Mark J Schervish
Biographic Data
| ID | 5969186 |
|---|---|
| NAME | Mark J Schervish |
| GIVEN NAMES | Mark J |
| FAMILY NAME | Schervish |
| SIGNATURE | SCHERVISH M J |
| AFFILIATIONS | Carnegie Mellon University |
| ORCID | 0000-0001-8550-9268 |
| VERIFIED | Yes |
| TOTAL WORKS | 11 |
| TOTAL CITATIONS | 31 |
| AUTHOR COUNT | 11 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1983 |
| LATEST PUBLICATION YEAR | 2025 |
| H-INDEX | 3 |
Finite Additivity, Complete Additivity, and the Comparative Principle
In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) Existence : Settings where no countably additive probability exists though finitely additive probabilities do. (2) Complete Additivity : Where reasons for countable additivity don’t stop there. Those reasons entail compl…
Deceptive Credences
A familiar defense of Personalist or Subjective Bayesian theory is that, under a variety of sufficient conditions, asymptotically—with increasing shared evidence—almost surely, each non-extreme, countably additive Bayesian opinion, when updated by conditionalization, converges to certainty that is veridical about the truth/falsity of hypotheses of interest. Then, with probability 1 over possible evidential histories, personal probabilities track …
Standards for Modest Bayesian Credences
Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be resp…
Sleeping Beauty’s Credences
The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational be…
Errors in Statistical Assumptions, Effects of
Probability and Statistics
The Effect of Exchange Rates on Statistical Decisions
Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisio…
Coherent choice functions under uncertainty
A Rate of Incoherence Applied to Fixed-Level Testing
It has long been known that the practice of testing all hypotheses at the same level (such as 0.05), regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti's “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to mea…
When Several Bayesians Agree that There will be no Reasoning to a Foregone Conclusion
When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspecti…
A Conflict between Finite Additivity and Avoiding Dutch Book
For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for previsions. ) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they ins…
Coherent choice functions under uncertainty
A Conflict between Finite Additivity and Avoiding Dutch Book
For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for previsions. ) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they ins…
Standards for Modest Bayesian Credences
Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be resp…
Sleeping Beauty’s Credences
The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational be…
A Rate of Incoherence Applied to Fixed-Level Testing
It has long been known that the practice of testing all hypotheses at the same level (such as 0.05), regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti's “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to mea…
When Several Bayesians Agree that There will be no Reasoning to a Foregone Conclusion
When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspecti…
The Effect of Exchange Rates on Statistical Decisions
Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisio…
A Conflict between Finite Additivity and Avoiding Dutch Book
For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for previsions. ) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they ins…
When Several Bayesians Agree that There will be no Reasoning to a Foregone Conclusion
When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspecti…
A Rate of Incoherence Applied to Fixed-Level Testing
It has long been known that the practice of testing all hypotheses at the same level (such as 0.05), regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti's “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to mea…
Coherent choice functions under uncertainty
Probability and Statistics
The Effect of Exchange Rates on Statistical Decisions
Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisio…
Errors in Statistical Assumptions, Effects of
Sleeping Beauty’s Credences
The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational be…
Standards for Modest Bayesian Credences
Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be resp…
Deceptive Credences
A familiar defense of Personalist or Subjective Bayesian theory is that, under a variety of sufficient conditions, asymptotically—with increasing shared evidence—almost surely, each non-extreme, countably additive Bayesian opinion, when updated by conditionalization, converges to certainty that is veridical about the truth/falsity of hypotheses of interest. Then, with probability 1 over possible evidential histories, personal probabilities track …
Finite Additivity, Complete Additivity, and the Comparative Principle
In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) Existence : Settings where no countably additive probability exists though finitely additive probabilities do. (2) Complete Additivity : Where reasons for countable additivity don’t stop there. Those reasons entail compl…
Mathematics (10 works) · Computer Science (8 works) · Mathematical economics (7 works) · Statistics (7 works) · Epistemology (6 works) · Bayesian probability (5 works) · Philosophy (5 works) · Artificial Intelligence (4 works) · Econometrics (4 works) · Expected utility hypothesis (4 works)