scholarly journals Distributed Hypothesis Testing over Noisy Broadcast Channels

Information ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 268
Author(s):  
Sadaf Salehkalaibar ◽  
Michèle Wigger
Keyword(s):  
Hypothesis Testing ◽  
Marginal Distribution ◽  
Alternative Hypothesis ◽  
Broadcast Channels ◽  
Type Ii ◽  
Type Ii Error ◽  
Error Exponents ◽  
Single Sensor ◽  
Distributed Hypothesis Testing ◽  
Binary Hypothesis

This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than 1/2 to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.

scholarly journals Distributed Hypothesis Testing with Privacy Constraints

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 478 ◽  
Author(s):  
Atefeh Gilani ◽  
Selma Belhadj Amor ◽  
Sadaf Salehkalaibar ◽  
Vincent Y. F. Tan
Keyword(s):  
Information Theory ◽  
Hypothesis Testing ◽  
Alternative Hypothesis ◽  
Side Information ◽  
Approximate Expression ◽  
Type Ii ◽  
Strong Converse ◽  
Privacy Constraints ◽  
Distributed Hypothesis Testing ◽  
Privacy Level

We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized version of it. We impose an upper bound on the mutual information between the raw and randomized data. Under this scenario, the receiver, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. We first provide a general lower bound on the type-II exponent for an arbitrary pair of hypotheses. Next, we show that if the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null (i.e., testing against independence), then the exponent is known exactly. Moreover, we show that the strong converse property holds. Using ideas from Euclidean information theory, we also provide an approximate expression for the exponent when the communication rate is low and the privacy level is high. Finally, we illustrate our results with a binary and a Gaussian example.

Statistical Inference and Decision Making in Conservation Biology

2010 ◽  
Vol 57 (4) ◽  
pp. 309-317 ◽  
Author(s):  
DAVID SALTZ
Keyword(s):  
Decision Making ◽  
Hypothesis Testing ◽  
Conservation Biology ◽  
Type I Error ◽  
Alternative Hypothesis ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Information Theoretic ◽  
Model Inference

Since the formulation of hypothesis testing by Neyman and Pearson in 1933, the approach has been subject to continuous criticism. Yet, until recently this criticism, for the most part, has gone unheeded. The negative appraisal focuses mainly on the fact thatP-valuesprovide no evidential support for either the null hypothesis (H0) or the alternative hypothesis (Ha). Although hypothesis testing done under tightly controlled conditions can provide some insight regarding the alternative hypothesis based on the uncertainty ofH0, strictly speaking, this does not constitute evidence. More importantly, well controlled research environments rarely exist in field-centered sciences such as ecology. These problems are manifestly more acute in applied field sciences, such as conservation biology, that are expected to support decision making, often under crisis conditions. In conservation biology, the consequences of a Type II error are often far worse than a Type I error. The "advantage" afforded toH0by setting the probability of committing a Type I error (α) to a low value (0.05), in effect, increases the probability of committing a Type II error, which can lead to disastrous practical consequences. In the past decade, multi-model inference using information-theoretic or Bayesian approaches have been offered as better alternatives. These techniques allow comparing a series of models on equal grounds. Using these approaches, it is unnecessary to select a single "best" model. Rather, the parameters needed for decision making can be averaged across all models, weighted according to the support accorded each model. Here, I present a hypothetical example of animal counts that suggest a possible population decline, and analyze the data using hypothesis testing and an information-theoretic approach. A comparison between the two approaches highlights the shortcomings of hypothesis testing and advantages of multi-model inference.

scholarly journals A Terra é Plana (p<0,05): Aprimorando as Inferências Estatísticas em Psicologia

2019 ◽  
Author(s):  
Caio Costa
Keyword(s):  
Hypothesis Testing ◽  
Type I Error ◽  
Scientific Research ◽  
Reliable Information ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Statistical Parameters ◽  
Scientific Investigations ◽  
Low Rate

The low rate of replication of studies in science and specifically in psychology has created a crisis of replicability. It is pointed out in the literature that problems of methodological orders and interpretation of data in scientific research make the results of scientific investigations unreliable. To address these problems, methodological and statistical parameters can be adjusted so that our results provide consistent and more reliable information. Thus, we highlight two types of errors that may occur in the execution of the hypothesis testing that are fundamental in the construction of a cumulative science, Type I Error and Type II Error in addition to possible approaches to reduce the probability of committing such errors.

scholarly journals Privacy-Aware Distributed Hypothesis Testing

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 665 ◽  
Author(s):  
Sreejith Sreekumar ◽  
Asaf Cohen ◽  
Deniz Gündüz
Keyword(s):  
Error Probability ◽  
Type I Error ◽  
Single Letter ◽  
Type I ◽  
Type Ii ◽  
Type Ii Error ◽  
Error Exponent ◽  
Trade Offs ◽  
Type I Error Probability ◽  
Binary Hypothesis

A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer’s observations from those of the detector, given some additional side information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counter-example where the strong converse which holds for distributed HT without a privacy constraint does not hold when a privacy constraint is imposed. This implies that in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint.

scholarly journals Deteksi Sinyal : Overview Model Parametrik menggunakan Kriteria Neyman-Pearson

2019 ◽  
Vol 7 (1) ◽  
pp. 14
Author(s):  
FIKY YOSEF SURATMAN ◽  
ALOYSIUS ADYA PRAMUDITA ◽  
DHARU ARSENO
Keyword(s):  
Signal Processing ◽  
Cognitive Radio ◽  
Signal Detection ◽  
Hypothesis Testing ◽  
Spectrum Sensing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Test Statistic ◽  
Binary Hypothesis Testing ◽  
Binary Hypothesis

ABSTRAKDeteksi sinyal banyak diimplementasikan dalam sistem pengolahan sinyal yang sangat kompleks. Sebagai contoh digunakan pada sub sistem pengolahan sinyal radar pengintai yang berfungsi untuk deteksi dan pelacakan target. Salah satu implementasi terbaru dari deteksi sinyal adalah untuk fungsi spectrum sensing pada Cognitive Radio. Deteksi sinyal dapat didefinisikan sebagai binary hypothesis testing, yaitu memutuskan satu dari dua keadaan: hanya derau atau tidak ada sinyal (null hypothesis), dan ada sinyal (alternative hypothesis). Teori deteksi sinyal merupakan bidang yang cukup luas, sehingga paper ini fokus pada pendekatan parametrik dengan Teorema Neyman-Pearson. Kedua hypothesis dimodelkan dengan variabel acak dengan distribusi rapat kemungkinan yang sama tetapi mempunyai parameter yang berbeda. Ditunjukkan penurunan test statistic untuk dua skenario, yaitu distribusi dengan diketahui sebagian dan diketahui penuh. Bagian simulasi menunjukkan kinerja detektor sinyal secara analitis mempunyai hasil yang serupa dengan simulasi Monte Carlo.Kata kunci: deteksi sinyal, Neyman-Pearson, hypothesis testing, spectrum sensing, radar. ABSTRACTSignal detection has been used in many sophisticated signal processing systems, such as for signal processing in surveillance radar which is to detect and to track a radar target. Recently, signal detection is widely used for spectrum sensing in Cognitive Radio. Signal detection is a binary hypothesis testing problem which is to choose one out of two conditions, i.e., noise only or signal absence (null hypothesis), and signal presence (alternative hypothesis). Since signal detection theory is a wide area, this paper only focuses on parametric approach using Neyman-Pearson theorem. The two hypotheses are modeled by random variables having the same distribution but different parameters. The derivations of test statistics (detectors) are shown for two scenarios, i.e., partially known and perfectly known distributions. Analytical results and Monte Carlo simulations of the derived detectors show similar performances.Keywords: signal detection, Neyman-Pearson, hypothesis testing, spectrum sensing, radar.

The decline and fall of Type II error rates

2005 ◽  
Author(s):  
Steve Verrill ◽  
Mark Durst
Keyword(s):  
Error Rates ◽  
Type Ii ◽  
Type Ii Error
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