I85PREP
⌘ K
IFoA SA10 study materials
IFoA SA10 study resources

IFoA SA10 practice questions

One question at a time. Build your IFoA SA10 understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Data science

In a GLM used to model claim counts, which distributional assumption makes the Poisson model a special case of the negative binomial model?

  1. The exposure offset is removed from the model specification
  2. The dispersion parameter tends to zero, so the variance equals the mean Correct answer.
  3. The dispersion parameter tends to one, so the variance equals the mean squared
  4. The linear predictor is applied to the log of the mean rather than to the mean itself

Explanation

The negative binomial has variance mu + mu^2/k (or mu + alpha*mu^2). As the dispersion parameter approaches zero (k tends to infinity), the extra variance term vanishes and the variance collapses to the mean, which is exactly the Poisson variance function. The link function and offset choices are separate from the variance assumption.

Question 2Data science

A pricing team fits a logistic regression to predict the probability that a policyholder makes at least one claim. Which link function is being used implicitly?

  1. Complementary log-log
  2. Logit Correct answer.
  3. Log
  4. Identity

Explanation

Logistic regression models the log-odds of the event as a linear function of predictors, so the link is the logit function log(p/(1-p)). The log link belongs to Poisson-type count models and the identity link to ordinary linear regression.

Question 3Data science

Which statement best describes the purpose of a hold-out test set when building a claims frequency model?

  1. It guarantees that the fitted model will not overfit the training data
  2. It increases the number of observations available for estimating coefficients
  3. It provides an unbiased estimate of out-of-sample predictive performance Correct answer.
  4. It removes the need to check for multicollinearity among predictors

Explanation

A hold-out set is data not used in fitting, so performance measured on it approximates how the model generalises to new policies. It does not add fitting data or guarantee anything; it is a diagnostic for generalisation.

Question 4Data science

In gradient boosting applied to insurance risk modelling, what is the role of the learning rate (shrinkage) parameter?

  1. It determines the fraction of rows sampled for each tree
  2. It sets the maximum depth allowed for each individual tree
  3. It scales the contribution of each newly fitted tree to the ensemble Correct answer.
  4. It controls the number of trees built in total

Explanation

Shrinkage multiplies each tree's fitted values by a small learning rate before adding them to the running prediction, slowing convergence and reducing variance. Tree depth, row subsampling and the number of trees are separate hyperparameters.

Question 5Data science

A classification model for fraudulent claims is evaluated on a highly imbalanced dataset where only 1% of claims are fraudulent. Which metric is most informative about the model's ability to identify fraud?

  1. Recall (sensitivity) for the fraud class Correct answer.
  2. Mean squared error
  3. Overall accuracy
  4. R-squared

Explanation

With 1% positives, a model predicting 'not fraud' always achieves 99% accuracy, so accuracy is misleading. Recall measures the proportion of actual frauds detected and directly reflects the model's usefulness for the minority class. MSE and R-squared are regression metrics.

Question 6Data science

Which of the following is the primary purpose of k-fold cross-validation in building a reserving or pricing model?

  1. To produce confidence intervals for the regression coefficients
  2. To eliminate the need for a separate variable selection step
  3. To reduce the number of predictors required in the final model
  4. To estimate generalisation error using all observations for both training and validation Correct answer.

Explanation

Cross-validation partitions data into k folds, fitting on k-1 folds and validating on the held-out fold, rotating so every observation is used for validation once. This gives a more stable estimate of out-of-sample error than a single split. Coefficient inference and variable selection are separate concerns.

Question 7Data science

In a decision tree used for motor insurance risk segmentation, what does a 'leaf' node represent?

  1. A predictor variable used for the split
  2. The root of the tree where the first split is made
  3. A threshold value applied to a predictor
  4. A terminal group of observations with an assigned prediction Correct answer.

Explanation

A leaf is a terminal node that is not split further; all observations reaching it receive the same predicted value, such as a mean claim frequency. Internal nodes hold split conditions, and the root is simply the topmost internal node.

Question 8Data science

A model is trained on 2015-2019 claims data and applied to 2021 data. Performance degrades sharply because claim patterns changed. What is this phenomenon called?

  1. Concept drift Correct answer.
  2. Multicollinearity
  3. Overfitting
  4. Data leakage

Explanation

Concept drift occurs when the relationship between predictors and the target changes over time, so a model trained on historical data becomes stale. Data leakage is contamination of training data with target information, overfitting is fitting noise, and multicollinearity is correlation among predictors.

Question 9Data science

An insurer fits a Poisson GLM to claim counts with a log link and an exposure offset. If a policy's exposure doubles while all other predictors are unchanged, what happens to the expected claim count?

  1. It increases by the square root of two
  2. It doubles Correct answer.
  3. It stays the same
  4. It increases by a factor equal to the intercept

Explanation

With a log link and an offset of log(exposure), the mean is exposure times exp(X*beta), so expected counts are proportional to exposure. Doubling exposure doubles the expected count while the expected frequency per unit exposure is unchanged.

Question 10Data science

A data scientist compares two nested GLMs using a likelihood ratio test. The unrestricted model has 6 parameters and the restricted model has 4, with a test statistic of 9.2. At the 5% significance level, using a chi-squared distribution with 2 degrees of freedom (critical value 5.99), what is the appropriate conclusion?

  1. The unrestricted model fits significantly better, so the two extra parameters are jointly useful Correct answer.
  2. The test is invalid because the models are nested
  3. The restricted model is preferred because it has fewer parameters
  4. The statistic must be compared with a t-distribution instead

Explanation

The likelihood ratio statistic of 9.2 exceeds the 5.99 critical value on 2 degrees of freedom, so the null hypothesis that the extra parameters are zero is rejected. The larger model therefore provides a statistically significant improvement in fit.

Question 11Data science

In a logistic regression for claim occurrence, the estimated coefficient on a binary 'telematics installed' predictor is -0.4. What is the approximate effect on the odds of a claim?

  1. The probability decreases by 0.40
  2. The odds are multiplied by about 0.67 Correct answer.
  3. The odds are multiplied by about 1.49
  4. The odds are multiplied by about 0.40

Explanation

In a logistic model the exponentiated coefficient gives the odds ratio, and exp(-0.4) is approximately 0.67. This means telematics installation is associated with a 33% reduction in the odds of a claim, all else equal.

Question 12Data science

A Poisson GLM of claim frequency shows a Pearson dispersion statistic of 2.3. What does this most likely indicate?

  1. The model is underdispersed and the standard errors are conservative
  2. The model is overdispersed and standard errors are understated Correct answer.
  3. The model fits perfectly because the statistic exceeds one
  4. The link function is misspecified and must be changed to identity

Explanation

A Pearson dispersion statistic well above one indicates overdispersion relative to the Poisson variance assumption. Ignoring it typically understates standard errors, so a quasi-Poisson or negative binomial approach may be warranted.

Question 13Data science

Which of the following best describes the difference between bagging and boosting in ensemble modelling?

  1. Bagging reduces bias, while boosting primarily reduces variance
  2. Bagging fits models in parallel on bootstrap samples, while boosting fits models sequentially to correct prior errors Correct answer.
  3. Bagging requires a single deep tree, while boosting requires shallow trees only
  4. Bagging can only be applied to classification, while boosting applies only to regression

Explanation

Bagging trains independent models on bootstrap resamples and averages them, mainly reducing variance. Boosting adds models sequentially, each focused on the residual errors of the current ensemble, primarily reducing bias. Both can be applied to classification and regression.

Question 14Data science

A random forest is used to rank variables by importance in a claims severity model. Which statement about impurity-based variable importance is most accurate?

  1. It always agrees with permutation importance
  2. It cannot be computed when predictors are correlated
  3. It is biased towards predictors with many distinct values or categories Correct answer.
  4. It is equivalent to the p-value of the predictor in a GLM

Explanation

Impurity-based importance sums reductions in node impurity and tends to favour predictors offering many possible split points, such as continuous or high-cardinality variables. It is not a significance test and can diverge from permutation importance, especially with correlated predictors.

Question 15Data science

A model predicting large-loss occurrence achieves an AUC of 0.72 on a validation set. How should this be interpreted?

  1. 72% of large losses are correctly identified
  2. 72% of predictions are correct
  3. The model explains 72% of the variance in the loss indicator
  4. There is a 72% chance that a randomly chosen large loss is scored higher than a randomly chosen non-large loss Correct answer.

Explanation

AUC is the probability that a randomly selected positive case receives a higher predicted score than a randomly selected negative case. It is a rank-based discrimination measure, not a classification accuracy or an explained-variance statistic.

Question 16Data science

In a neural network used for claim severity prediction, what is the purpose of an activation function in a hidden layer?

  1. To introduce non-linearity so the network can represent complex relationships Correct answer.
  2. To select the optimal number of hidden layers automatically
  3. To prevent the weights from being updated during backpropagation
  4. To normalise the input features before training

Explanation

Without a non-linear activation function, a multi-layer network collapses to an equivalent linear model. Activation functions such as ReLU or sigmoid allow the network to approximate non-linear mappings between predictors and severity.

Question 17Data science

A data scientist applies ridge regression to a set of highly correlated rating factors. What is the primary effect of the penalty?

  1. It forces some coefficients exactly to zero, performing variable selection
  2. It shrinks coefficients towards zero, stabilising estimates under collinearity Correct answer.
  3. It removes the need to standardise the predictors
  4. It guarantees that all coefficients are unbiased

Explanation

Ridge regression adds an L2 penalty, which shrinks coefficients towards zero and reduces variance in the presence of collinearity, at the cost of some bias. Unlike the lasso, it does not generally set coefficients exactly to zero.

Question 18Data science

A claims triage model flags 200 claims as potentially fraudulent. Of these, 120 are confirmed fraudulent, and there are 80 confirmed fraudulent claims in total. What is the precision of the model?

  1. 0.40
  2. 0.67
  3. 1.50
  4. 0.60 Correct answer.

Explanation

Precision is the number of true positives divided by the number flagged, that is 120/200 = 0.60. Recall would be 120/80 = 1.5 in this hypothetical, which is impossible, indicating the figures in a real setting would need checking; here the question asks specifically for precision.

Question 19Data science

An insurer wants to model the total aggregate loss from a policy as the product of claim frequency and average severity. Which approach best captures the dependence between the two components?

  1. Assume severity is deterministic and equal to its mean
  2. Multiply the separately estimated frequency and severity models without adjustment
  3. Fit a single Poisson GLM to the aggregate loss directly
  4. Use a copula or joint model that allows for dependence between frequency and severity Correct answer.

Explanation

The product of independent frequency and severity expectations is valid only when the two are independent. Where dependence exists, a copula or joint modelling framework is needed to capture the association and produce correct aggregate loss distributions.

Question 20Data science

A reserving team uses a GLM with a Tweedie distribution to model incurred claim amounts. Which feature makes the Tweedie family attractive for this purpose?

  1. It assumes the variance is constant regardless of the mean
  2. It requires the response to be binary
  3. It forces all claim amounts to be strictly positive
  4. It can accommodate a point mass at zero together with a continuous positive component Correct answer.

Explanation

The Tweedie family, with power parameter between one and two, combines a probability mass at zero with a continuous positive distribution. This matches incurred amounts where many policies have zero claims and the rest have positive amounts.

Question 21Data science

Which of the following is the most appropriate way to handle missing values in a predictor used in a claims model when the missingness is believed to be informative?

  1. Include a missing-indicator variable alongside an imputed value Correct answer.
  2. Delete all rows with missing values
  3. Replace missing values with zero without further adjustment
  4. Impute the mean and ignore the missingness

Explanation

When missingness may carry information, an indicator flag allows the model to estimate a separate effect for missing cases while imputation supplies a usable value. Simple deletion or mean imputation discards that information and can bias results.

Question 22Data science

A machine learning model for claim frequency is deployed, and the data science team monitors the population stability index (PSI) of key predictors monthly. A PSI of 0.30 for the age band variable is observed. What is the most reasonable interpretation?

  1. The model's predictions are unbiased and no action is needed
  2. The model has achieved a 30% improvement in accuracy
  3. The predictor distribution has shifted materially and the model should be reviewed Correct answer.
  4. The predictor has become perfectly correlated with the target

Explanation

PSI measures the shift in a variable's distribution between a reference and a current population. Values around 0.1 or below are typically considered stable, while 0.25 or more signals significant drift requiring investigation.

Question 23Data science

A modeller wants to compare a gradient boosting model against a GLM for claim frequency using a proper scoring rule. Which metric is most appropriate?

  1. Area under the ROC curve
  2. Adjusted R-squared
  3. Deviance or log-loss Correct answer.
  4. Mean absolute error of predicted counts

Explanation

Deviance and log-loss are proper scoring rules for probabilistic predictions, rewarding calibrated probabilities as well as discrimination. AUC measures ranking only, and R-squared is not defined for count models in the same way.

Question 24Data science

In a GLM with a log link, a modeller includes an interaction between region and vehicle group. What does a significant interaction term imply?

  1. The effect of vehicle group on the log of expected frequency depends on the region Correct answer.
  2. The model is misspecified because interactions are not permitted in GLMs
  3. The response distribution must be changed to normal
  4. The main effects of region and vehicle group must be removed

Explanation

An interaction allows the effect of one predictor to vary across levels of another. On the log scale this means the multiplicative effect of vehicle group differs by region, so a single averaged effect is inadequate.

Question 25Data science

A model's calibration is assessed by plotting observed against predicted claim frequencies across deciles of predicted risk. The plot shows a systematic S-shape, with under-prediction at low risk and over-prediction at high risk. What does this indicate?

  1. The model discriminates well but is poorly calibrated across the risk range Correct answer.
  2. The model requires more training data before any conclusion can be drawn
  3. The model has excellent calibration because predictions track observations on average
  4. The model has no discriminative power at all

Explanation

A systematic S-shaped calibration curve shows that predicted probabilities are distorted across the risk spectrum even if overall averages match. Discrimination and calibration are distinct properties, so good ranking does not imply good calibration.

Question 26Data science

A pricing team wants a single number that summarises how much a frequency model's predicted claim counts deviate from observed counts, penalising large errors more heavily than small ones. Which metric is designed for this purpose?

  1. Mean absolute error
  2. Poisson deviance Correct answer.
  3. Gini coefficient
  4. Root mean squared error

Explanation

Poisson deviance is the likelihood-based loss for count data and is the natural goodness-of-fit measure for a Poisson GLM, weighting errors relative to the variance implied by the mean. Mean absolute error and RMSE are generic regression metrics that ignore the mean-variance relationship of counts.

Question 27Data science

An insurer wants to detect whether the mix of policyholder ages entering a motor book has shifted since the model was built. Which technique is most directly suited to this check?

  1. Likelihood ratio test on nested GLMs
  2. Population stability index on the age band distribution Correct answer.
  3. Hosmer-Lemeshow test on predicted frequencies
  4. Variance inflation factor on the age predictor

Explanation

Population stability index compares the distribution of a variable or score between a baseline and a current sample, so it directly measures shift in the age mix. The other tools address model fit, calibration or multicollinearity rather than distributional drift.

Question 28Data science

A modeller is imputing missing values for a 'number of prior claims' predictor in a home insurance dataset. Which imputation approach is most defensible when missingness is believed to be informative?

  1. Replacing missing values with the overall portfolio average
  2. Multiple imputation that includes an indicator for missingness Correct answer.
  3. Single mean imputation of the observed values
  4. Listwise deletion of all records with any missing predictor

Explanation

When missingness may carry information, multiple imputation combined with a missingness indicator preserves that signal and propagates imputation uncertainty. Single-value imputation and deletion either discard information or bias the estimates.

Question 29Data science

In a gradient boosted tree model for claim frequency, what does the learning rate (shrinkage) parameter control?

  1. The number of trees fitted in the ensemble
  2. The proportion of rows sampled for each tree
  3. The fraction of each tree's contribution added to the running prediction Correct answer.
  4. The maximum depth permitted for each tree

Explanation

Shrinkage scales each newly fitted tree's contribution before it is added to the model, trading a smaller step size for the need to fit more trees. Depth, tree count and row sampling are separate hyperparameters.

Question 30Data science

Which statement correctly describes how a confusion matrix is used when evaluating a claims fraud detection model at a chosen threshold?

  1. It tabulates predicted against actual classes to give counts of true and false positives and negatives Correct answer.
  2. It measures the average squared difference between predicted and actual loss amounts
  3. It plots true positive rate against false positive rate across all thresholds
  4. It ranks policies by predicted fraud probability for lift analysis

Explanation

A confusion matrix cross-tabulates predicted and actual class labels at a specific decision threshold, yielding counts of true positives, false positives, true negatives and false negatives. The ROC curve, by contrast, summarises performance across all thresholds.

Question 31Data science

A reserving actuary fits a model to development triangle data and wants to ensure that the model's predictions generalise to future accident years rather than fitting historical noise. Which validation design best matches this aim?

  1. Selecting the model with the highest number of parameters
  2. Using all cells for training and reporting in-sample deviance
  3. Holding out the most recent accident years as a test set Correct answer.
  4. Randomly splitting individual cells of the triangle into training and test sets

Explanation

Holding out recent accident years mimics the forward projection the model must perform and tests extrapolation to unseen development. Random cell splits leak information across the same accident years and overstate generalisation.

Question 32Data science

When preparing features for a GLM in a pricing model, why is it common to bin a continuous variable such as driver age?

  1. It automatically corrects for overdispersion in the claim counts
  2. It removes the need to check for multicollinearity
  3. It allows the linear predictor to capture non-linear effects and eases interpretability Correct answer.
  4. It guarantees the resulting model will be well calibrated

Explanation

Binning lets a linear predictor represent a non-linear relationship through separate factor levels, and the resulting relativities are easy to communicate to underwriters. It does not guarantee calibration, remove collinearity or fix overdispersion.

Question 33Data science

A data scientist wants to reduce a large set of correlated telematics variables to a smaller number of uncorrelated components before modelling. Which technique is designed for this?

  1. Logistic regression
  2. Principal component analysis Correct answer.
  3. Isotonic regression
  4. K-means clustering

Explanation

Principal component analysis constructs orthogonal linear combinations that capture variance in descending order, producing uncorrelated components. The other methods perform classification, clustering or monotone calibration rather than dimension reduction.

Question 34Data science

An insurer models claim counts with a Poisson GLM and finds substantial overdispersion. Which change is most appropriate to accommodate the extra variability?

  1. Switch to a negative binomial model that estimates an additional dispersion parameter Correct answer.
  2. Remove the exposure offset from the linear predictor
  3. Reduce the number of observations used in fitting
  4. Replace the log link with an identity link

Explanation

The negative binomial model introduces a variance function that exceeds the mean, explicitly allowing for overdispersion beyond the Poisson assumption. Changing the link, offset or sample size does not address the variance-mean relationship.

Question 35Data science

A modeller includes a predictor with a variance inflation factor of 12 alongside other rating factors. What is the most likely consequence for the fitted coefficients?

  1. Large standard errors and unstable coefficient estimates Correct answer.
  2. Automatic loss of the model's calibration property
  3. Systematically biased predictions for every policy
  4. A guaranteed increase in the model's discriminatory power

Explanation

High VIF signals that a predictor is nearly a linear combination of others, inflating the variance of its estimated coefficient and making estimates unstable. Predictions need not be biased and discrimination is not guaranteed to improve.

Question 36Data science

A severity model is fitted on claim amounts, which include many small claims and a few very large ones. Which loss function makes the fitted model least sensitive to the extreme values?

  1. Mean squared error
  2. Mean absolute error Correct answer.
  3. Root mean squared percentage error
  4. Poisson deviance

Explanation

Mean absolute error grows linearly with the residual, so a single very large claim exerts less leverage than under squared-error losses, which grow quadratically. Percentage-error and Poisson-deviance losses are not natural for continuous severity with heavy tails.

Question 37Data science

A team builds a claims triage model and wants to choose an operating threshold that balances the cost of missed fraudulent claims against the cost of manual review. Which approach is most appropriate?

  1. Select the threshold equal to the observed base rate of fraud
  2. Select the threshold at which the ROC curve reaches its steepest point
  3. Select the threshold that maximises overall classification accuracy
  4. Select the threshold minimising expected total cost using estimated costs of each error type Correct answer.

Explanation

When false positives and false negatives carry different costs, the optimal threshold minimises expected cost, weighting each error by its monetary consequence. Accuracy, ROC geometry and base-rate rules ignore the cost asymmetry.

Question 38Data science

A modeller wants to explain why a gradient boosting model assigned a high predicted claim frequency to a particular policy. Which technique provides a local, model-agnostic attribution of the prediction to individual features?

  1. The model's overall training deviance
  2. Variable importance from impurity reduction
  3. SHAP values for that policy Correct answer.
  4. A partial dependence plot for the whole portfolio

Explanation

SHAP values decompose an individual prediction into additive feature contributions grounded in cooperative game theory, giving local explanations. Impurity importance and partial dependence describe global behaviour, and training deviance is a single summary.

Question 39Data science

A modeller compares two candidate frequency models using out-of-sample Poisson deviance and finds model A has a lower value than model B. What is the most reasonable conclusion?

  1. Model B must be overfitted to the training data
  2. Model A is guaranteed to be better calibrated across all deciles
  3. Model A fits the held-out counts better in the likelihood sense Correct answer.
  4. Model A will necessarily produce higher premium income

Explanation

Lower out-of-sample Poisson deviance means the held-out data are more probable under model A's fitted distribution, indicating a better likelihood-based fit. It does not by itself guarantee decile calibration, revenue outcomes or that the other model is overfitted.

Question 40Data science

A team wants to use a neural network for claim frequency and needs the output to be a valid expected count per unit exposure. Which output specification is most appropriate?

  1. A sigmoid output with a binary cross-entropy loss
  2. A softplus or exponential output activation with a Poisson deviance loss Correct answer.
  3. A linear output with a squared-error loss
  4. A softmax output across all policies in the batch

Explanation

A non-negative output activation combined with a Poisson deviance loss matches the count data's mean-variance structure and guarantees non-negative fitted means. Linear outputs with squared error can predict negative counts, and softmax across policies is meaningless here.

Question 41Data science

A modeller applies k-means clustering to policyholder behaviour features to create segments for a pricing model. Which statement about the resulting segments is correct?

  1. The clusters are guaranteed to be ordered by risk level
  2. The clusters minimise within-cluster variance for the chosen number of clusters Correct answer.
  3. The method provides a probabilistic membership for each policyholder
  4. The number of clusters is determined automatically by the algorithm

Explanation

K-means partitions records so that the within-cluster sum of squared distances to each centroid is minimised for a fixed number of clusters. It does not order clusters by risk, give probabilistic memberships, or choose the cluster count itself.

Question 42Data science

A data scientist builds a model on a portfolio where 0.5% of policies have a large loss. Which sampling strategy helps a tree model learn the large-loss pattern without discarding information?

  1. Randomly relabel some non-large losses as large losses
  2. Duplicate the rare large-loss records several times without adjustment
  3. Remove all policies without a large loss from the dataset
  4. Downsample the majority class and apply a prior correction to the predicted probabilities Correct answer.

Explanation

Downsampling the majority class rebalances the training signal, and a prior correction restores the original event rate in the predicted probabilities. Deleting majority records, naive duplication or relabelling distorts the data and the resulting probabilities.

Question 43Data science

A team wants to combine a GLM and a gradient boosting model for claim frequency into a single predictor. Which statement about a simple average of their predictions is correct?

  1. It removes the need for validating the combined model
  2. It can reduce variance relative to either component if their errors are not perfectly correlated Correct answer.
  3. It guarantees a lower bias than the better of the two models
  4. It always improves out-of-sample deviance

Explanation

Averaging forecasts with imperfectly correlated errors tends to reduce variance, which is the basis of ensemble gains. It does not guarantee lower bias, improved deviance or freedom from validation.

Question 44Data science

A modeller uses a train/validation/test split for a pricing model. Which statement best explains why the test set should be touched only once at the end?

  1. The test set contains fewer observations than the training set
  2. Repeated use of the test set to guide choices leaks information and biases the performance estimate Correct answer.
  3. The training set must always be larger than the validation set
  4. The test set cannot be used with GLMs

Explanation

If the test set informs model selection it effectively becomes part of training, so the reported performance is optimistic. Keeping it untouched until the final evaluation preserves an unbiased estimate of generalisation.

Question 45Data science

A modeller wants to tune the regularisation strength of a ridge-penalised frequency model. Which procedure gives the most reliable choice of the penalty parameter?

  1. Cross-validation over a grid of penalty values, choosing the value with lowest average validation deviance Correct answer.
  2. Choosing the penalty that minimises training deviance
  3. Selecting the largest penalty value in the grid
  4. Setting the penalty so that all coefficients become exactly zero

Explanation

Cross-validation estimates out-of-sample performance for each candidate penalty, and the value with the lowest average validation loss is selected. Training deviance always favours weaker penalties, and extreme choices degrade the model.

Question 46Data science

A modeller is deciding between a GLM and a gradient boosting model for a frequency model that must be explained to a regulator. Which consideration is most relevant to the choice?

  1. The processing speed of the fitting software
  2. The trade-off between predictive gain and the transparency of the rating structure Correct answer.
  3. Whether the response variable is integer-valued
  4. The number of rows in the training dataset alone

Explanation

Regulatory review often requires a clear, auditable relationship between rating factors and premiums, so the transparency cost of a complex model must be weighed against its predictive benefit. Dataset size, response type and software speed are secondary.

Question 47Data science

A data scientist applies a Box-Cox transformation to claim severity before fitting a model. What is the primary purpose of this transformation?

  1. To convert severity into a count variable
  2. To make the severity distribution closer to the assumptions of the chosen model Correct answer.
  3. To eliminate the need for an exposure variable
  4. To guarantee the model's predictions are unbiased

Explanation

The Box-Cox family of power transformations is chosen to stabilise variance and approximate normality or the assumed error structure. It does not create counts, replace exposure adjustment or guarantee unbiasedness.

Question 48Data science

A portfolio has a small number of large commercial risks that dominate the total loss. A data scientist fits a severity model and finds the coefficient on a key rating factor changes sign when those risks are removed. What does this most suggest?

  1. The estimate is heavily influenced by a few high-leverage observations Correct answer.
  2. The rating factor has no relationship with severity in any segment
  3. The model is overdispersed and needs a negative binomial distribution
  4. The training data are too large to fit the model reliably

Explanation

A sign reversal on removing a handful of records indicates high leverage, where a few observations dominate the coefficient. This calls for robust methods, sensitivity analysis or separate treatment of large risks.

Question 49Data science

A modeller fits a GLM with a Tweedie distribution to aggregate claim amounts and considers adding a spline term for vehicle age. Which statement best describes the effect of the spline on the model?

  1. It forces the fitted relationship to be monotone in vehicle age
  2. It removes the need for a link function in the GLM
  3. It allows smooth non-linear effects while the Tweedie variance function continues to handle the mass at zero Correct answer.
  4. It converts the aggregate loss model into a frequency model

Explanation

Spline basis terms relax linearity in the linear predictor while the chosen Tweedie distribution and link continue to model the zero-inflated, right-skewed response. A link function is still required, the model remains a severity/aggregate model, and splines do not impose monotonicity.

Question 50Data science

A model's predicted frequencies are well ranked but systematically 15% too low across all deciles. Which action most directly addresses the issue?

  1. Change the discrimination metric used for validation
  2. Increase the model's complexity by adding interaction terms
  3. Re-rank the policies within each decile
  4. Recalibrate the intercept or apply an offset adjustment to restore the overall level Correct answer.

Explanation

A uniform proportional shortfall is a level or calibration problem, addressed by adjusting the intercept or an offset so that total predicted equals total observed. Added complexity or different metrics do not fix a systematic scale error.