Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [risk]

Risk has several meanings in different contexts within statistics

Risk has several meanings in different contexts within statistics and is often used in combination with other terms, such as Bayes risk.

According to Everitt & Skrondal (2002), risk is a term often used in medicine for the probability that an event will occur, for example, that a person will become ill, will die, etc. In decision theory, risk describes a situation in which an agent is facing a random variable with known outcomes and their probabilities (Luce & Raiffa, 1958) or either known or unknown probabilities that exist and can be estimated or somehow else arrived at (Knight, 1921).

References:

  • Everitt, B., & Skrondal, A. (2002). The Cambridge Dictionary of Statistics (Vol. 106). Cambridge: Cambridge University Press.
  • Knight, F. H. (1921). Risk, uncertainty and profit (Vol. 31). Houghton Mifflin.
  • Luce, R. D., & Raiffa, H. (1958). Games and Decisions: Introduction and Critical Survey. New York: Wiley.
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Is it wrong to rephrase "1 in 80 deaths is caused by a car accident" as "1 in 80 people die as a result of a car accident?"

Statement One (S1): "One in 80 deaths is caused by a car accident." Statement Two (S2): "One in 80 people dies as a result of a car accident." Now, I personally don't see very much difference at all between these two statements. When writing, I…
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Implementation of CoVaR (a systemic risk measure) in R

I'm trying to estimate CoVaR using bivariate DCC GARCH in R. The concept of CoVaR is the dependence adjusted of VaR, which was first introduced by Adrian and Brunnermeier (2011). However, this original definition of CoVaR presented some limitations,…
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Example Of Strict von Neumann Inequality

Let $r(\pi, \delta)$ denote the Bayes risk of an estimator $\delta$ with respect to a prior $\pi$, let $\Pi$ denote the set of all priors on the parameter space $\Theta$, and let $\Delta$ denote the set of all (possibly randomized) decision rules.…
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Different definitions of Bayes risk

I'm having trouble understanding the proper definition of Bayes risk. Let the data/variate $x \sim P(X|\theta)$, $\theta\in \Theta$, $\pi$ be a distribution on $\Theta$ (prior), $\hat \theta(x)$ be an estimator of $\theta$ based on a variates $x$,…
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Model fitting vs minimizing expected risk

I'm confused about the mechanics of model fitting vs minimizing risk in decision theory. There's numerous resources online, but I can't seem to find a straight answer regarding what I'm confused about. Model fitting (via e.g. maximum…
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How does an estimator that minimizes a weighted sum of squared bias and variance fit into decision theory?

Okay--my original message failed to elicit a response; so, let me put the question a differently. I will start by explaining my understanding of estimation from a decision theoretic perspective. I have no formal training and it would not surprise me…
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Is there a word for the phenomenon that the old are generally less affected by risk factors?

In epidemiology, this occurs often: Old people are less prone to the influence of risk factors. For example, the Framingham risk score, which tries to estimate cardiovascular risk, gives 8 or 9 points to smokers in their twenties and thirties, but…
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How to calculate 95% CI of vaccine with 90% efficacy?

A vaccine is reported in the news to have 90% efficacy. I'd like to know how much confidence there is in that efficacy measure. The protocol for this reports that a vaccine or placebo was administered to 43538 patients. Half received the vaccine,…
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Case-mix adjustment versus risk adjustment, what are their differences in practice and objective?

I have encountered in swathes of medical literature the use of the terms "case-mix" and "risk" adjustment without any citations or explanations of their exact usage and motivation from a modeling perspective. I understand the principles of covariate…
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Computing VaR with AR-GARCH

I have the following AR(1)-GARCH(1,1) model for the daily returns $r_t$ $$r_t=\theta r_{t-1}+u_t\;\;\;u_t=\sigma_t\epsilon_t\;\;\;\sigma_t^2=\omega+\alpha u_{t-1}^2+\beta \sigma_{t-1}^2 $$ where $-1<\theta<1$, $\theta \neq0$, $\omega>0$,…
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Credit Risk and Concentration

I am working with a UK credit-union and we are looking to build a model to assess our credit risk and changes to this over time. We have a number of loans to borrowers who each have a credit rating (lets say these are banded A, AA, AAA, B, BBB,…
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Cross entropy vs KL divergence: What's minimized directly in practice?

My understanding is that in ML one can establish a connection between these quantities using the following line of reasoning: Assuming we plan to use ML to make decisions, we choose to minimize our Risk against a well defined loss function that…
Josh
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Why is the risk function defined to be the expectation of loss function?

In decision theory, we define the risk associated with a particular predictor function as the expected value of the loss function. Since the input and output are considered random variables therefore the loss function is also a random variable. I…
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Mapping Frequentist Risk Notation to Regression

The frequentist risk in literature is defined as follows: $R(\theta, \delta) = E_{X|\theta} L(\theta,\delta(x)) = \int L(\theta,\delta(x)) p(x|\theta) dx$ This risk is focused on the quality of the estimate of $\theta$ parameter. In a predictive…
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Why is empirical risk minimization prone to overfitting?

According to Chapter 8 of the book Deep Learning, "..empirical risk minimization is prone to overfitting. models with high capacity can simply memorize the training se." My question why is it so? Models with high capacity can also memorise the…
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