*Peter Sedlmeier*

- Published in print:
- 2002
- Published Online:
- March 2012
- ISBN:
- 9780198508632
- eISBN:
- 9780191687365
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508632.003.0009
- Subject:
- Psychology, Cognitive Psychology

This chapter argues that associative learning is the obvious mechanism to simulate judgements of relative frequency. PASS (Probability ASSociator), the specific associationist model proposed, ...
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This chapter argues that associative learning is the obvious mechanism to simulate judgements of relative frequency. PASS (Probability ASSociator), the specific associationist model proposed, consists of two parts, FEN (Frequency Encoding Network), a neural network, and the CA (Cognitive Algorithms)-module, which operates on the output of the neural network. FEN encodes events, including their contexts, by their featural description and builds up a representation of the frequency with which features co-occur. The CA-module consists of only two algorithms that suffice to model the results usually found in studies on relative frequency estimates as well as on confidence judgements about such estimates. Several extensions of PASS that allow judgements of absolute frequencies and the simulation of biased estimates are suggested, and PASS is compared to competing models that have been used to simulate relative frequency judgements.Less

This chapter argues that associative learning is the obvious mechanism to simulate judgements of relative frequency. PASS (Probability ASSociator), the specific associationist model proposed, consists of two parts, FEN (Frequency Encoding Network), a neural network, and the CA (Cognitive Algorithms)-module, which operates on the output of the neural network. FEN encodes events, including their contexts, by their featural description and builds up a representation of the frequency with which features co-occur. The CA-module consists of only two algorithms that suffice to model the results usually found in studies on relative frequency estimates as well as on confidence judgements about such estimates. Several extensions of PASS that allow judgements of absolute frequencies and the simulation of biased estimates are suggested, and PASS is compared to competing models that have been used to simulate relative frequency judgements.

- Published in print:
- 2011
- Published Online:
- June 2013
- ISBN:
- 9780804772624
- eISBN:
- 9780804777209
- Item type:
- chapter

- Publisher:
- Stanford University Press
- DOI:
- 10.11126/stanford/9780804772624.003.0011
- Subject:
- Economics and Finance, Econometrics

This chapter shows that if the population relationship includes two explanatory variables, but the sample regression contains only one, then the estimate of the effect of the included variable is ...
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This chapter shows that if the population relationship includes two explanatory variables, but the sample regression contains only one, then the estimate of the effect of the included variable is almost surely biased. The best remedy is to include the omitted variable in the sample regression. Minimizing the sum of squared errors from a regression with two explanatory variables yields two slopes, each of which represents the relationship between the parts of the dependent variable and the associated explanatory variable that are not related to the other explanatory variable. These slopes are unbiased estimators of the population coefficients.Less

This chapter shows that if the population relationship includes two explanatory variables, but the sample regression contains only one, then the estimate of the effect of the included variable is almost surely biased. The best remedy is to include the omitted variable in the sample regression. Minimizing the sum of squared errors from a regression with two explanatory variables yields two slopes, each of which represents the relationship between the parts of the dependent variable and the associated explanatory variable that are not related to the other explanatory variable. These slopes are unbiased estimators of the population coefficients.

- Published in print:
- 2011
- Published Online:
- June 2013
- ISBN:
- 9780804772624
- eISBN:
- 9780804777209
- Item type:
- chapter

- Publisher:
- Stanford University Press
- DOI:
- 10.11126/stanford/9780804772624.003.0014
- Subject:
- Economics and Finance, Econometrics

This chapter shows that the addition of a second explanatory variable in Chapter 11 adds only four new things to what there is to know about regression. First, regression uses only the parts of each ...
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This chapter shows that the addition of a second explanatory variable in Chapter 11 adds only four new things to what there is to know about regression. First, regression uses only the parts of each variable that are unrelated to all of the other variables. Second, omitting a variable from the sample relationship that appears in the population relationship almost surely biases our estimates. Third, including an irrelevant variable does not bias estimates but reduces their precision. Fourth, the number of interesting joint tests increases with the number of slopes. All four remain valid when we add additional explanatory variables.Less

This chapter shows that the addition of a second explanatory variable in Chapter 11 adds only four new things to what there is to know about regression. First, regression uses only the parts of each variable that are unrelated to all of the other variables. Second, omitting a variable from the sample relationship that appears in the population relationship almost surely biases our estimates. Third, including an irrelevant variable does not bias estimates but reduces their precision. Fourth, the number of interesting joint tests increases with the number of slopes. All four remain valid when we add additional explanatory variables.

*Robert J Marks II*

- Published in print:
- 2009
- Published Online:
- November 2020
- ISBN:
- 9780195335927
- eISBN:
- 9780197562567
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195335927.003.0012
- Subject:
- Computer Science, Mathematical Theory of Computation

Exact interpolation using the cardinal series from unaliased samples assumes that (a) the values of the samples are known exactly, (b) the sample locations are known ...
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Exact interpolation using the cardinal series from unaliased samples assumes that (a) the values of the samples are known exactly, (b) the sample locations are known exactly (c) an infinite number of terms are used in the series, and (d) sampling is performed at a sufficiently fast rate. Deviation from these requirements results in interpolation error due to (a) data noise (b) jitter (c) truncation and (d) aliasing respectively. The perturbation to the interpolation from these sources of error is the subject of this chapter. If noise is superimposed on sample data, the corresponding interpolation will be perturbed. In this section, the nature of this perturbation is examined. The effect of data noise on continuous sampling interpolation is treated in Section 10.3.1.2. The multidimensional case is the topic of Section 8.10.2. Suppose that the signal we sample is corrupted by real additive zero mean wide sense stationary noise, ξ (t).
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Exact interpolation using the cardinal series from unaliased samples assumes that (a) the values of the samples are known exactly, (b) the sample locations are known exactly (c) an infinite number of terms are used in the series, and (d) sampling is performed at a sufficiently fast rate. Deviation from these requirements results in interpolation error due to (a) data noise (b) jitter (c) truncation and (d) aliasing respectively. The perturbation to the interpolation from these sources of error is the subject of this chapter. If noise is superimposed on sample data, the corresponding interpolation will be perturbed. In this section, the nature of this perturbation is examined. The effect of data noise on continuous sampling interpolation is treated in Section 10.3.1.2. The multidimensional case is the topic of Section 8.10.2. Suppose that the signal we sample is corrupted by real additive zero mean wide sense stationary noise, ξ (t).