scholarly journals Making Better Decisions: Can Minimizing Frequentist Risk Help?

2016 ◽  
Vol 5 (3) ◽  
pp. 80 ◽  
Author(s):  
Rose D. Baker ◽  
Ian G. McHale
Keyword(s):  
Decision Making ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Risk Minimization ◽  
Likelihood Principle ◽  
Complete Class ◽  
Bet Size

The concept of shrinking bet size in Kelly betting to minimize estimated frequentist risk has recently been mooted. This rescaling appears to conflict with Bayesian decision theory through the likelihood principle and the complete class theorem; the Bayesian solution should already be optimal. We show theoretically and through examples that when the modeldetermining the likelihood function is correct, the prior distribution (if not dominated by data) is `correct' in a frequentist sense, and the posterior distribution is proper, then no further rescaling is required. However, if the model or the prior distribution is incorrect, or the posterior distribution improper, frequentist risk minimization can be a useful technique. We discuss how it might best be exploited. Another example, from maintenance, is used to show the wider applicability of the methodology; these conclusionsapply generally to decision-making.

Metropolis-Hastings Algorithms for DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Random Walk ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Large Scale ◽  
Likelihood Function ◽  
Dsge Models ◽  
Posterior Distributions ◽  
Dsge Model ◽  
Alternative Proposal ◽  
Posterior Moments

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in combination with the prior distribution leads to a posterior distribution that has a fairly regular elliptical shape. In turn, the draws from a simple RWMH algorithm can be used to obtain an accurate numerical approximation of posterior moments. However, in many other applications, particularly those involving medium- and large-scale DSGE models, the posterior distributions could be very non-elliptical. Irregularly shaped posterior distributions are often caused by identification problems or misspecification. In lieu of the difficulties caused by irregularly shaped posterior surfaces, the chapter reviews various alternative MH samplers, which use alternative proposal distributions.

scholarly journals ANALISIS METODE BAYESIAN PADA SISTEM ANTREAN RAWAT JALAN DI RSUP Dr. KARIADI DENGAN DISTRIBUSI SAMPEL POISSON DAN GEOMETRIK

2021 ◽  
Vol 10 (3) ◽  
pp. 413-422
Author(s):  
Nur Azizah ◽  
Sugito Sugito ◽  
Hasbi Yasin
Keyword(s):  
Internal Medicine ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Likelihood Function ◽  
Queuing System ◽  
Hospital Service ◽  
Queuing Model ◽  
Sample Distribution ◽  
New Information

Hospital service facilities cannot be separated from queuing events. Queues are an unavoidable part of life, but they can be minimized with a good system. The purpose of this study was to find out how the queuing system at Dr. Kariadi. Bayesian method is used to combine previous research and this research in order to obtain new information. The sample distribution and prior distribution obtained from previous studies are combined with the sample likelihood function to obtain a posterior distribution. After calculating the posterior distribution, it was found that the queuing model in the outpatient installation at Dr. Kariadi Semarang is (G/G/c): (GD/∞/∞) where each polyclinic has met steady state conditions and the level of busyness is greater than the unemployment rate so that the queuing system at Dr. Kariadi is categorized as good, except in internal medicine poly. 

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (01) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

The first steps on long marches: The costs of active observation

2020 ◽  
pp. 213-228
Author(s):  
Peter Dayan ◽  
Jonathan P. Roiser ◽  
Essi Viding
Keyword(s):  
Decision Making ◽  
Individual Differences ◽  
Decision Theory ◽  
Path Dependency ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Simple Formulation ◽  
Substantial Form ◽  
Gene Environment ◽  
Active Observation

That we shape our environment, and our environment shapes us, are truisms with deep and complicated consequences. The resulting feedback interaction leads to a substantial form of what is known as path dependency. This is that small initial variations, stemming from individual differences or even just the vicissitudes of chance, can potentially result in large and persistent divergence in outcomes. This has implications for the nature and interpretation of adaptive and maladaptive choice. This chapter offers a simple formulation in terms of active observers—a formalization of decision-making problems in which actors have the choice of whether and how to gather information to improve what happens. The chapter notes that, according to Bayesian decision theory, it is often optimal for active observers to remain incorrectly calibrated with their surroundings; it explores consequences of this in non-interactive environments, and environments containing other people who might compete or cooperate. The chapter draws loose parallels with the literature on active and evocative gene–environment correlations.

scholarly journals An Accurate Asymptotic Approximation for Experience Rated Premiums

2004 ◽  
Vol 34 (1) ◽  
pp. 113-124
Author(s):  
Riccardo Gatto
Keyword(s):  
Numerical Methods ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Asymptotic Approximation ◽  
Good Accuracy ◽  
Likelihood Function ◽  
Analytical Calculation ◽  
Expected Loss ◽  
Exact Calculations ◽  
The Bayesian Approach

In the Bayesian approach, the experience rated premium is the value which minimizes an expected loss with respect to a posterior distribution. The posterior distribution is conditioned on the claim experience of the risk insured, represented by a n-tuple of observations. An exact analytical calculation for the experience rated premium is possible under restrictive circumstances only, regarding the prior distribution, the likelihood function, and the loss function. In this article we provide an analytical asymptotic approximation as n → ∞ for the experience rated premium. This approximation can be obtained under more general circumstances, it is simple to compute, and it inherits the good accuracy of the Laplace approximation on which it is based. In contrast with numerical methods, this approximation allows for analytical interpretations. When exact calculations are possible, some analytical comparisons confirm the good accuracy of this approximation, which can even lead to the exact experience rated premium.

Decision theory and the rationality of further deliberation

2002 ◽  
Vol 18 (2) ◽  
pp. 303-328 ◽  
Author(s):  
Igor Douven
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Rational Agency

Bayesian decision theory operates under the fiction that in any decision-making situation the agent is simply given the options from which he is to choose. It thereby sets aside some characteristics of the decision-making situation that are pre-analytically of vital concern to the verdict on the agent's eventual decision. In this paper it is shown that and how these characteristics can be accommodated within a still recognizably Bayesian account of rational agency.

USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS

2001 ◽  
Vol 17 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Frank E. Harrell ◽  
Ya-Chen Tina Shih
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Scientific Evidence ◽  
A Priori ◽  
Relevant Information ◽  
Decision Makers ◽  
Probability Models ◽  
The Bayesian Approach

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori; the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a “probabilistic” manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the “similarity region” of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

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