Questions tagged [risk]

Risk has several meanings in different contexts within statistics

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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 ...
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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 ...
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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 ...
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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 ...
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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....
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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 ...
178 views

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 ...
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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 ...
990 views

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 ...
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Copula-based Value-at-risk in R

I'm working on a value-at-risk calculation using copulas on different stock market indices. I know how to fit the copula, but I can't figure out how to apply the VaR approach in the next step. The ...
738 views

Calculating the risk of an estimator using zero-one loss

Consider two observations where $$P_\theta(x=\theta+1)=P_\theta(x=\theta-1)=0.5,\ \ \theta\in\mathbb{R}$$Let $\mathbb{D}=\Theta=\mathbb{R}$ the decision space. Suppose that the associated loss ...
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Bayesian Risk and Subjectivity

I am studying the differences in bayesian and frequentist approaches to point estimation. I understand that there are objective and subjective approaches to Bayesian and some people don't like the ...
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Bayes risk of Normal-Normal model

Consider $x\sim N(\theta,1)$ and $\theta\sim N(0,n)$. Show that the Bayes risk is equal to $\frac{n}{n+1}$. I know that r(\theta,\delta)=\int_\chi\int_\Theta L(\theta,\delta(x))\pi(\theta|x)d\...
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Interpretation of standard deviation if data is not normally distributed

This is very basic question. But I want to know how one can interpret the standard deviation if data is not normally distributed. My concern is regarding financial market. Investors generally use ...
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Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
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How to estimate the probability that the mean of an unknown distribution is over a threshold given small sample size

I am trying to quantify my concerns regarding a proposed incinerator in our community. The company is basing its potential to emit dioxins (a class of chlorinated organic compounds with a reference ...
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Where did this risk exposure 'estimation-formula' come from?

I was reading a book and the authors metioned that risk exposure can be estimated scientifically using this forumula: $risk(\$) = \frac{(a + 4m + b)}{6}$and standard deviation$\sigma = \frac{b-a}{...
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How does probability of default evolve over time?

Say I have a probability of default of 0.02 (which is annual so over next year) for a certain client. Then say this client takes out a 180 day loan, how can I adjust my probability of default for this ...
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Convert classifier output for disease to probability using Bayes

Method 1 I am given a classifier for some disease that takes as input patient characteristics and has some sensitivity and specificity. Hence the classifier is a function c(patient characteristics) ...
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Empirical Risk Minimization: empirical vs expected and true vs surrogate

In Tie-Yan Liu's book, he says that in a statistical learning theory for empirical risk minimization has to observe four risk functions: We also need to deﬁne the true loss of the learning problem, ...
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Conditional correlation, copula, portfolio optimization and diversification

I have a data set which consists of > 500 hedge funds, their historical monthly returns, and their benchmark (index) monthly returns. The number of data points (# of monthly returns) differs from a ...
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Predict probability of rare event

Let's say I have a dataset about passages of cars on a road. The dataset contains information about time, driver, car, weather, and most importantly whether the car was involved in an accident. Of ...
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How to find a conditional probability using copula-based Markov process?

I have a monthly time series of a water quality parameter. I used copula-based Markov process of C(Y(t), Y(t-1) and I forecasted the mean behavior of Yt by following equation: Now, I need to find ...