Questions tagged [risk]
Risk has several meanings in different contexts within statistics
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How to compute the combined probability of loss for 2 time series (consisting of historical stock prices)?
May I please ask the community's support with the following problem?
I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily ...
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26 views
Why FZ0 loss function will leave log(-e) term when forecasts have no error? Can FZ0 loss function formula be interpreted simply?
I'm working on my thesis about using FZ0 loss function for estimating the model parameter. And I have trouble with interpreting why FZ0 loss function have this form.
Fissler and Ziegel(2016) had ...
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9 views
Hazard X population density
Not quite able to calculate risk ... I know the hazard across a given geographic region (probability an intensity threshold will be exceeded in a given window of time) and I know the population ...
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1answer
14 views
Predict risk from pre-trained Cox PH model
I came accross this article about AMD (age-related macular degeneration, a kind of eye diseases) recently. The article fitted a Cox PH model to predict risk of disease advancing to advanced stage. The ...
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75 views
Why do we need the concept of Risk in Bayesian Decision theory?
I'm studying Bayesian decision theory as introduction to machine learning and I see the concept of Risk in a lot of places. In the course I read, they define risk as:
Risk is the expected error ...
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79 views
What is the difference between the risk function used in Bayesian inference and the one used in supervised learning?
In the context of Bayesian inference, given
the random parameter $\Theta$,
the observed data $\mathcal{D} = \{x_1,x_2,\dots,x_N\}$,
the posterior $p(\theta\mid \mathcal{D})$,
the estimator $\hat\...
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2answers
20 views
Combined relative risk in meta study
I am looking at a meta study, and I've never done one (or looked at it much) before. From what I've learned about it so far, the way you calculate the compounded effect is by first calculating this $\...
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14 views
Jump diffusion -advantages
What would people say is the advantage of using a Merton jump-diffusion model, in terms of what it models and it's key characteristics/ features?
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110 views
Convergence of Empirical Risk Minimizer and True Risk Minimizer
Let $D:= \{ (x_1, y_1), \dots, (x_n, y_n) | x_i \in \mathbb{R}^d, y\in\mathbb{R}\}$ be our dataset.
Let $F$ be some function class and $f\in F$.
Furthermore, $l$ is some loss function. E.g. the ...
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23 views
Risk function equation
How to show risk function = (3-theta)^2? I tried using the mean squared error formula to no avail.
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7 views
Delinquency pre strategy implementation
I have recently implemented a new strategy for our bank customers where the customers cannot take any advance from the bank after x% of their limit
Question- Now let us suppose if the delinquency rate ...
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9 views
Cramer Lundberg risk model
I am trying to apply this model real situation. I can not understand the premium rate. I know the model, that is
Y_t=r_0 + ct- \sum{X_i}.
What is the premium rate c?
Is the rate or percentage of what ...
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10 views
Model Validation for Aggregate Loss
I have loss data that consists of 134 severity (for 54 years, already adjusted for inflation). I want to create aggregate loss model from this data. I can sum up the severity (loss sizes) in each year ...
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21 views
show X~$N(\mu,\sigma^2)$ is not risk-unbiased under standardized square loss function
Let X follow the $N(\mu, \sigma^2)$ distribution with parameter $\theta=(\mu,\sigma^2)$.
First, I try to show X is not risk-unbiased under the standardized square loss function $𝐿(\theta,\delta)= \...
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36 views
How does the risk calculation of the EMA / Paul-Ehrlich-Institut regarding AstraZeneca vaccine side effects look like?
When the german government announced that they would stop administering AstraZeneca because of potentially deadly side effects, I was wondering what kind of risk calculation would be happening in the ...
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55 views
MSE of randomized decision in Normal distribution
Suppose a sample $\bf{X}$$=(X_1,...,X_n)$ is from $X\sim N(\theta,1)$. The sample mean $T(\bf{X}$$)=\bar{X}$ is sufficient to the population mean $\theta$.
For $\delta(\bf{X}$$)=X_1$, the decision $\...
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13 views
Relative risk value depending on number of inherent risks and size of each inherent risk
If this is a beginner question, then I apologize in advance.
I have a set of population with multiple risk factors:
Every population member can have a combination of 30 different risk factors.
Every ...
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19 views
Calculate 60-day risk/probability of outcome under competing risk of death
I am analysing a dataset of patients. The patients have all experienced a defining event which marks incusion into the study and time t=0. I am interested in estimating the 60-day risk/probability of ...
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22 views
Credit risk book reference
Credit risk is a beautiful field that relies on basic notions of statistics and stochastic processes.
I have been studying it, and now I am trying to understand the market models such as KMV, ...
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62 views
Is Bayes risk under MSE (i.e. conditional variance) strictly monotonic?
Formal question: Let $Y,X,X'$ be r.v.s . Let $E_{X}[Var(Y|X)]$ denote the expected conditional variance (i.e. Bayes risk when predicting $Y$ using $X$ under squared error) and $f$ be a bijective ...
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73 views
Distribution for ${1^TX}/\sqrt{X^TQX}$, when $X$~$N(\mu, \Sigma)$?
I have been looking for an illustrative way to quantify the risk of an investor not being able stay above the minimum capital requirement. I would like to find a neat solution for the probability that ...
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1answer
17 views
Single Choice Test
I will have a big exam next week that involves 64 Single-choice questions. There will be two statements of which only one will be correct. I will need to mark only the correct answer.
For the correct ...
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994 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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1answer
73 views
How about evaluating an estimator using the VARIANCE of loss (instead of the expectation of loss)?
The risk of an estimator $\delta$ is defined as $$E_\theta[L(\theta,\delta(X))],$$
where, say, $L(\theta,\delta(X)) = (\theta-\delta(X))^2$, and $E_\theta(X)$ is defined as $\int XdP_\theta$, namely ...
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1answer
56 views
Cause-specific survival function in survival analysis
In survival analysis, when there are competing risks, it is well-known that although the cause-specific hazard function, $\lambda_j^\#(t)$, is interpretable, $S_j^\#(t) = e^{-\Lambda_j^\#(t)}$ may not ...
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17 views
Calculating the (colloquial) likelihood of a result
A project that I am working on wants to use two factors to determine risk. First is an assessment by a subject matter expert (SME) on how much damage a calculated result would cause. Second is a ...
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1answer
80 views
What is the entropy of a riskless random variable?
Variance and standard deviation are often used as proxies for risk and volatility. I make the analogy to information theory as follows, correct if it's wrong: a random variable $x\in \mathbb{R}$ that ...
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41 views
Relation between test and train error with gradient descent iterates
My question is about establishing an inequality between population error and expected training error (i.e, expected training error < population error) for a model trained with gradient descent on a ...
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24 views
Estimating CVaR for non-Gaussian distributions
Calculating CVaR needs Gaussian distribution, however, what if the distribution is not Gaussian? Or the distribution is unknown? Can I use many Dirac Delta functions to estimate a distribution and ...
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1answer
189 views
Logistic regression risk prediction model - poor calibration but good discrimination
I am trying to create risk prediction model in R. I am new to logistic regression risk prediction analysis. I obtained reliability curve using ...
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1answer
92 views
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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141 views
annualized probability of default for loan including time component
i am struggling with this. say i am given an annual probabilty of default for a company going insolvent as 0.02. so 2%.
say this client then takes out a 100k , 150 day loan on jan 1st 2018, what is ...
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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 ...
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16 views
Is the risk a probability?
The Ktest function in the dbmss package returns:
the risk to reject CSR erroneously, based on the distribution of the K ...
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1answer
332 views
Calculating Conditional Value at Risk given any distribution
Many CVaR methods calculations are based on VaR, which is based on the assumption on the normal distribution. How can I calculate CVaR given any distributions?
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107 views
When do expected KL-divergence and expected MSE coincide?
The AIC is an approximately unbiased estimator of the (relative) risk of the Kullback-Leibler loss. I read that If you use AIC to choose among a family of models, AIC (approximately) yields the model ...
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2answers
127 views
Value-at-Risk formula with GARCH-model
I'm totally aware of that if we look at some loss process $L_t$, then $\text{VaR}(\alpha)$ is a quantile of the loss distribution. If we assume that $L_t=-X_t$ is the negative returns and they follow ...
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22 views
Player based betting odds VS analysis based odds
there are two kinds of betting sites
Player based odds sites (thunderpick.com , csgopositive.com , ...)
analysis based odds sited (1xbet , bwin , and almost all of the huge betting sites)
when you ...
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249 views
We know that The empirical risk is an unbiased estimate of the risk. Then why Is the training error biased ? (How does to proof for the former break)
Setting:
Let $S$ be a set of $m$ samples from a set $Z$ and $w^{*}$ be an arbitrary vector. (Samples Are I.I.D and we are operating in a binary classification setting)
Then $\mathbb{E}_{S \sim D^{m}}...
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1answer
67 views
VaR backtesting: counting the number of rejections
Let's say you calculate the number of VaR rejections for every $r_{1,t}$, $r_{2,t}$,
should you have the same number of rejections in a model, irrespectively of the weights being different?
$[w,\ 1-w]...
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157 views
solvency capital requirement using copulas in R
I want to prove that using copulas the SCR for solvency 2 can be lower than using the standard formula. In the following code I simulate three different distributions, I calculate the scr and then I ...
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57 views
Expected Shortfall for ARMA-GARCH two day forecast
I need to find the 99% confidence expected shortfall (CVaR) for a long position of 100 dollars at time $t$ for an asset with returns modeled by an ARMA(1,1)-GARCH(1,1) model with $r_t = θr_{t−1} + u_t ...
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1answer
204 views
Inconsistent Empirical Risk Minimization procedure, but why?
Given a random variable $Y$ and the typical squared loss function:
$$L(Y,\hat{Y}) = (Y-\hat{Y})^2$$
the minimizer for expected loss $E[L(Y,\hat{Y})]$ is know to be the mean, $\hat{Y} = E[Y] = \mu$.
...
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108 views
Calculating risk score
I'm trying to construct a medical risk score. I was given some advice by a statistician and they said that one of the stages after the variable selection stage is to take the regression coefficients ...
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437 views
Compute the Risk function
Suppose we are given $(X_1,...,X_n)$ random variables which are iid. from $\mathcal{N}(\mu,\theta)$ and finite variance. Let $Y=\frac{1}{n}\sum_{i=1}^n(X_i-\overline X)^2$ and define a loss function $...
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42 views
Definitions of VaR (Value at Risk)
Here is the definition of VaR (Value at Risk) taken from McNeil, Alexander J., Rüdiger Frey and Paul Embrechts (2015), Quantitative risk
management: Concepts, techniques and tools:
$$
\textrm{VaR}_{\...
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1answer
38 views
Accidents as precursors of condition: how does that fit with Bayesian inference?
I'm currently trying to identify what approach should I use for my problem. I want to make a risk assessment for each subject having or not a specific condition C (5% of prevalence), sample size ...
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1answer
31 views
Predicting risk factors
i'm trying to find predictive risk factors
i already found out that young age at diagnosis is a risk factor ( binary logistic regression) But now i want to know the exact age when the risk is highest....
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0answers
32 views
Characterization of risk factors for a very rare condition
I am looking at a cohort of patients including 13000 patients, out of which only 160 have condition A. Out of these patients, only 6 have condition B. I would like to be able to characterize those ...
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Independent and Identically distributed random variables with value at risk [duplicate]
Suppose that $W_1$ and $W_2$ are i.i.d. and $P(W_i>x)=x^{-1/2}$ and $x$ is greater than or equal to $1$ and $i=1,2.$ How do you show that $P(W_1+W_2>x)=(2\sqrt{x-1})/x$? I know it involves ...
