeled data set. Now I'm using the same entries and predict their scores using the model. For example, I have an entry with label ...
0
votes
1answer
26 views

Correct Type of Statistical/Machine Learning Analysis For Inflow

I want to predict the number of people joining (inflow e.g. 4000, 5000, 6000 etc) online subscription. The dependent variable is ‘inflow in the first 4 weeks for a certain content title’ as this is ...
3
votes
2answers
138 views

Independence of events in real-life data

Most of statistical methods (if not all) rely on independence of events. How do we know that this assumption is valid in real-life problems like clinical trials or web crawling? What might be the ...
-1
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1answer
115 views

Is Maximum Likelihood Estimation the median? [closed]

I asked what maximum likelihood estimation to a friend of mine. He told me that it is the median which I don't understand.
0
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0answers
23 views

How important is research on model selection methods in Statistics?

My question is nothing technical. I just wanted your opinion on how important is the model selection problem in the field of Statistics considering the age of big data. Are the current methods such as ...
1
vote
1answer
64 views

How can I use linear/logistic regression for inference with colinear variables and a smallish dataset?

I have a dataset of around 120 observations, with 30 calculated variables and I am trying to predict a continuous response (result of an experiment) using those 30 variables. Ideally the smallest ...
0
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2answers
24 views

How can I predict the value after a point with a short time of data?

I have a customer's online data. I have data such as the number of items purchased by the customer, the number and number of keyword queries for the customer, the age of the customer, the residential ...
0
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0answers
311 views

Step-by-step tutorials on Bayesian Networks

I'm trying to study Bayesian Networks (BN), but during classes [1] we covered just some theory and no exercises were given. Therefore I'm looking for step-by-step tutorials or solved exercises for BN ...
0
votes
1answer
102 views

Why use the square transform to reduce left skew?

Suppose all the data is positive. Squaring it means that the bigger values in the hump will get multiplied by a bigger number than the smaller values in the tail. Doesn't that just exacerbate the ...
1
vote
1answer
62 views

Rules based Model (Function) - Derive Probability & Ensembling

Basically, let's assume I have a simple rules-based function/model (if weight >= 150) -> return true. Simple binary answer (true or false) from a single feature input. If I have a range of samples/...
0
votes
1answer
93 views

How to handle 'unfairness' of missing data in machine learning?

Let me explain what I mean by unfairness. Let's say I have a multi-class classification problem where I am trying to predict the 'best drug' (among multiple candidate drugs) for each patient. So ...
1
vote
1answer
67 views

Objective function of Bayesian Model Averaging

I am quite confused about the objective function of the bayesian model averaging in the paper "Bayesian Averaging of Classifiers and the overfitting Problem".1 On the section 2, here is the first ...
0
votes
1answer
43 views

Train a model on a “fleet” of related datasets

Suppose I have a machine that has some output behavior y over some independent variable x. I set up a predictive model to predict the value of y for an arbitrary x and it's working well. Then I get ...
0
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0answers
13 views

Can we calculate the best possible test set loss given the information in the training set?

Given a training set and a test set for machine learning, I am wondering if I can somehow measure if the information to predict the labels of the test set correctly is present in the training set. In ...
2
votes
2answers
217 views

Intersections of chemistry and statistics

I am asking this question for a friend who knows a lot of chemistry and is now studying statistics, primarily since he heard this is the age of data and one should know statistics. However, he is ...
0
votes
0answers
36 views

How to include new data into existing algorithm?

I have a complex ensembel algorithm X (divide data with k means that learn ensembel for each subgroup). Learning time of X is approx. 20 hours. I cannot afford to relearn algorithm for every new ...
0
votes
1answer
80 views

Does mutual information capture interactions?

Suppose I have a response $Y$ and two features, $X$ and $Z$. Individually the features are not very predictive but their interaction is strongly predictive. Something like $$Y = 0.5X + 0.5Z + 20XZ + \...
1
vote
0answers
18 views

Help with computing message on TrueSkill factor graph

I want to better understand the step for calculating the message from the game factor $h_{g}$ down to the difference variable $d_g$ on the TrueSkill factor. Such message is shown in the Rasmussen's ...
0
votes
1answer
81 views

Approximate a CDF

Suppose we have $n$ equations with an integral of the form $\int_0^{x_i} F(z)dz = c_i,\ i=1,\ldots,n$ where $F(y)=\mathbb{P}(X \le y)$ is an unknown cumulative distribution function of a non-negative ...