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3228Regularization as an Implicit PriorWhy do people say that ridge or lasso regularization has a Bayesian interpretation, even if the optimization is carried out in a frequentist workflow?统计中等essay未尝试面试订阅3229When Large-Sample Frequentist Asymptotics Are AttractiveGive one practical reason a quant team might prefer a frequentist asymptotic analysis over a full Bayesian analysis when the sample is enormous and arrives from a stable high-liquidity environment.统计中等essay未尝试面试订阅3230Sparse Event Rates and Online CalibrationWhy is a Bayesian approach often attractive when you are updating a very sparse event rate online, such as rare failures or rare fills?统计中等essay未尝试面试订阅3231Why a Sharpe Confidence Interval Is Not a Posterior BeliefA PM says, "The frequentist 95% confidence interval for Sharpe is mostly above zero, so there is a 95% chance the true Sharpe is positive." Why is that statement mixing two frameworks?统计中等essay未尝试面试订阅3232BIC Versus Bayes FactorWhy is BIC often described as an approximation to Bayesian model comparison rather than the same thing as a Bayes factor?统计中等essay未尝试面试订阅3233Frequentist Risk Does Not Condition on a PriorWhat is the key conceptual difference between minimizing Bayes risk under a prior and minimizing frequentist risk or regret uniformly over parameter values?统计中等essay未尝试面试订阅3234Partial Pooling Versus Separate FitsWhy does a hierarchical Bayesian model for many related assets often produce more stable estimates than fitting each asset separately and then testing them one by one?统计简单essay未尝试面试订阅3235Predictive Interval Versus Interval for the MeanWhy is a Bayesian posterior predictive interval for next week's count answering a different question from a frequentist confidence interval for the underlying mean count?统计简单essay未尝试面试订阅3236Can a p-Value Be Combined with Prior Conviction?A trader says, "I had a strong prior view, and the p-value came out 0.03, so now I can blend the two and call the trade 97% likely." Why is that not a coherent frequentist calculation?统计简单essay未尝试面试订阅3237Why a Posterior Mean Can Move While the MLE Does NotA desk observes only 4 new defaults for a rare event. Using a strong historical Beta prior, the Bayesian posterior mean default rate is much lower than the sample proportion, while the frequentist MLE equals the sample proportion exactly. Explain why these two answers can legitimately differ and what each one is conditioning on.统计简单essay未尝试面试订阅3238Empirical Bayes Sits Between the CampsWhy does empirical Bayes often feel like it sits between Bayesian and frequentist workflows?统计简单essay未尝试面试订阅3239Large p-Value Does Not Mean High Posterior Null ProbabilityWhy is it dangerous to read a large p-value as strong evidence that the null is true?统计简单essay未尝试面试订阅3240Prior Sensitivity Is a Feature, Not Always a BugWhy can prior sensitivity analysis be a feature rather than a bug in a high-stakes decision problem?统计简单essay未尝试面试订阅6013Power of a One-Sided Z-TestYou run a one-sided z-test at level alpha = 0.05 (critical value 1.645) for a positive mean edge. The true edge is delta = 3 bp, the per-observation standard deviation is sigma = 8 bp, and you collect n = 64 observations. The power equals Phi(delta*sqrt(n)/sigma - 1.645). Compute the power, using Phi(1.355) approx 0.9123.统计中等数值题未尝试免费6014Quadrupling the SampleYour current backtest detects a minimum edge of 6 bp at the desired power. You extend the sample so the number of observations is multiplied by 4, keeping sigma, alpha, and target power fixed. Because the minimum detectable effect scales as 1/sqrt(n), what is the new minimum detectable edge, in basis points?统计简单数值题未尝试免费6015Track Record to Confirm a SharpeA strategy has a true annualized Sharpe ratio of 0.5. The t-statistic of the mean return over a track record of T years is approximately t = SR * sqrt(T). How many years of returns are needed before the t-statistic reaches 2 (the usual significance bar)?统计中等数值题未尝试免费6016Posterior Mean Hit Rate After a Cold StreakA signal's hit probability p has prior Beta (4,4). Over the next batch you record 3 hits and 9 misses. By integrating the posterior density, what is the posterior mean of p?统计简单derivation未尝试免费6017Posterior Distribution After Ten Wins in TwelveA win probability p has the uniform prior Beta (1,1). You then see k=10 wins out of n=12 games. Name the exact posterior distribution of p and give its mode.统计简单数值题未尝试免费6018Posterior Mean Rate for a Rare FaultFaults arrive as a Poisson process with rate per day, prior Gamma (2,0.5) in shape-rate form. Over 3.5 days you observe 7 faults. What is the posterior mean of ?统计中等derivation未尝试免费6019Blending a Prior View With Four Noisy QuotesA latent fair value \sim N(10,4). You collect n=4 independent quotes with known per-quote variance 2=8 and sample mean x=12. Compute the posterior mean of .统计中等derivation未尝试免费